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due to the importance of the primes , the mathematicians have been investigating about them since long centuries ago . in 1801 , carl gauss , one of the greatest mathematician , submitted that the problem of distinguishing the primes among the non - primes has been one of the outstanding problems of arithmetic @xcite . proving the infinity of prime numbers by euclid is one of the first and most brilliant works of the human being in the numbers theory @xcite . greek people knew prime numbers and were aware of their role as building blocks of other numbers . more , the most natural question asked by human being was this what order prime numbers are following and how one could find prime numbers ? until this time , there have been more attempts for finding a formula producing the prime numbers and or a model for appearance of prime numbers among other numbers and although they could be more helpful for developing the numbers theory , however , the complicated structure of prime numbers could not be decoded . during last years , the prime numbers attained an exceptional situation in the field of coding . for example , `` rsa '' system is one of the most applicable system in this field used in industries relying on prime numbers . `` rsa '' system is used in most computerized systems and counted as main protocol for secure internet connections used by states and huge companies and universities in most computerized systems @xcite . on 2004 , manindra agrawal and his students in indian institute of technology kanpur could develop an algorithm called aks for detecting prime numbers @xcite . on 2006 , 2008 , 2009 and recently on 2013 , mathematics students in a project called detecting the mersenne prime numbers by computer network gimps succeeded to discover the greatest prime number . all such cases indicate the importance of mersenne theorem or any other approach for finding the largest prime numbers @xcite . generalizing the mersenne theorem , this paper could accelerate finding the largest prime numbers . in addition , there have been provided new equations and algorithm for attaining the largest primes . assume that @xmath0 is a natural number greater than 1 , @xmath1 related to n and natural numbers @xmath2 and @xmath3 are defined as below : @xmath4 if @xmath1 is a prime number , then @xmath0 is a prime number , too . if @xmath0 is not the prime number so we can write @xmath0 as the multiplication of two natural numbers except @xmath5 meaning : @xmath6 @xmath7 @xmath8 @xmath9 @xmath10 @xmath11 therefore , @xmath1 is not the prime number . so , @xmath0 must be a prime number . this theorem is a generalization for mersenne theorem in which @xmath2 and @xmath3 are arbitrary natural numbers . if in the theorem @xmath12 , c is chosen as a multiple to @xmath2 and @xmath13 , thus , @xmath1 will not be a prime number . suppose : @xmath14 therefore : @xmath15 @xmath16 @xmath17 @xmath18 @xmath19 @xmath20 the last equality shows that @xmath1 is not a prime number . suppose @xmath0 is a natural number greater than @xmath5 , function @xmath1 related to @xmath0 and natural number @xmath2 are defined as below : @xmath21 if @xmath1 is a prime number , then @xmath0 is a prime number , too . in this theorem @xmath22 , based on @xmath0 constant , please consider a sequence @xmath23 we prove that sequence @xmath24 is strictly ascending , i.e. @xmath25 to prove the last inequality , we write : @xmath26 @xmath27 @xmath28 @xmath29 status 1 . if @xmath0 is a multiple of @xmath30 : @xmath31 status 2 . if @xmath0 is not a multiple of @xmath30 : @xmath32 therefore , inequity is accepted . in this theorem , each number is higher than mersenne number , meaning : @xmath33 suppose @xmath2 be a natural number and @xmath34 are the primes smaller than or equal @xmath35 and @xmath36 , @xmath37 are natural numbers which limitations are intended for them indicated as follows : @xmath38 assume that @xmath39 is a function of @xmath40 which is displayed as bellow : @xmath41 if the @xmath42 and @xmath37 circumstances are followed , @xmath39 can obtain all the primes less than @xmath2 . knowing that @xmath39 is odd , because it is non prime , therefore it comprises from two odd numbers except @xmath5 , and because @xmath43 , @xmath39 has at least a prime factor @xmath44 . therefore , @xmath39 is divided at least on one of the prime factors @xmath45 . @xmath46 @xmath47 it is clear that above equalities are in discrepancy of the assumption of the theorem . 1 . if : @xmath48 2 . interval @xmath49 : + it is clear that by putting minimum @xmath37 in the definition @xmath50 minimum @xmath51 followed by minimum @xmath39 is obtained as below : @xmath52 according to recent equation , it is obvious that being as prime number in prime numbers smaller than @xmath53 , r may not be divided into prime factors smaller than @xmath54 . on the other hand , it is not necessary to see if prime numbers smaller than @xmath53 are divided into @xmath55 to detect it as a prime number . indeed , for obtaining the prime numbers , we only require @xmath56 in @xmath57 to enter the provision of prime factor @xmath58 . if @xmath59 is considered as a prime number bigger than @xmath60 , we could use @xmath61 instead of @xmath2 in this theorem because prime numbers smaller than @xmath35 include prime numbers smaller than @xmath62 . prime numbers smaller than 120 : @xmath63 \ { @xmath64 , prime numbers smaller than @xmath35 : @xmath65 } + @xmath66 @xmath67 @xmath68 @xmath69 @xmath70 @xmath71 @xmath72 @xmath73 @xmath74 @xmath75 suppose @xmath2 be the natural number and @xmath76 are the primes smaller than or equal @xmath35 and also consider that @xmath77 are the primes larger than @xmath35 . suppose that @xmath78 and @xmath42 be the members of the natural numbers and also @xmath79 be the members of the account numbers , these variables are selected arbitrarily . function @xmath39 related to values @xmath80 , natural numbers @xmath81 and arithmetic numbers @xmath82 are defined as below : @xmath83 @xmath84 if @xmath56 be as the natural number less than @xmath2 , then @xmath39 is a prime number . if @xmath39 is not prime number , it has a prime factor @xmath85 . on the other side , because @xmath86 , @xmath39 has at least one prime factor @xmath87 . so , it is arbitrarily supposed that @xmath39 is divisible in @xmath88 . @xmath89 @xmath90 because @xmath54 is not denominator of any @xmath91 . we have : @xmath92 @xmath93 we reached a contradiction to the assumption . thus , the theorem was verified . we obtain prime numbers smaller than 119 . + @xmath94 @xmath95 @xmath96 table 1 [ cols="^,^,^,^,^,^",options="header " , ] and continuing so suppose that : @xmath97 ( the order is considered in the primes ) general speaking , the theorem @xmath98 comes true to @xmath99 because @xmath100 includes the same primes . @xmath39 is obviously not divisible to @xmath101 and according to prime of the number @xmath39 , we have : @xmath102 to attain prime numbers , we divide the intervals as below : @xmath103 with regard to the relationship easier to be written . in example of the primes less than @xmath104 , the rang can be divided into three sections of @xmath105 , @xmath106 and @xmath107 . then , a distinct relation asserted for each . prime numbers smaller than 48 : @xmath108 @xmath109 @xmath110 @xmath111 and continuing so by integrating the relations , particularly using the relation 2 and notation 5.4 , we can attain an algorithm to obtain the largest prime number . ; one of them is as below : first of all , assign @xmath36 as one @xmath119 so as to obtain the minimum of @xmath0 . then in the following equation , give a counter to @xmath0 through the minimum @xmath0 so long as k be a member of the natural numbers @xmath120 . meanwhile , @xmath36 should not be even . @xmath121 if @xmath39 is not prime number , it has a prime factor @xmath85 . on the other side , because @xmath125 , @xmath39 has at least one prime factor @xmath126 therefore , with no interruption in the generality of the subject , we can assume that @xmath39 is divisible on @xmath127 : @xmath128 @xmath129 @xmath130 we reached a contradiction to the assumption . thus , the theorem was verified . 99 p. ribenboim , the little book of bigger primes , 2nd ed . springer science & business media , 2004 . w. stein , `` elementary number theory : primes , congruences , and secrets '' , book , pp . 1 - 172 , 2009 . r. crandall and c. b. pomerance , prime numbers : a computational perspective . springer science & business media , 2006 . m. agrawal , n. kayal , and n. saxena , `` primes is in p '' , ann . 781 - 793 , 2004 . `` list of known mersenne prime numbers - primenet '' . [ online ] . available : + http://www.mersenne.org/primes/ [ accessed : 08-apr-2015 ] .

today , prime numbers attained exceptional situation in the area of numbers theory and cryptography . as we know , the trend for accessing to the largest prime numbers due to using mersenne theorem , although resulted in vast development of related numbers , however it has reduced the speed of accessing to prime numbers from one to five years . this paper could attain to theorems that are more extended than mersenne theorem with accelerating the speed of accessing to prime numbers . since that time , the reason for frequently using mersenne theorem was that no one could find an efficient formula for accessing to the largest prime numbers . this paper provided some relations for prime numbers that one could define several formulas for attaining prime numbers in any interval ; therefore , according to flexibility of these relations , it could be found a new branch in the field of accessing to great prime numbers followed by providing an algorithm at the end of this paper for finding the largest prime numbers .

the spectroscopic signature of the presence of @xmath1li in the atmospheres of metal - poor halo stars is a subtle extra depression in the red wing of the @xmath2li doublet , which can only be detected in spectra of the highest quality . based on high - resolution , high signal - to - noise vlt / uves spectra of 24 bright metal - poor stars , ( * ? ? ? * asplund ( 2006 ) ) report the detection of @xmath1li in nine of these objects . the average @xmath1li/@xmath2li isotopic ratio in the nine stars in which @xmath1li has been detected is about 4% and is very similar in each of these stars , defining a @xmath1li plateau at approximately @xmath5li@xmath6 ( on the scale @xmath7h@xmath8 ) . a convincing theoretical explanation of this new @xmath1li plateau turned out to be problematic : the high abundances of @xmath1li at the lowest metallicities can not be explained by current models of galactic cosmic - ray production , even if the depletion of @xmath1li during the pre - main - sequence phase is ignored ( see reviews by e.g. ( * ? ? ? * christlieb 2008 ) , ( * ? ? ? * cayrel 2008 ) , prantzos 2010 [ this volume ] and references therein ) . a possible solution of the so - called ` second lithium problem ' was proposed by ( * ? ? ? * cayrel ( 2007 ) ) , who point out that the intrinsic line asymmetry caused by convection in the photospheres of metal - poor turn - off stars is almost indistinguishable from the asymmetry produced by a weak @xmath1li blend on a presumed symmetric @xmath2li profile . as a consequence , the derived @xmath1li abundance should be significantly reduced when the intrinsic line asymmetry in properly taken into account . using 3d nlte line formation calculations based on 3d hydrodynamical model atmospheres computed with the co@xmath0bold code ( ( * ? ? ? * freytag 2002 ) , ( * ? ? ? * wedemeyer 2004 ) , see also http://www.astro.uu.se/@xmath9bf/co5bold_main.html ) , we quantify the theoretical effect of the convection - induced line asymmetry on the resulting @xmath1li abundance as a function of effective temperature , gravity , and metallicity , for a parameter range that covers the stars of the ( * ? ? ? * asplund ( 2006 ) ) sample . a careful reanalysis of individual objects is under way , in which we consider two alternative approaches for fixing the residual line broadening , @xmath10 , the combined effect of macroturbulence ( 1d only ) and instrumental broadening , for given microturbulence ( 1d only ) and rotational velocity : ( i ) treating @xmath10 as a free parameter when fitting the li feature , ( ii ) deriving @xmath10 from additional unblended spectral lines with similar properties as lii@xmath4 . we show that method ( ii ) is potentially dangerous , because the inferred broadening parameter shows considerable line - to - line variations , and the resulting @xmath1li abundance depends rather sensitively on the adopted value of @xmath10 . + the hydrodynamical atmospheres used in the present study are part of the cifist 3d model atmosphere grid ( ( * ? ? ? * ludwig 2009 ) ) . they have been obtained from realistic numerical simulations with the co@xmath0bold code which solves the time - dependent equations of compressible hydrodynamics in a constant gravity field together with the equations of non - local , frequency - dependent radiative transfer in a cartesian box representative of a volume located at the stellar surface . the computational domain is periodic in @xmath11 and @xmath12 direction , has open top and bottom boundaries , and is resolved by typically 140@xmath13140@xmath13150 grid cells . the vertical optical depth of the box varies from @xmath14 ( top ) to @xmath15 ( bottom ) , and the radiative transfer is solved in 6 or 12 opacity bins . further information about the models used in the present study is compiled in table[tab1 ] . each of the models is represented by a number of snapshots , indicated in column ( 6 ) , chosen from the full time sequence of the corresponding simulation . these representative snapshots are processed by the non - lte code nlte3d that solves the statistical equilibrium equations for a 17 level lithium atom with 34 line transitions , fully taking into account the 3d thermal structure of the respective model atmosphere . the photo - ionizing radiation field is computed at @xmath16 frequency points between @xmath17 and 32407 , using the opacity distribution functions of @xcite to allow for metallicity - dependent line - blanketing , including the hi h@xmath18 and hi hi quasi - molecular absorption near @xmath19 and @xmath20 , respectively . collisional ionization by neutral hydrogen via the charge transfer reaction h(@xmath21 ) + li(@xmath22 ) @xmath23 li@xmath18(@xmath24 ) + h@xmath25 is treated according to @xcite . more details are given in @xcite . finally , 3d nlte synthetic line profiles of the lii @xmath26 doublet are computed with the line formation code linfor3d ( http://www.aip.de/@xmath9mst/linfor3d_main.html ) , using the departure coefficients @xmath27=@xmath28 provided by nlte3d for each level @xmath29 of the lithium model atom as a function of geometrical position within the 3d model atmospheres . as demonstrated in fig.[fig1 ] , 3d nlte effects are very important for the metal - poor dwarfs considered here : they strongly reduce the height range of line formation such that the 3d nlte equivalent width is smaller by roughly a factor 2 compared to 3d lte . ironically , the line strength predicted by standard 1d mixing - length models in lte are close to the results obtained from elaborate 3d nlte calculations . we note that the half - width of the 3d nlte line profile , fwhm(nlte)=8.5 km / s , is larger by about 10% : fwhm(lte)=@xmath30 and @xmath31 km / s , respectively , before and after reducing the li abundance such that 3d lte and 3d nlte equivalent widths agree . this is because 3d lte profile senses the higher photosphere where both thermal and hydrodynamical velocities are lower . however , the nlte line profile is significantly less asymmetric than the lte profile , even if the latter is broadened to the same half - width ( fig.[fig1 ] , bottom panel ) . + .list of models used in the present study . columns ( 2)-(6 ) give effective temperature , surface gravity , metallicity , number of opacity bins used in the radiation hydrodynamics simulation , and number of snapshots selected for spectrum synthesis . the equivalent width of the synthetic 3d non - lte @xmath2li doublet at @xmath26 , assuming a(li)=2.2 and no @xmath1li , is given in column ( 7 ) . columns ( 8) and ( 9 ) show @xmath32(li ) and @xmath33(li ) , the @xmath1li/@xmath2li isotopic ratio inferred from fitting this 3d non - lte line profile with two different kinds of 1d profiles , in each case assuming a rotational broadening of @xmath34 = 0.0 / 2.0 km / s , respectively ( see text for details ) . [ cols="^,^,^,^,^,^,^,^,^ " , ] the @xmath1li/@xmath2li isotopic ratio derived from fitting of the lii doublet with 3d nlte synthetic line profiles is shown to be about 1% to 2% lower than what is obtained with 1d lte profiles . based on this result , we conclude that only @xmath35 out of the @xmath36 stars of the @xcite sample would remain significant @xmath1li detections when subjected to a 3d non - lte analysis , suggesting that the presence of @xmath1li in the atmospheres of galactic halo stars is rather the exception than the rule , and hence does not necessarily constitute a _ cosmological _ @xmath1li problem . if we adopt the approach by @xcite , relying on additional spectral lines to fix the residual line broadening , the difference between 3d nlte and 1d lte results increases even more , as far as we can judge from our case study hd74000 . until the 3d nlte effects are fully understood for all involved lines , we consider this method as potentially dangerous .

based on 3d hydrodynamical model atmospheres computed with the co@xmath0bold code and 3d non - lte ( nlte ) line formation calculations , we study the effect of the convection - induced line asymmetry on the derived @xmath1li abundance for a range in effective temperature , gravity , and metallicity covering the stars of the ( * ? ? ? * asplund ( 2006 ) ) sample . when the asymmetry effect is taken into account for this sample of stars , the resulting @xmath1li/@xmath2li ratios are reduced by about 1.5% on average with respect to the isotopic ratios determined by ( * ? ? ? * asplund ( 2006 ) ) . this purely theoretical correction diminishes the number of significant @xmath1li detections from 9 to 4 ( 2@xmath3 criterion ) , or from 5 to 2 ( 3@xmath3 criterion ) . in view of this result the existence of a @xmath1li plateau appears questionable . a careful reanalysis of individual objects by fitting the observed lithium @xmath4 doublet both with 3d nlte and 1d lte synthetic line profiles confirms that the inferred @xmath1li abundance is systematically lower when using 3d nlte instead of 1d lte line fitting . nevertheless , halo stars with unquestionable @xmath1li detection do exist even if analyzed in 3d - nlte , the most prominent example being hd84937 .

in lattice qcd , the finite lattice spacing and finite lattice volume effects on the gluon propagator can be investigated with the help of lattice simulations at several lattice spacings and physical volumes . here we report on such a calculation . for details on the lattice setup see @xcite . in figure [ fig : gluevol ] , we show the renormalized gluon propagator at @xmath0 gev for all lattice simulations . note that we compare our data with the large volume simulations performed by the berlin - moscow - adelaide collaboration @xcite see @xcite for details . in each plot we show data for a given value of @xmath1 , i.e. data in the same plot has the same lattice spacing . the plots show that , for a given lattice spacing , the infrared gluon propagator decreases as the lattice volume increases . for larger momenta , the lattice data is less dependent on the lattice volume ; indeed , for momenta above @xmath2900 mev the lattice data define a unique curve . we can also investigate finite volume effects by comparing the renormalized gluon propagator computed using the same physical volume but different @xmath1 values . we are able to consider 4 different sets with similar physical volumes see figure [ fig : gluespac ] . although the physical volumes considered do not match perfectly , one can see in figure [ fig : gluespac ] that for momenta above @xmath2 900 mev the lattice data define a unique curve . this means that the renormalization procedure has been able to remove all dependence on the ultraviolet cut - off @xmath3 for the mid and high momentum regions . however , a comparison between figures [ fig : gluevol ] and [ fig : gluespac ] shows that , in the infrared region , the corrections due to the finite lattice spacing seem to be larger than the corrections associated with the finite lattice volume . in particular , figure [ fig : gluespac ] shows that the simulations performed with @xmath4 , i.e. , with a coarse lattice spacing , underestimate the gluon propagator in the infrared region . in this sense , the large volume simulations performed by the berlin - moscow - adelaide collaboration provide a lower bound for the continuum infrared propagator . we also aim to study how temperature changes the gluon propagator . at finite temperature , the gluon propagator is described by two tensor structures , @xmath5 where the transverse and longitudinal projectors are defined by @xmath6 the transverse @xmath7 and longitudinal @xmath8 propagators are given by @xmath9 @xmath10 on the lattice , finite temperature is introduced by reducing the temporal extent of the lattice , i.e. we work with lattices @xmath11 , with @xmath12 . the temperature is defined by @xmath13 . in table [ tempsetup ] we show the lattice setup of our simulation . simulations in this section have been performed with the help of chroma library @xcite . for the determination of the lattice spacing we fit the string tension data in @xcite in order to have a function @xmath14 . note also that we have been careful in the choice of the parameters , in particular we have only two different spatial physical volumes : @xmath15 and @xmath16 . this allows for a better control of finite size effects . .lattice setup used for the computation of the gluon propagator at finite temperature . [ cols="^,^,^,^,^,^",options="header " , ] [ tempsetup ] figures [ fig : transtemp ] and [ fig : longtemp ] show the results obtained up to date . we see that the transverse propagator , in the infrared region , decreases with the temperature . moreover , this component shows finite volume effects ; in particular , the large volume data exhibits a turnover in the infrared , not seen at the small volume data . the longitudinal component increases for temperatures below @xmath17 . then the data exhibits a discontinuity around @xmath18 , and the propagator decreases for @xmath19 . the behaviour of the gluon propagator as a function of the temperature can also be seen in the 3d plots shown in figure [ fig:3dtemp ] . as shown above , data for different physical ( spatial ) volumes exhibits finite volume effects . this can be seen in more detail in figure [ fig : finvoltemp ] , where we show the propagators for two volumes at t=324 mev . moreover , we are also able to check for finite lattice spacing effects at t=305 mev , where we worked out two different simulations with similar physical volumes and temperatures , but different lattice spacings . for this case , it seems that finite lattice spacing effects are under control , with the exception of the zero momentum for the transverse component see figure [ fig : lattspactemp ] . our results show that a better understanding of lattice effects is needed before our ultimate goal , which is the modelling of the propagators as a function of momentum and temperature . paulo silva is supported by fct under contract sfrh / bpd/40998/2007 . work supported by projects cern / fp/123612/2011 , cern / fp/123620/2011 and ptdc / fis/100968/2008 , projects developed under initiative qren financed by ue / feder through programme compete .

we study the landau gauge gluon propagator at zero and finite temperature using lattice simulations . particular attention is given to the finite size effects and to the infrared behaviour .

the author would like to thank c. bunster , c. martnez , r. troncoso , s. willison , and j. zanelli for useful comments . the author thanks kjell tangen for the crucial information of the paper by fonarev . this work was supported by the grant nos . 1071125 from fondecyt ( chile ) and the grant - in - aid for scientific research fund of the ministry of education , culture , sports , science and technology , japan ( young scientists ( b ) 18740162 ) . 99 h. stephani , d. kramer , m. maccullum , c. hoenselaers and e. herlt , _ exact solutions of einsteins field equations : second edition _ , ( cambridge university press , cambridge , 2003 ) . a. krasiski , _ inhomogeneous cosmological models _ ( cambridge : cambridge university press , 1997 ) . peebles , _ principles of physical cosmology _ ( princeton univ . press , 1976 ) . linde , _ particle physics and inflationary cosmology _ ( harwood academic publishers , chur , switzerland 1990 ) . a. liddle , _ an introduction to modern cosmology _ ( wiley , 2003 ) . s.w . hawking and g.f.r . ellis , _ `` the large scale structure of space - time '' _ ( cambridge university press , cambridge , england , 1973 ) . `` general relativity '' _ ( university of chicago press , chicago , united states of america , 1983 ) . roberts , gen . rel . grav . * 21 * , 907 ( 1989 ) . v. husain , e.a . martinez and d. nez , d * 50 * , 3783 ( 1994 ) . choptuik , phys . * 70 * , 9 ( 1993 ) . c. gundlach , liv . * 2 * , 4 ( 1999 ) . d. christodoulou , commun . phys . * 109 * , 613 ( 1987 ) ; commun . pure appl . math . * 44 * , 339 ( 1991 ) ; commun . pure appl . math . * 46 * , 1131 ( 1993 ) ; ann . of math . * 140 * , 607 ( 1994 ) ; ann . of math . * 149 * , 187 ( 1999 ) . townsend , jhep * 11 * , 042 ( 2001 ) . a.m. green and j.e . lidsey , phys . d * 61 * , 067301 ( 2000 ) . r. emparan and j. garriga , jhep * 05 * , 028 ( 2003 ) . fonarev , class . quantum grav . * 12 * , 1739 ( 1995 ) . y. kitada and k. maeda , phys . d * 45 * , 1416 ( 1992 ) ; y. kitada and k. maeda , class . quantum grav . * 10 * , 703 ( 1993 ) ; a.r . liddle , a. mazumdar and f.e . schunck , phys . d * 58 * , 061301 ( 1998 ) ; k.a . malik and d. wands , phys . d * 59 * , 123501 ( 1999 ) ; a.a . coley and r.j . van den hoogen , phys . d * 62 * , 023517 ( 2000 ) ; z - k . guo , y - s . piao , r - g . cai and y - z . zhang , phys . b * 576 * , 12 ( 2003 ) . hayward , phys . d*49 * , 6467 ( 1994 ) . m. heusler , j. math . * 33 * , 3497 ( 1992 ) . j. d. bekenstein , phys . rev . d * 51 * , 6608 ( 1995 ) . d. sudarsky , class . * 12 * , 579 ( 1995 ) . t. torii , k. maeda and m. narita , phys . rev . d * 59 * , 064027 ( 1999 ) . t. torii , k. maeda and m. narita , phys . d * 64 * , 044007 ( 2001 ) .

we discuss the physical interpretation of a dynamical and inhomogeneous spherically symmetric solution obtained by fonarev for a scalar field with an exponential potential . there is a single parameter @xmath0 in the solution which can be set to @xmath1 if it is non - zero , in addition to the steepness parameter @xmath2 in the potential . the spacetime is conformally static and asymptotically flat friedmann - robertson - walker spacetime . the solution reduces to the friedmann - robertson - walker solution for @xmath3 . there are two curvature singularities , of which one is a timelike central singularity and the other is a big - bang or big - crunch type singularity . depending on the parameters , the spacetime can possess a future outer trapping horizon in the collapsing case . then the solution represents a dynamical black hole in the sense of hayward although there is a locally naked singularity at the center and no black - hole event horizon . this demonstrates a weak point of the local definition of a black hole in terms of a trapping horizon . einstein equations are so complicated simultaneous nonlinear partial differential equations that it is hopeless to obtain general solutions . thus , spacetime symmetries are often assumed to make the system more tractable . although such spacetimes with high symmetries are idealized ones , they have occupied an important position in the history of gravitation research as touchstones to know the essential physics @xcite . for example , the friedmann - robertson - walker ( frw ) cosmological model plays a central role in modern cosmology as the zeroth - order approximation of the present universe , on which the behavior of the density perturbations has been particularly investigated to clarify the origin of the large - scale structure of the universe or to determine the cosmological parameters from the observations of the cosmic microwave background @xcite . from the analyses of the stationary and asymptotically flat black - hole spacetime such as the schwarzschild or kerr solution , tremendous results have been derived , among which the most remarkable one is the black - hole thermodynamics @xcite . on the other hand , there are many open problems on the dynamical aspects of einstein equations such as dynamical black holes or their formations . in homogeneous or stationary spacetimes , einstein equations reduce to a set of ordinary differential equations , which is comparatively easy to handle , however , the formation or the growth of a black hole is essentially a dynamical and inhomogeneous process , where we have to struggle with a set of partial differential equations . for this reason , numerical methods have often been used to study such systems . nevertheless , the few dynamical and inhomogeneous exact solutions have been found . such precious solutions should be intensively investigated to complement the numerical works . scalar fields are fundamental fields which naturally exist in a variety of theories . in spherically symmetric spacetimes , the system with the simplest massless scalar field has been fully investigated . there are two important dynamical and inhomogeneous exact solutions in this case . the first one was obtained by roberts @xcite , and subsequently the other one was obtained by husain , martinez and nez @xcite . the dynamical aspects of the system with a massless scalar field have been investigated in the numerical studies of the gravitational collapse , especially in the context of critical phenomena pioneered by choptuik @xcite ( see @xcite for the review ) . the analytic proof of the cosmic censorship hypothesis by christodoulou is a significant milestone @xcite . although these two exact solutions are not directly related to these results , the potential importance of them would go without saying . the case with potentials is a natural generalization of the massless case . in various theories , scalar fields have their specific potentials . among them , an exponential potential arises naturally in supergravity @xcite or theories obtained through dimensional reduction to effective four - dimensional theories @xcite . indeed , the existence of exact solutions in such systems must be useful as a touchstone for the future research . the generalized husain - martinez - nez ( hmn ) solution in the presence of an exponential potential was obtained by fonarev @xcite . however , the properties of the solution have not been studied in details and the physical interpretation of the solution is still not clear . in this letter , we discuss the physical interpretation of the fonarev solution . we investigate the properties of the trapping horizon and show the global structure of the solution . we adopt the units such that @xmath4 . we begin with the action which describes the system with a scalar field with an exponential potential : @xmath5 , \label{action}\ ] ] where @xmath6 is the potential of a scalar field @xmath7 given by @xmath8 where @xmath9 and @xmath2 are real constants . a scalar field with an exponential potential has been particularly studied in spatially homogeneous cosmology @xcite . if @xmath10 , then @xmath7 is massless and @xmath2 is meaningless . we assume that @xmath9 is non - negative . then the energy - momentum tensor for a scalar field is given by @xmath11 the einstein equation is @xmath12 while equations of motion for @xmath7 is given by @xmath13 the spherically symmetric solution obtained by fonarev @xcite is @xmath14 , \label{sol } \\ \phi & = & \frac{1}{4\sqrt{\pi}}\ln\biggl[d\biggl(1-\frac{2w}{r}\biggl)^{\sqrt{2/(\lambda^2 + 2)}}a^{\sqrt{2}\lambda}\biggl],\label{sol2}\end{aligned}\ ] ] where @xmath15^{-\sqrt{2}/\lambda}.\end{aligned}\ ] ] here @xmath0 and @xmath16 are constants . when we set @xmath3 , the solution reduces to the frw solution . hereafter we only consider the case with @xmath17 . the potential form is then given by @xmath18 so the steepness parameter @xmath2 must satisfy the relation @xmath19 and @xmath20 for non - negative potential , which corresponds to @xmath21 with @xmath22 . this solution is asymptotically frw solution for @xmath23 . for @xmath24 ( corresponding to @xmath25 ) , the asymptotic frw solution is accelerated , while for @xmath26 ( corresponding to @xmath27 ) , it is decelerated . when we set @xmath28 , this solution reduces to the hmn solution for a massless scalar field , in which @xmath29 is an arbitrary constant and meaningless @xcite . because this solution is invariant for @xmath30 with @xmath31 , we consider only the region of @xmath32 . for @xmath33 , there are central curvature singularities at @xmath34 and @xmath35 , which are both timelike . thus , the domain of definition for @xmath36 is @xmath37 for @xmath38 , while it is @xmath39 for @xmath40 . then , we can set @xmath41 for positive ( negative ) @xmath0 without loss of generality by the coordinate transformations @xmath42 and @xmath43 $ ] and the redefinition of the constant @xmath16 . in addition to them , @xmath44 is a null curvature singularity for @xmath24 , in which case @xmath45 corresponds to past ( future ) infinity , while @xmath46 is a spacelike curvature singularity for @xmath26 , in which case @xmath47 corresponds to future ( past ) infinity . these are the big - bang or big - crunch type singularities . the domain of definition for @xmath48 is thus @xmath49 and @xmath50 . the physical ( areal ) radius @xmath51 is given by @xmath52 . @xmath51 is a monotonically increasing function of @xmath36 for @xmath37 and @xmath23 corresponds to the spacelike infinity . for @xmath24 , @xmath51 is a monotonically increasing ( decreasing ) function of @xmath48 for @xmath53 , i.e. , the spacetime is expanding ( collapsing ) . for @xmath26 , on the other hand , it is a monotonically increasing ( decreasing ) function of @xmath48 for @xmath54 . here let us consider whether the scalar field has a non - trivial configuration or not . we should be careful that there is no natural time - slicing in general spherically symmetric spacetimes , so the derivative of the scalar field must have a spacelike portion to have the non - trivial configuration in a correct sense . for the fonarev solution , we have @xmath55 and there is indeed a region with @xmath56 . the misner - sharp mass @xmath57 is given by @xmath58 where we have @xmath59 it is noted that @xmath60 and @xmath61 for @xmath21 with @xmath22 . a trapping horizon is obtained by @xmath62 , or equivalently @xmath63 , which is given by @xmath64 it is noted that outgoing ( ingoing ) null geodesics are trapped on the trapped regions in the collapsing ( expanding ) regions . the normal vector @xmath65 to the surface @xmath66 is given by @xmath67 . we obtain @xmath68 ^ 2g(r)}{a^2(2\alpha^2 - 1)^2[r-(1+\alpha)w]^4},\\ g(r)&:=&(3\alpha^2 - 2)r^2 \nonumber \\ & & -2(1+\alpha)(4\alpha^2-\alpha-2)wr \\ & & + ( 4\alpha^2 - 3)(1+\alpha)^2w^2\end{aligned}\ ] ] for both signs in eq . ( [ t - horizon ] ) . the function @xmath69 is negative for @xmath70 , which implies that the trapping horizon is timelike . the case of @xmath71 is rather complicated . we obtain @xmath72 which is non - positive for @xmath73 . the solution of @xmath74 exists only for @xmath75 . for @xmath76 , we have @xmath77 . thus , for @xmath78 , the trapping horizon is timelike for @xmath79 , while for @xmath80 , the trapping horizon is timelike ( spacelike ) for @xmath81 , where @xmath82 is defined by @xmath83 . next let us consider the case with @xmath84 . the solutions of @xmath74 are then given as @xmath85 defined by @xmath86}{2(3\alpha^2 - 2)}.\end{aligned}\ ] ] we can show that @xmath87 holds for @xmath88 , @xmath89 , and @xmath90 with equality holding for @xmath91 , while @xmath92 holds for @xmath93 . we can also show that @xmath94 holds for @xmath95 , while @xmath96 holds for @xmath88 , @xmath97 , and @xmath90 . thus , it is concluded that the trapping horizon is timelike for @xmath93 and spacelike for @xmath91 , while in other cases it has both timelike and spacelike portions . for @xmath98 , the trapping horizon is timelike for @xmath99 and spacelike for @xmath100 . for @xmath95 , the trapping horizon is timelike for @xmath101 and @xmath102 , while it is spacelike for @xmath103 . we have now found that the properties of the trapping horizon are different from that in the hmn solution corresponding to @xmath91 , which is spacelike . a local definition of a black hole in terms of a trapping horizon was given by hayward @xcite . then , a future outer trapping horizon is a black - hole horizon , which corresponds to a spacelike trapping horizon in the collapsing region . on the other hand , a spacelike trapping horizon in the expanding region is a future inner trapping horizon corresponding to a white - hole or cosmological horizon . thus , there exists a black - hole trapping horizon for @xmath88 ( corresponding to @xmath104 ) and @xmath105 ( corresponding to @xmath106 ) . in summary , the solution represents a dynamical black hole in the sense of hayward with the non - trivial configuration of a scalar field , i.e. , a scalar hair , in the collapsing case with @xmath107 , where the asymptotic frw solution is decelerating . the penrose diagrams of the fonarev solution are given in fig . [ penrose ] . the penrose diagrams for the fonarev solution in the collapsing case with @xmath33 and ( a ) @xmath108 and ( b ) @xmath26 . a zigzag line corresponds to a curvature singularity . the central timelike singularity is at @xmath109 and @xmath34 for @xmath110 and @xmath111 , respectively . for @xmath3 , it is replaced by a regular center . the diagrams in the expanding cases are obtained by setting the figures upside - down . ] in the static and asymptotically flat case , the scalar no - hair theorem is available , in which the scalar field must have a trivial configuration for a black - hole solution for the arbitrary positive semidefinite potential @xcite . this scalar no - hair theorem was extended into the asymptotically de sitter case in the presence of the convex potential @xcite . on the other hand , a counter example was numerically constructed in the asymptotically anti - de sitter case , which violates the null energy condition @xcite . if the scalar no - hair theorem also holds in general dynamical and inhomogeneous spherically symmetric spacetimes with certain energy conditions , a scalar field must have a trivial configuration for black - hole solutions . the contraposition of this statement is that if a scalar field has a non - trivial configuration , the solution is not a black - hole solution . then , does the fonarev solution suggest that the scalar no - hair theorem can be extended into general spherically symmetric spacetimes ? the answer is `` no '' in the sense of hayward . however , here we face with the subtlety of the definition of a black hole . although the solution represents a dynamical black hole in the sense of hayward , the singularity inside that trapping horizon is the big - crunch type spacelike singularity , and the central singularity is timelike and not covered by trapped surfaces . furthermore , there is no black - hole event horizon in this spacetime since there is no future null infinity . from these viewpoints , it might be proper to say that the fonarev solution as well as the hmn solution represents not a black hole but a naked singularity . then , the answer to the above question turns to be `` yes '' . these solutions may demonstrate a weak point of the local definition of a black hole in terms of a trapping horizon . in order to rule out such solutions , we should require additional conditions in the definition by a trapping horizon or another local definition of a black hole . further investigations are needed to have much insight into this problem .

since the spring of 1995 , the fnc has been operating in the zeus experiment at hera where it is used in the study of leading neutrons produced at small angles with energies @xmath92 100 gev . because the calorimeter has been calibrated and tested only in beams of energy up to 120 gev , and because the top was not present for the beam tests , we must rely on a monte carlo simulation to predict the response of the calorimeter to high energy particles . we have modeled the fnc using the geant 3.13@xcite program , upon which the simulation of the full zeus detector is based . in this section we present some results from the simulation which can be compared to our test beam data . for 120 gev electrons and pions incident on the center of towers 5 and 6 the geant simulation predicts an electron to hadron response ratio of 0.98 , in agreement with the measured value of 0.96 . the simulated response to pions incident on the center of each tower is shown in fig . [ mc_eres ] . the energy loss due to leakage when the beam is incident near the edge of the calorimeter is also in agreement with the data as is the degradation of the energy resolution ( compare with the data shown in fig . [ ptower ] ) . the monte carlo gives an energy resolution due to shower fluctuations alone , that is , neglecting fluctuations due to photostatistics , of 0.66/@xmath35 for hadrons incident at the center of towers 5 and 6 . we have also used the monte carlo to predict , at higher energies , the overall energy response of the calorimeter and its expected energy resolution due to shower fluctuations . the monte carlo predicts that for neutrons centered on the calorimeter without the top , the energy response is linear up 800 gev . fitting the energy resolution as a function of incident energy , we find @xmath93 where @xmath94 is in gev . if fluctuations due to photostatistics are added , the sampling constant 0.54 will increase to 0.58 . the top section is present at hera , but the neutrons are predominantly incident on towers 7 and 8 . just as for data , 120 gev pions were studied with a grid over the face of the calorimeter . [ mc_ys ] shows the predicted dependence of @xmath15 on @xmath12 , the vertical impact position , for three values of horizontal impact position , @xmath95 , 10.1 , and 20.1 cm . @xmath15 is calculated with logarithmic weights and a cutoff parameter of f=10% . the simulation shows behavior and biases similar to the data ( fig . [ ys ] , lower inset ) ; in particular , the value of @xmath15 is biased towards the nearest tower center . the @xmath12 residual distribution is gaussian with mean 0 and width 7.3 cm/@xmath35 ( compare to the data width of 8.0 cm/@xmath35 ) . the @xmath11 residual distribution is gaussian with mean 0 and width 10.3 cm/@xmath35 . this width is due to transverse shower fluctuations . if photostatistics fluctuations are also included , the width constant increases to 20.7 cm . this should be compared with the data value of 22.3 cm . the simulated energy response for pions as a function of position , shown in fig . [ mc_eofy ] , is in agreement with the data shown in fig . [ eofy ] . fig [ mc_ywidth ] shows simulations of the vertical shower widths for 70 and 120 gev electrons and pions . the monte carlo results are narrower than the data shown in fig . [ ehsep ] . we have designed and constructed a lead scintillator sandwich calorimeter for the zeus experiment at hera . the calorimeter is divided into 5 cm vertical towers read out on two sides with wavelength shifting light guides coupled to photomultiplier tubes . the calorimeter was tested in the h6 beam line at cern with 120 gev electrons , muons , pions and protons . electrons can be cleanly separated from hadrons using the energy weighted vertical width of a shower . at 120 gev the calorimeter is slightly over compensating , with an electron to hadron response ratio of 0.96 and an energy resolution 6% at 120 gev . the horizontal position resolution , measured by charge sharing between the two sides , is 20 cm/@xmath35 , assuming a @xmath96 dependence ; the vertical position resolution , measured by energy sharing between the towers , is 10 cm/@xmath35 . by using energetic neutrons produced by proton interactions in a lucite target , the overall energy scale was determined to 1.5% . since the spring of 1995 , the calorimeter has operated successfully in the hera tunnel 105.6 m downstream of the zeus detector on the zero degree line . we thank t. tymieniecka for modeling the fnc during the design stage , and using fluka to study its energy resolution and @xmath47 response . e. borsato , f. czempik , c. fanin , r. fernholz , t. kiang , k. loeffler , h. stehfest , v. sturm , and k. westphal provided us with much help constructing the calorimeter , shipping it to cern , and installing it in the hera tunnel . m. roseman helped with the pmt tests and at cern . we thank m. brki for his assistance in setting up the computer readout system for the cern tests . b. racky kindly arranged for us the transport of our @xmath97co source to and from cern . we also thank f. dittus for making available the adjustable table on which we mounted the calorimeter , and k. elsener for his invaluable assistance with the h6 beam . we are also grateful to cern for making the beam test possible . j. prentice helped with cosmic ray tests during the initial stages . the zeus collaboration has been continually enthusiastic and supportive , in particular , r. klanner , g. wolf and u. koetz . we also thank the hera machine group who helped install the fnc , and who provided the beam line modifications which greatly enhance the performance for physics of the fnc . finally , we especially thank the desy directorate for the continual interest they have shown in the project , and for the financial support they provided . d. bintinger , in _ proceedings of the workshop on calorimetry for the supercollider _ , tuscaloosa , al , march 13 - 17 , 1989 , r. donaldson and m. g. d. gilchriese , ed . , ( world scientific , teaneck , nj , 1989 ) , p. 91 .

a lead scintillator sandwich sampling calorimeter has been installed in the hera tunnel 105.6 m from the central zeus detector in the proton beam direction . it is designed to measure the energy and scattering angle of neutrons produced in charge exchange @xmath0 collisions . before installation the calorimeter was tested and calibrated in the h6 beam at cern where 120 gev electrons , muons , pions and protons were made incident on the calorimeter . in addition , the spectrum of fast neutrons from charge exchange proton - lucite collisions was measured . the design and construction of the calorimeter is described , and the results of the cern test reported . special attention is paid to the measurement of shower position , shower width , and the separation of electromagnetic showers from hadronic showers . the overall energy scale as determined from the energy spectrum of charge exchange neutrons is compared to that obtained from direct beam hadrons . hep - ex/9701015 + desy 97 - 006 + design and test of a + forward neutron calorimeter + for the zeus experiment + the zeus fnc group + s. bhadra@xmath1 , i. bohnet@xmath2 , m. cardy@xmath1 , u. dosselli@xmath3 , c .- p . fagerstroem@xmath1 , w. frisken@xmath1 , k. furutani@xmath1 , d. hanna@xmath4 , u. holm@xmath2 , k. f. johnson@xmath5 , m. khakzad@xmath1 , g. levman@xmath6 , j. n. lim@xmath4 , b. loehr@xmath7 , j. f. martin@xmath6 , c. muhl@xmath7 , t. neumann@xmath2 , m. rohde@xmath7 , w. b. schmidke@xmath1 , d. g. stairs@xmath4 , h. tiecke@xmath8 , c. voci@xmath3 + [ cols= " > , < " , ] the photomultipliers were read out with lecroy 4300 charge integrating adcs . the adcs were gated so that 160 ns of the pulse from the calorimeter was integrated . during data taking the adc pedestals were regularly measured , and the gains were monitored with an internal test function in the units . the gains were also checked daily using an external charge injector . over the course of the beam test , which lasted one week , individual adc gains varied less than 1 part per mil , and all gains were uniform to within 5 parts per mil . in the following we use a right - handed coordinate system with @xmath9 vertically up and @xmath10 into the face of the calorimeter . the origin ( 0,0 ) is taken to be between the two central towers halfway between the sides ( the center of the face of the calorimeter ) . @xmath11 and @xmath12 are measurements of @xmath13 and @xmath9 based on the table position ; @xmath14 and @xmath15 , measurements based on energy deposits in the fnc . the vertical position of a shower is determined using the centroid method by taking an energy weighted average of the the tower positions : @xmath16 where the sum is over towers in the front part of the fnc , and the weights @xmath17 are functions of the energy deposits , @xmath18 , in each tower . the weights are chosen to minimize bias and to maximize resolution in the position measurement . the simplest method of estimating @xmath9 corresponds to choosing weights which are linear in energy , @xmath19 . awes et al.@xcite have suggested that the weights be chosen to have instead a logarithmic dependence on the energy deposits : @xmath20 , \label{eqn_w}\ ] ] where @xmath21 , and @xmath22 is a fractional cutoff . when the energy deposited in a tower satisfies @xmath23 , that tower is not used in the determination of the vertical position . the logarithmic dependence of the @xmath17 more closely matches the true transverse profile of energy deposits in a hadronic shower than the linear dependence . this estimator is simple , but it has an undetermined free parameter @xmath24 which may be a function of the deposited energy . in addition the optimal value of the cutoff parameter may depend on particle type , electron or hadron . the vertical segmentation also allows us to estimate the size of the shower using the rms vertical shower width : @xmath25 since the width of electromagnetic showers is much less than the width of hadronic showers , this estimator enables us to distinguish incident electrons from incident hadrons . the optimal weights for the width determination are not necessarily the same as those for the position measurement . since we use the width @xmath26 to separate electromagnetic from hadronic showers , it is most convenient to have an estimator that does not depend on knowledge of the nature of the incident particle . otherwise an iterative procedure must be employed . as we will discuss in more detail below , linear weights for the shower size measurement give a hadron - electron separation which is close to that obtained with logarithmic weights whose cutoff parameter has been optimized . the horizontal position of a shower can be estimated from the division of scintillation light between the left and right sides of the calorimeter : @xmath27 where @xmath28 is the effective attenuation length of the scintillator strips , and @xmath29 is the charge from the left(right ) pmt . if the light attenuation behaves as @xmath30 where @xmath31 , @xmath32 are constants , and @xmath13 is the displacement of the incident particle from the center of the tower , then @xmath14 is independent of @xmath32 and @xmath33 . the calorimeter was calibrated with 120 gev electrons incident on the center of each tower . the high voltage for the tubes in the front was adjusted so that their mean response to 120 gev electrons as measured in the lecroy adcs was 100 pc ( 400 counts ) . after lifting and rotating the calorimeter by 180 degrees to make electrons incident on the rear towers , the high voltage of each rear tube was set so that the response of the rear section to a muon passing through the calorimeter would approximately equal the response of the front section . since the ratio of the number of front layers to the number of rear layers is 95/39 , the gain is considerably higher in the rear ; however , the energy deposits in the rear for electrons and hadrons are small , so there is no saturation problem for the very high energy particles at hera . figure [ energy]a shows the distribution of deposited energy , after calibration , for 120 gev electrons centered on towers 3 through 7 , inclusive . pion contamination has been removed be requiring that the vertical shower width be less than 3 cm ( section [ separation ] ) . the energy resolution for electrons centered on a tower averaged 33%/@xmath34 independent of tower . electrons centered in the edge towers had an energy response reduced by 3% due to transverse energy leakage . the response of the calorimeter to electrons is dependent on the position of the electron with respect to the gap between the scintillator strips . figure [ crack_width]a shows the energy deposited in tower 6 when the electron beam is scanned from tower 6 to tower 7 . the total signal for electrons incident between two towers is 90% of the signal of an electron incident on the center of a tower . moreover , the energy resolution is degraded to 60%/@xmath35 . these effects are due to the narrowness of electromagnetic showers compared to the width of the region between strips . the small width of the shower compared with the strip width , combined with the reduction in response at the tower boundaries , is responsible for the large bias towards the tower center in the measured electron vertical position shown in fig . [ crack_pos ] . the bias grows with increasing cutoff parameter since for sufficiently large @xmath24 only the struck tower contributes to the sums in equations [ eqn_y ] and [ eqn_yw ] . the rms deviation of the distribution also tends to increase . the variation with vertical position of the shower width ( linear weights ) of electrons is shown in fig . [ crack_width]b , and is small compared to the average width of hadronic showers ( see section [ separation ] ) . electrons were also used to determine the effective attenuation length for light in the scintillator strips . one half of each tower was scanned horizontally . for each position the response of the right and the left photomultiplier tubes was plotted as a function of the offset @xmath13 of the beam from the center of the calorimeter , positive @xmath13 representing an offset away from the pmt . figure [ attenl ] shows the resulting attenuation curve for a typical tower . the response is well represented by equation [ eqn_atten ] the tower - to - tower average value of @xmath31 was found to be 1.08@xmath36 @xmath37 with a 3% rms spread , corresponding to an average effective attenuation length of 92 cm ; @xmath32 averaged 9.60@xmath38 @xmath39 with a 20% rms spread . to compare the efficiencies of the wavelength shifting material in the front and rear section we measured the number of photoelectrons collected by the photomultiplier tubes , @xmath40 , which is related to the width , @xmath41 , of the difference distribution by @xmath42 where @xmath43 is the mean of the sum . by rotating the calorimeter 180 degrees to make electrons incident both front and rear , we found that although in the rear we averaged 92 pe / gev , in the front we obtained only 26 pe / gev . this difference is due to different wls lengths , wls material , and optical geometry between front and rear , and it worsens the @xmath13 position resolution by a factor of @xmath44 compared to the estimate in section [ description ] . photostatistics makes only a small contribution to the energy resolution since , for 120 gev electrons and 26 pe / gev , the fluctuations are only about 2% . electron showers penetrate only about an interaction length into the calorimeter . to refine the calibration constants determined by electrons , 120 gev pions were made incident on the center of each tower . using these data , correction factors were determined which equalized the response of each pmt to hadrons . the correction factors for hadrons were forced to average 1.0 , and had an rms spread of 5% . the distribution of deposited energy for 120 gev hadrons ( pions and protons ) incident on the center of the calorimeter , between towers 5 and 6 , is shown in fig . [ energy]b . for pions incident in the center of each tower , the average response of the calorimeter is shown in fig . [ ptower ] . the curves are quadratic in @xmath45 . leakage loss is important whenever the beam is outside the four central towers . when the beam is incident in the center of the calorimeter , between towers 5 and 6 , about 2.5% of the energy is lost compared to the case when the beam is in the center of tower 5 or 6 because of the gap between the scintillator strips ( see inset of fig . [ eofy ] ) . parameterized as @xmath46 , the energy resolution for hadrons incident at the center of towers 5 and 6 is 0.70/@xmath35 ( fig . [ ptower ] ) . this improves to 0.62/@xmath35 for hadrons incident at the center of the calorimeter , between towers 5 and 6 . these results can be compared to the results for electrons discussed above . the electron to hadron ratio @xmath47 is 0.96 when the beams are incident on the center of a tower , but it falls to about 0.9 when both are incident on the center of the calorimeter in the gap between towers 5 and 6 . for electrons centered on a tower , but hadrons incident on the center of the calorimeter @xmath48 ( see fig . [ energy ] ) . if the electron calibration constants are used instead of the hadron calibration constants , @xmath47 changes by 0.01 . as expected from the ratio of lead to scintillator thickness , the calorimeter is over compensating . this effect is magnified for electrons by the gap between the scintillator strips ; however , since compared to the electrons the electromagnetic component of a hadronic shower is more spread out transversely , we expect the ` effective ' @xmath47 to be higher . in order to study energy leakage and position resolution for hadrons , the face of the calorimeter was scanned with 120 gev pion over an @xmath49 grid . using this grid the effective attenuation length of the scintillator was determined with hadronic showers . the resulting average attenuation length , 91.9 cm , was in good agreement with the electron scan results . figure [ ys ] shows the true vertical position of the calorimeter as a function of its position determined using the centroid algorithm with linear weights ( @xmath19 ) . the effect of the finite strip size is clearly evident in the oscillation superimposed on an average behavior . in addition , towards the edge of the calorimeter the measured value falls below the true value because of leakage . the average behavior can be parameterized conveniently as @xmath50 . the residuals , shown in the upper inset , follow an approximate sine curve with period 5 cm , the tower height . the overall vertical resolution is determined by plotting the @xmath9 residuals for the centroid algorithm with the polynomial correction for all points of the grid . the residual distribution is well fit by a sum of two gaussian ( fig . [ yres]a ) . the largest component has a weight of 0.91 and an rms width of 0.8 cm for 120 gev pions . because this width is larger than the size of the oscillation , the @xmath9 position can not be corrected for the oscillation on an event by event basis . in contrast to linear weights , logarithmic weights depend on an arbitrary cutoff parameter @xmath24 which may be chosen to optimize the position resolution , minimizing bias . residuals for logarithmic weights with @xmath51 are shown in the lower inset in fig . [ ys ] and in fig . [ yres]b . the bias due to leakage has been considerably reduced ( @xmath52 ) , and the resolution improved , compared with the use of linear weights . a measure of the effective overall resolution is @xmath53 @xmath54 where @xmath55 is the variance of gaussian @xmath56 , and @xmath57 is its fractional contribution to the overall distribution . the resulting @xmath53 is plotted in fig . [ fval ] as a function of @xmath24 . the best vertical position resolution for 120 gev pions is 8 cm/@xmath35 for @xmath58 , where the curve has a minimum . like the @xmath9 residuals , the distribution of @xmath13 residuals is also well represented by a sum of two gaussians : 97% with @xmath59 cm/@xmath35 , and 3% with @xmath60 cm/@xmath35 , giving @xmath61 cm/@xmath35 . the resolution in @xmath13 is much poorer than in @xmath9 ; nevertheless , it is close to the value expected since for 1 gev incident energy @xmath62 the energy response varies over the grid as a result of two competing effects : a ) energy leakage , and b ) light enhancement . as the beam is moved towards the edge of the calorimeter , energy is lost due to leakage , and the measured signal tends to decrease . on the other hand , as the beam moves horizontally away from the center the light collected by the pmts increases because of the characteristic light attenuation of the scintillator strips : @xmath63 the net result is that the signal increases for horizontal displacements at fixed @xmath9 . the increase is approximately linear in @xmath13 with @xmath64.\ ] ] figure [ eofy ] shows the energy response as a function of y for all grid values with the @xmath13 dependence removed . energy loss due to the gap between the scintillator strips is clearly visible as is also loss due to leakage . the leakage component has a quadratic dependence in @xmath45 ; the loss due to the gaps between strips behaves as a superposed oscillation . a calorimetric measurement with the capability of distinguishing between electromagnetic and hadronic showers is important for physics studies . because electromagnetic showers are much narrower than hadronic showers , the measurement of the shower width allows a separation of particles by type . the use of logarithmic weights for the determination of the vertical shower position reduces the bias due to the finite strip size and lateral leakage , and improves the resolution ; however , the optimal choice of the cutoff parameter depends on incident particle type . at 120 gev , @xmath24 should be chosen to be about 10% for hadrons , but should be close to 0 ( no cutoff ) for electrons . the choice of cutoff for the width measurement can be chosen to optimize the separation of electromagnetic and hadronic showers . to estimate the optimal value of @xmath24 we define @xmath65 as a measure of the electron - hadron separation , where @xmath66 and @xmath67 are the means and standard deviations , respectively , of the width distributions for hadrons ( @xmath68 ) and electrons ( @xmath69 ) . all are implicitly functions of the cutoff @xmath24 , so the value of @xmath24 can be chosen to maximize @xmath70 . the dependence of @xmath70 on @xmath24 for 120 gev electrons and hadrons is shown in fig . [ ehsep ] . @xmath70 is insensitive to @xmath24 at low values of @xmath24 , but falls approximately linearly for @xmath71% . linear weights give the result shown by the dashed line , @xmath72 , close to best values obtained with logarithmic weights , and have the advantage of being independent of @xmath24 , which may depend on the incident energy . as a result , we use linear weights for measurement of shower widths instead of the logarithmic weights chosen for the shower centroid measurement . the vertical width distribution is plotted in fig . [ ehsep]b and c for 70 and 120 gev electrons and pions incident on towers 2 through 9 . although the distributions do not change much with energy , there is a small reduction in spread and decrease in mean . figures [ ehsep]c and [ ywidthy]a show that mean and standard deviation of the shower width distribution for hadrons does not change significantly with the incident vertical position . a @xmath26 cut chosen in the range 2 - 4 cm will clearly separate electrons from hadrons . only 2.3% of hadrons incident at the center of the calorimeter will be lost with a @xmath26 cut of 3.5 cm ; the loss rises to 4.0% for hadrons incident at the center of a strip ( fig . [ ehsep ] ) . the same analysis for electrons is complicated by pion contamination in the electron sample , which is shown as a broken line in fig . [ ehsep ] . to subtract the pion contamination , we normalize the width distribution for pions to the raw ( unsubtracted ) distribution for electrons in the region @xmath73 cm . the result is shown in fig . [ ywidthy]b for electrons incident in the center of a tower , and electrons scanned vertically from tower 6 to 7 . the inset shows the tail of the distribution for centered electrons . about 1.5% of the electron showers have a width greater than 3.5 . although the signal from penetrating muons is low because of their small energy deposits , they can be useful for calibrating and monitoring the fnc in hera using either cosmic rays or beam halo muons . to study the response of the calorimeter to high energy muons , a special trigger was implemented for beam particles which penetrated the calorimeter . figure [ muon ] shows a typical energy distribution for a muon in the bottom front tower . the peak position @xmath74 is determined by fitting the distribution to a convenient functional form : @xmath75 and @xmath76 , @xmath31 , @xmath74 , and @xmath77 are parameters . when @xmath78 , @xmath79 is the moyal function@xcite , an analytic approximation for the landau distribution . the tower - to - tower spread of the peak position is 4% . the absolute energy scale is best determined by making a beam of known energy incident on the calorimeter . if deuterons were to be accelerated at hera , nuclear stripping reactions would make neutrons of known energy incident on the calorimeter . at present only protons are accelerated , and the absolute energy scale must be determined using beam gas interactions which produce leading neutrons by charge exchange . if deuterons were accelerated at hera in order to test the feasibility of using charge exchange reactions to determine the absolute energy scale , a short experiment was performed . figure [ cern_tb ] shows the experimental arrangement . a lucite target was placed in the beam 20 m in front of the calorimeter . immediately after the target a sweeping magnet was tuned to deflect beam particles downward . with the magnet tuned to full field beam particles ( protons and pions ) were deflected downwards by 11 cm at the calorimeter . it was necessary to devise a trigger that ensured that only events arising from the impact of a neutral particle in the central part of the calorimeter were accepted . crossed finger counters in front of the target defined the beam position ( see table [ countertab ] and fig . [ cern_tb ] ) . the trigger required a coincidence of these two counters and energy deposited in the center of the calorimeter for the trigger , the deposited energy was measured by summing and discriminating the signals from the last dynode of the pmts of the four central towers . in order to veto charged particles , three scintillation counters were placed directly in front of the calorimeter . in addition , only showers near the center of the calorimeter were considered in order to reduce energy leakage . in summary the data were required to satisfy : @xmath80 where @xmath81 the shower position @xmath14 was determined by light division ; @xmath15 , by the centroid method with logarithmic weights . the observed energy distribution is shown in fig . [ neutron ] . in the same figure , the hatched histogram shows the response of the calorimeter to 120 gev hadrons . the mean value of the latter distribution determines the energy scale for the figure . the one pion exchange ( ope ) model of the reaction @xmath82 predicts that the cross section , integrated over scattering angles , is given by @xmath83 where @xmath84 is the flux of virtual pions associated with the incoming proton ; @xmath85 is the total pion - target cross section for a virtual pion beam energy of @xmath86 . any dependence of @xmath87 on the virtuality of the exchanged pion has been ignored in equation [ eqn_ope ] , so @xmath87 can be estimated using a parameterization ( @xmath88 gev ) , or an interpolation table ( @xmath89 gev)@xcite . several forms have been postulated for the flux factor @xmath84 in theoretical and phenomenological studies of ope . they fall into two classes : regge@xcite and light cone@xcite . accordingly , to compare data and theory , we extended the herwig@xcite monte carlo program to generate events according to ope folded with the measured experimental resolutions . the predicted energy distribution , for the light cone flux factor@xcite , adjusted for resolution and acceptance is shown as the open histogram in fig . [ neutron ] . the ope prediction is normalized to the data by the number of events . as can be seen , agreement is good for energies larger than 100 gev . the energy scale was varied and then compared with the ope prediction for @xmath90 gev by computing the @xmath91 of the difference distribution . the variation of @xmath91 with the scale factor is shown in the inset to fig . [ neutron ] . the minimum occurs for a scale factor of 0.985 . if the regge@xcite form for the flux factor is used instead , the same procedure yields a minimum at 1.003 , in complete agreement with the incident proton beam ; in this case , however , the minimum @xmath91 is worse ( 17 rather than 10 ) . we conclude that using charge exchange neutrons the absolute energy scale can be determined to better than 1.5% with the chief source of error being the theoretical uncertainty on the form of the virtual pion flux factor .

peculiar velocity surveys covering a fair fraction of the sky are now reaching to 6000 and beyond ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) and are being interpreted as evidence for substantial flows on these scales ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) . however , the amplitude , direction , and scale of these flows remain very much in contention , with resulting uncertainties in the theoretical interpretation and implications of these measurements ( @xcite , @xcite ) . indeed , recently published conflicting results suggest that the motion of the lg is either due , or is not due , to material within 6000 , and that _ iras _ galaxies either trace , or do not trace , the dark matter which gives rise to the observed peculiar velocities . the most recent potent reconstruction of the markiii velocities ( @xcite ) shows that the bulk velocity can be decomposed into two components arising from the mass fluctuation field within the sphere of radius @xmath3 about the lg and a component dominated by the mass distribution outside that volume . for convenience , we refer to this boundary at @xmath3 as the `` supergalactic shell '' since it includes the main local attractors in the supergalactic plane , the great attractor and perseus - pisces . this new analysis shows dominant infall patterns by the ga and pp but very little bulk flow within the supergalactic shell . the tidal component inside this volume is dominated by a flow of amplitude @xmath4 in the supergalactic direction @xmath5 , which is likely generated by the external mass distribution on very large scales ( see also @xcite , @xcite ) . this interpretation is also supported by an increasingly large number of tf / fp investigations ( based on the distribution and motion of abell clusters ) which report the detection of streaming motions of amplitudes greater than 700 beyond @xmath6 and away from the cmb dipole ( @xcite , @xcite , @xcite , @xcite ) . other investigations using nearly homogeneous samples of galaxies within and outside the supergalactic shell find motion consistent with the amplitude and direction of the cmb dipole @xcite . this suggests that the reflex motion of the local group could be explained by material contained within the supergalactic shell . this confusion stems , in large part , in our inability to perfectly match the many heterogeneous samples for flow studies into one self - consistent homogeneous catalogue . much of the problem lies in the fact that , with the exception of a few surveys beyond @xmath7 ( @xcite , @xcite , @xcite ) , none of the surveys within the supergalactic sphere sample the _ entire _ sky uniformly . in an attempt to overcome this problem , two of us ( jw & sc @xmath8 collaborators ) have recently combined the major distance - redshift surveys from both hemispheres ( published before 1994 ) into a catalog of 3100 galaxies ( @xcite ) , but showed that full homogenization at the @xmath9% level , the minimum required for a @xmath10 bulk flow detection at 6000 , can not be achieved . due to subjective reduction techniques and varying selection criteria , fundamental uncertainties remain when trying to match greatly disparate tf datasets ( @xcite ) . furthermore , a revised calibration of the markiii tf zero - points based on maximal agreement with the peculiar velocities predicted by the iras 1.2jy redshift survey suggests a possible source of systematic error for the data sets which cover the pp cone ( @xcite ) . this uncertainty has not seriously affected mass density reconstructions within the supergalactic shell ( @xcite ) but it could lead to spurious estimates of the bulk flows on larger scales . a newer calibration of the courteau / faber catalogue of northern spirals , not included in markiii , has been published ( @xcite , @xcite ) but a revision of the markiii catalogue is in progress ( @xcite ) . the need to tie all existing data bases for cosmic flow studies in an unambiguous fashion is clear . to that effect , we initiated a new survey in 1996 using noao facilities to measure tf distances for a complete , full - sky sample of sb@xmath0sc galaxies in the supergalactic shell for which we will obtain _ precise _ and _ uniform _ photometric and spectroscopic data . this will be the first well - defined full - sky survey to sample this scale , free of uncertainties from matching heterogeneous data sets . the sfi survey of giovanelli @xcite resembles ours in its scope and sky coverage , but it relies on a separate dataset ( @xcite ) for coverage of the southern sky and thus can not attain full - sky homogeneity . our survey , on the other hand , is designed from the outset to be homogeneous to the minimum level required for unambiguous bulk flow detection at the supergalactic shell . because of the overlap with existing surveys at comparable depth ( markiii + sfi ) , this new compilation will be of fundamental importance in tying the majority of existing data sets together in a uniform way , which will greatly increase their usefulness for global analyses of mass fluctuations in the universe . our sample is selected from the optical redshift survey ( @xcite ) , consisting of galaxies over the whole sky with m@xmath11 and @xmath12 from the ugc , eso , and esgc ( @xcite ) . it includes all non - interacting sb and sc galaxies with redshifts between 4500 and 7000 from the local group and inclinations between @xmath13 and @xmath14 , in regions where burstein - heiles extinction is less than 03 . this yields an all - sky catalog of 297 galaxies . following the approach of @xcite , we use the sample itself to calibrate the distance indicator relation ; this mitigates the need to tie the sample to external tf calibrators such as clusters ( although it precludes measurement of a monopole term in the velocity field ) . given a tf fractional distance error of 20% , the statistical uncertainty on a bulk flow from @xmath15 galaxies at common distance @xmath16 is @xmath17 . as the measured ( and much contested ) bulk motions on these scales are of the order of 300 , a detection of high statistical significance is well within reach . data taking and reduction techniques follow the basic guidelines of previous optical tf surveys ( @xcite , @xcite , @xcite , @xcite ) . our survey is now complete , which is essential to achieve our statistical requirements and ensure a rigorous analysis . the spectroscopy relies on measurement of h@xmath18 rotation velocities at 2.2 disk scale lengths for the tightest tf calibration and best match to analogous 21 cm line widths ( @xcite , @xcite ) . the photometry is based on the kron - cousins @xmath19 and @xmath20 systems which will allow direct matching with two largest tf field samples to date ( @xcite,@xcite ) . one of the key features of this study is not only its all - sky sample selection but the independent duplication of all data reductions ( by at least 2 , if not 3 , of us ) . these reductions and a first flow analysis based on the shellflow sample alone should be published soon ( @xcite ) . we also plan a more extensive analysis using the recalibrated markiii combined with other new catalogs not included in the original markiii . 99 corwin , h. g , & skiff , b. a. 1994 , extension to the southern galaxies catalogue , in preparation clutton - brock , m . , & peebles , p.j.e . 1981 , aj , 86 , 1115 courteau , s. 1992 , phd . thesis , uc santa cruz courteau , s. , faber , s.m . , dressler , a. , & willick , j.a . 1993 , apj , 412 , l51 courteau , s. 1996 , apjs , 103 , 363 courteau , s. 1997 , aj , 114 , 2402 courteau , s. ( + shellflow team ) 1999 ( in preparation ) da costa , l. n. , freudling , w. , wegner , g. , giovanelli , r. , haynes , m.p . , & salzer , j.j . 1996 , apj , 468 , l5 dekel , a. , eldar , a. , kolatt , t. , yahil , a. , willick , j. a. , faber , s. m. , courteau , s. , & burstein , d. 1999 , apj ( submitted ) giovanelli , r. , haynes , m.p . , freudling , w. , da costa , l. n. , salzer , j.j . , & wegner , g. 1998 , apjl , in print , astro - ph/9807274 han , m .- s . , & mould , j. r. 1992 , apj , 396 , 453 hudson , m. ( + smac team ) 1998 ( in preparation ) lauer , t. r. , & postman , m. 1994 , apj , 425 , 418 mathewson , d. s. , & ford , v. l. 1994 , apj , 434 , l39 mathewson , d. s. , ford , v. l , & buchhorn , m. 1992 , apjs , 81 , 413 [ m92 ] postman , m. 1995 , in _ dark matter _ , aip conf . series 336 , 371 postman , m. , & lauer , t. r. 1995 , apj , 440 , 28 riess , a. , press , w. , & kirshner , r. p. 1995 , apj , 445 , l91 santiago , b. x. , strauss , m. a. , lahav , o. , davis , m. , & huchra , j. p. 1995 , apj , 446 , 457 scaramella , r. , 1989 , nature , 338 , 562 schlegel , d. 1996 , phd . thesis , uc berkeley strauss , m.a . 1996 , in _ critical dialogues in cosmology _ , ed . neil turok ( singapore : world scientific ) strauss , m.a . , & willick , j.a . 1995 , physics reports , 261 , 271 willick , j. a. , courteau , s. , faber , s. m. , burstein , d. , dekel , a. , & strauss , m. a. 1997 , apjs , 109 , 333 willick , j. a. & strauss , m. s. 1998 , apj , in press ( astro - ph/9801307 ) willick , j.a . 1998 , apj ( submitted ) willick , j.a . 1999 ( in preparation )

we present a new optical tully - fisher ( tf ) investigation for a complete , full - sky sample of 297 sb@xmath0sc spirals with redshifts between 4500 and 7000 . the survey was specifically designed to provide _ uniform , well - calibrated _ data over both hemispheres . all previous tf surveys within the supergalactic shell ( @xmath1 ) have relied on matching separate data sets in the northern and southern hemispheres and thus can not attain full - sky homogeneity . analyses of the cosmological dipole and peculiar velocities based on these studies have produced contradictory claims for the amplitude of the bulk flow and whether it is generated by internal or external mass fluctuations . with shellflow , and further zero - point calibration of existing tf data sets , we expect a high - accuracy detection of the bulk flow amplitude and an unambiguous characterization of the tidal field at 6000 . # 1#1@xmath2

our work is concerned with the kinetics of electrons in a stellar atmosphere , modelled as a parallel - plane slab irradiated on a face . our models of atmospheres start in the deep layers of stars , where the radiative field can be described in the diffusion approximation , and end with the layers of minimal temperature , before the chromospheric raise whose effects are ignored . the free electrons are characterized by their velocity distribution function : the electron distribution function ( edf ) , which is calculated with the other thermodynamical quantities of the atmosphere . our main objective is to understand the mechanism leading to the thermalisation of electrons , where the edf tends toward the maxwell - boltzmann distribution . it is accepted , in stellar atmospheres theory , that the thermalisation of electrons is effective as long as elastic collisions dominate inelastic interactions of electrons with the plasma , a rather well verified hypothesis for electrons having energies greatly below the first excitation energies of atoms and ions composing the atmosphere . this hypothesis is not necessarily correct for faster electrons . our work follows the line drawn by some plasma physicists at the beginning of the 70s ( peyraud 1968 , 1970 ; peyraud 1969 ; oxenius 1970 , 1974 ; shoub 1977 ) . their work demonstrated the important role played by inelastic ( collisional or radiative ) processes in the equilibrium reached by electrons , which can deviate considerably from the maxwellian equilibrium at high energies . we present below a stellar atmosphere model which is not in local thermodynamical equilibrium ( lte ) , confirming the results anticipated in the 70s on the basis of mainly theoretical developments . this problem consists in solving the equations generally used to model a non - lte stellar atmosphere ( equation of radiative transfer , equations of statistical equilibrium , pressure equation , equation of energy , conservation of charge ) , coupled with the kinetic equation of electrons . this non - linear system is difficult to solve numerically because it contains two coupled kinetic equations : one for photons , the other for electrons . therefore we have used the simplest model of non - lte atmosphere : homogeneous ( constant density of heavy particles @xmath0 ) , isotherm ( constant temperature @xmath1 ) , and composed with hydrogen atoms with only two energy levels . the deviation from lte is then due to the escape of photons by the free surface . on the other hand we have included in our model the main collision processes existing in a stellar atmosphere ( elastic collisions , collisional or radiative inelastic interactions ) . the elastic collision term of the kinetic equation of electrons is written in a bgk model with a velocity dependent collision frequency . this model accuratly fits the main properties of the usual landau term ( fokker - planck ) . to solve the equation of radiative transfer , we used the codes of the transfer group in cral ( rutily 1992 ) . in our model , we choosed @xmath2 and @xmath3 , which are typical values in the solar photosphere . the plasma is optically thick at all frequencies ( optical thickness greater than 100 ) , leading to a high geometrical thickness @xmath4 since there is no temperature or heavy particles density gradient . finally the atmosphere is irradiated on its internal boundary layer by a planck radiation of temperature @xmath1 . the figure [ fig1]a is a classical diagram showing the superficial regions where the non - lte effects are important . figure [ fig1]b shows that the edf is not a maxwell - boltzmann distribution in the non - lte region of the atmosphere ( see @xmath5 ) , the deviation from a maxwellian distribution being important very close to the surface ( @xmath6 , corresponding to an optical depth @xmath7 in the ly@xmath8 spectral line ) . in figure [ fig1]c , we drawn the superficial edf at @xmath9 as a function of the electronic velocity . the edf tail of fast electrons is strongly depleted when electron energies are greater than the minimum excitation energy of the hydrogen atom ( @xmath10 , @xmath11 , @xmath12 ) . the edf tail shows successive platforms centered on @xmath13 and @xmath14 . these features were already described by the authors at the origin of this work , referenced at the beginning of this article . the mechanism responsible for this effect is very well explained in oxenius s monograph ( 1986 ) , where the author outlines an interesting _ feedback effect _ tending to amplify the deviation of the edf from a maxwellian distribution . this mechanism starts when elastic and inelastic collision frequencies become comparable at high electronic velocities , which is the case for a weak ionization degree . a ) deviations of the populations from their lte values as a function of the reduced geometrical depth @xmath15 . coefficients @xmath16 , where @xmath17 are the saha densities of the hydrogen atom in energy states @xmath18 , are used to characterize non - lte regions ( @xmath19 ) . b ) deviation of the edf to the maxwellian distribution @xmath20 as a function of the reduced geometrical depth @xmath15 . both curves are drawn for a given velocity @xmath21 , where @xmath22 is the velocity corresponding to the rydberg energy @xmath23 . c ) deviation of the edf to the maxwellian distribution as a function of the electronic velocity @xmath24 , at the surface of the atmosphere @xmath9.,width=472,height=377 ] astrophysical consequences of this work are numerous . in general the deviation of the edf from a maxwellian distribution has a direct effect on all thermodynamic quantities involving the edf , _ e.g. _ collisional transition rates or spectral lines profiles . it has an indirect effect on all other characteristics of the atmosphere , because of the coupling of all equations . transition rates are used to solve the equations of statistical equilibrium , which lead to the populations and ionization degree of the atmosphere . inversion techniques of spectral lines observed by spectroscopy are also sensitive to the edf shape , so that temperatures or densities calculated with these techniques are affected by deviation of the edf from a maxwellian distribution ( shoub 1983 , owocki 1983 , salzmann 1995 ) . finally the non thermodynamical equilibrium of electrons may be at the origin of physical processes which are still not very well understood at present , for example the heating of the sun corona ( scudder 1992,1994 ) . the results presented in this article are based on a very simple atmosphere model , which guarants a numerically stable solution . in non - lte regions close to the surface , the edf shows important deviations from the maxwellian distribution in the fast electrons tail . our model confirm , by means of numerical codes accurate enough to handle this complex problem , most of the physical ideas advanced thirty years ago . our main contribution consists in the construction of a selfconsistent model of a stellar atmosphere with non thermalized electrons . also we have used very accurate radiative transfer codes . it remains to make this model more realistic for comparison with observations . peyraud , n. 1968 , le journal de physique , 29 , 201 ; 29 , 747 ; 29 , 997 . peyraud , n. , peyraud j. 1969 , le journal de physique , 30 , 773 . peyraud , n. 1970 , le journal de physique , 31 , 565 . owocki , s. p. , scudder , j. d. 1983 , astrophys . j. , 270 , 758 . oxenius , j. 1970 , z. naturforsch . , 25 , 101 ; 25 , 1302 . oxenius , j. 1974 , j. quant . transfer , 14 , 731 . oxenius , j. 1986 , kinetic theory of particles and photons , springer - 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we are interested in electrons kinetics in a stellar atmosphere to validate or invalidate the usually accepted hypothesis of thermalisation of electrons . for this purpose , we calculate the velocity distribution function of electrons by solving the kinetic equation of these particles together with the equations of radiative transfer and statistical equilibrium . we note that this distribution can deviate strongly from a maxwell - boltzmann distribution if non - lte effects are important . some results and astrophysical consequences are examined .

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we present and discuss a variance - reduced stochastic particle method for simulating the relaxation - time model of the boltzmann transport equation . the present paper focuses on the dilute gas case , although the method is expected to directly extend to all fields ( carriers ) for which the relaxation - time approximation is reasonable . the variance reduction , achieved by simulating only the deviation from equilibrium , results in a significant computational efficiency advantage compared to traditional stochastic particle methods in the limit of small deviation from equilibrium . more specifically , the proposed method can efficiently simulate arbitrarily small deviations from equilibrium at a computational cost that is independent of the deviation from equilibrium , which is in sharp contrast to traditional particle methods . the boltzmann transport equation @xmath0 _ { \textrm{coll}}}}\ ] ] where @xmath1 is the single - particle distribution function @xcite , @xmath2 _ { \textrm{coll}}}}$ ] denotes the collision operator , @xmath3 is the acceleration due to an external field , @xmath4 is the position vector in physical space , @xmath5 is the molecular velocity vector , and @xmath6 is time , is used to describe ( under appropriate conditions ) transport processes in a wide variety of fields @xcite including dilute gas flow @xcite , phonon @xcite , electron @xcite , neutron @xcite and photon transport @xcite . recently , it has received renewed attention in connection to micro- and nano - scale science and technology where transport at lengthscales of the order of , or smaller than , the carrier mean free path is frequently considered ( e.g. nanoscale solid - state heat transfer @xcite ) numerical solution of the boltzmann equation remains a formidable task due to the complexity associated with the collision operator and the high dimensionality of the distribution function . both these features have contributed to the prevalence of particle solution methods , which are typically able to simulate the collision operator through simple and physically intuitive stochastic processes while employing importance sampling , which reduces computational cost and memory usage @xcite . another contributing factor to the prevalence of particle schemes is their natural treatment of the advection operator , which results in a numerical method that can easily handle and accurately capture traveling discontinuities in the distribution function @xcite . an example of a particle method is the direct simulation monte carlo ( dsmc ) @xcite which has become the prevalent simulation method for dilute gas flow . one of the most important disadvantages of particle methods for solving the boltzmann equation derives from their reliance on statistical averaging for extracting field quantities from particle data . when simulating processes close to equilibrium , thermal noise typically exceeds the available signal . when coupled with the slow convergence of statistical sampling ( statistical error decreases with the square root of the number of samples ) , this often leads to computationally intractable problems @xcite . for example , to resolve a flow speed of the order of 1 m / s to 1% statistical uncertainty in a dilute gas , on the order of @xmath7 independent samples are needed @xcite . in a recent paper , baker and hadjiconstantinou have shown @xcite that this rather severe limitation can be overcome with a form of variance reduction achieved by simulating only the deviation from equilibrium . by adopting this approach , it is possible to construct monte carlo simulation methods that can capture arbitrarily small deviations from equilibrium at a computational cost that is independent of the magnitude of this deviation . this is in sharp contrast to regular monte carlo methods , such as dsmc , whose computational cost for the same signal - to - noise ratio increases _ sharply _ @xcite as the deviation from equilibrium decreases . the work in refs @xcite focused on the boltzmann equation for hard spheres and the associated hard - sphere collision operator . the complexity associated with this collision operator , as well as others in related fields , has prompted scientists to search for simplified models ; one particularly popular model is the relaxation - time approximation @xcite @xmath8 _ { \textrm{coll}}}}=-\frac{1}{\tau } \left(f - f^{loc}\right)\ ] ] where @xmath9 is the _ local equilibrium _ distribution function and @xmath10 is a relaxation time . despite the approximation involved , this collision model has enjoyed widespread application in a variety of disciplines concerned with transport processes @xcite . in response to this widespread use , in the present paper , we present a variance - reduced particle method for simulating the boltzmann equation under the relaxation - time approximation . to focus the discussion , we specialize our treatment to the dilute gas case ; however , we hope that this exposition can serve as a prototype for development of similar techniques in all fields where the relaxation - time approximation is applicable . within the rarefied gas dynamics literature , the relaxation - time approximation is known as the bgk model @xcite . in the interest of simplicity , in the present paper we assume @xmath11 and that no external forces are present . the first assumption can be easily relaxed , as discussed below . external fields also require relatively straightforward modifications to the algorithm presented below . as discussed in previous work @xcite , a variance - reduced formulation is obtained by simulating only the deviation @xmath12 from an _ arbitrary _ , but judiciously chosen , underlying equilibrium distribution @xmath13 . in other words , computational particles represent the deviation from equilibrium and , as a result , they may be positive or negative , depending on the sign of the deviation from equilibrium at the location in phase space where they reside . as in other particle schemes @xcite , in the interest of computational efficiency , each _ computational _ deviational particle represents an _ effective number _ @xmath14 of physical deviational particles . a dilute gas in equilibrium is described by a maxwell - boltzmann distribution , leading to a local equilibrium distribution @xmath15 that is parametrized by the local number density @xmath16 , the local flow velocity @xmath17 , and the most probable speed @xmath18 based on local temperature @xmath19 . here , @xmath20 is boltzmann s constant and @xmath21 is the molecular mass . in the work that follows , the underlying equilibrium distribution ( @xmath13 ) will be identified with absolute equilibrium @xmath22 where @xmath23 is a reference ( equilibrium ) number density and @xmath24 is the most probable molecular speed based on the reference temperature @xmath25 . this choice provides a reasonable balance between generality , computational efficiency and simplicity . other choices are of course possible and , depending on the problem , perhaps more efficient . however , care needs to be taken if a spatially varying or time dependent underlying equilibrium distribution is chosen since this results in a more complex algorithm @xcite . particle methods typically solve the boltzmann equation by applying a splitting scheme , in which molecular motion is simulated as a series of collisionless advection and collision steps of length @xmath26 . in such a scheme , the collisionless advection step integrates @xmath27 by simply advecting particles for a timestep @xmath26 , while the collision step integrates @xmath28 _ { \textrm{coll}}}}\label{collision}\ ] ] by changing the distribution by an amount @xmath2 _ { \textrm{coll}}}}({\bf r},{\bf c},t)\delta t$ ] . spatial discretization is introduced by treating collisions as spatially homogeneous within ( small ) computational cells of volume @xmath29 . our approach retains this basic structure ; the particular form of these steps can be summarized as follows . _ advection step : _ it can be easily verified that when the underlying equilibrium distribution is not a function of space or time , as is the case here , the advection step for deviational particles is identical to that of physical particles [ i.e. @xmath30 is also governed by equation ( [ advection ] ) during the advection step ] . boundary condition implementation , however , differs somewhat because the mass flux to boundaries is now split into a deviational contribution and an equilibrium contribution . a more extensive discussion , as well as algorithmic details can be found in @xcite . _ collision step : _ the variance - reduced form of ( [ collision ] ) can be written as @xmath8 _ { \textrm{coll}}}}= \frac{1}{\tau } \left(f^{loc}-f\right)-\frac{1}{\tau } f^d \label{start}\ ] ] _ within each computational cell _ we integrate equation ( [ start ] ) using a two - part process . this integration requires local ( cell ) values of various quantities , denoted here by hats , which are updated every timestep by sampling the instantaneous state of the gas . in the first part we remove a random sample of particles by deleting particles with probability @xmath31 to satisfy @xmath32 in our implementation , this is achieved through an acceptance - rejection process which can also treat the case @xmath33 . in the second part , we create a set of positive and negative particles ( using an acceptance - rejection process ) to satisfy @xmath34\ , \delta t \label{add}\ ] ] this step can be achieved by the following procedure . let @xmath35 be a ( positive ) value such that @xmath36 is negligible for @xmath37 , where @xmath38 is an @xmath39-norm . furthermore , let @xmath40 bound @xmath41 from above . then , repeat @xmath42 times : 1 . generate uniformly distributed , random velocity vectors @xmath43 with @xmath44 . 2 . if @xmath45 , create a particle with velocity @xmath46 , at a randomly chosen position within the cell and sign @xmath47 $ ] . here , @xmath48 is a random number uniformly distributed on [ 0,1 ] . to find @xmath49 we note that the number of particles ( of all velocities and signs ) that should be generated in a cell to obtain the proper change in the distribution function is @xmath50 where @xmath51 is the cell volume . the ( expected ) total number of particles ultimately generated by the above algorithm is @xmath52 by equating the two expressions we obtain @xmath53 . we have verified the above algorithm using a variety of test cases ; some representative results are presented below . figure [ heat ] shows a comparison between numerical solution of the bgk model of the boltzmann equation @xcite and our simulation results for the heat flux , @xmath54 , between two parallel , infinite , fully - accommodating plates at slightly different temperatures ( @xmath25 and @xmath55 ) and a distance @xmath56 apart . the figure compares the heat flux normalized by the free - molecular ( ballistic ) value @xmath57 as a function of a knudsen number @xcite @xmath58 , where @xmath59 is the equilibrium gas pressure . the agreement is excellent . the simulations used approximately 50,000 particles yielding a relative statistical uncertainty of less than 0.5% . these simulations were performed at @xmath60k , although as shown below , the cost is expected to be independent of the magnitude of @xmath61 in the limit of small deviation from equilibrium . we also performed dsmc simulations of the bgk model using @xmath62k and otherwise identical discretization and sampling parameters ; @xmath62k was chosen as a compromise between best performance and a deviation from equilibrium that is small enough for the linearized conditions , and thus the benchmark results of @xcite , to be valid . figure [ poi ] shows a comparison between a numerical solution of the linearized bgk model of the boltzmann equation @xcite and our simulation results for pressure - driven flow ( for small pressure gradients ) . under linear conditions , pressure - driven flow can be described @xcite by @xmath63 _ { \textrm{coll}}}}- \kappa c_z f\ ] ] where @xmath64 is the normalized pressure gradient ( here assumed to be in the @xmath65direction ) , and @xmath66 is the channel transverse direction . for @xmath67 , the term @xmath68 can be included in our formulation as a source of @xmath69 positive and an equal number of negative deviational physical . ] particles per unit volume drawn from the distribution @xmath70 for @xmath71 and @xmath72 , respectively . figure [ poi ] shows the normalized flowrate @xmath73 as a function of @xmath74 , where @xmath75 is the gas density and @xmath76 is the average flow velocity ( averaged across the channel width ) . excellent agreement is observed . as stated above and shown in @xcite , this class of deviational methods exhibit statistical uncertainties that scale with the local deviation from equilibrium thus allowing the simulation of arbitrarily low deviations from equilibrium at a cost that is independent of this deviation . here we demonstrate this feature by studying the statistical uncertainty of the temperature in a problem involving heat transfer . specifically , figure [ fluct ] shows the relative statistical uncertainty in the temperature ( @xmath77 ) as a function of the normalized wall temperature difference @xmath78 in the heat transfer problem discussed above , for @xmath79 and @xmath80k ; in evaluating @xmath77 , the characteristic value for temperature was taken to be the difference @xmath81 . the standard deviation is measured from two computational cells in the middle of the computational domain , each containing approximately 950 particles . the figure shows that , for small @xmath81 , the relative statistical uncertainty remains independent of this quantity in sharp contrast to `` non - deviational '' methods . moreover , the variance reduction achieved is such that significant computational savings are expected for @xmath82 . the algorithm described above imposes no restrictions on the magnitude of @xmath30 , although it is expected that the deviational approach will be significantly more efficient than traditional approaches when @xmath30 is small . if @xmath30 is sufficiently small for linearization to be appropriate , under some conditions , significant gains in computational efficiency can be achieved by taking the following into consideration . under linear conditions , for the present model , we can write @xmath83 \label{lin}\ ] ] where @xmath84 and @xmath85 . this representation can be very useful for improving the computational efficiency of update ( [ add ] ) . for example , for isothermal constant density flows , particles can be generated from a combination of a normal distribution and analytic inversion of the cumulative distribution function , which is significantly more efficient than acceptance - rejection . alternatively , ( [ lin ] ) provides a means of obtaining tight bounds for @xmath86 and thus reducing the number of rejections if the acceptance - rejection route is followed . we have presented an efficient variance - reduced particle method for solving the boltzmann equation in the relaxation - time approximation . the method combines simplicity with a number of desirable properties associated with particle methods , such as robust capture of traveling discontinuities in the distribution function and efficient collision operator evaluation using importance sampling @xcite , without the high relative statistical uncertainty associated with traditional particle methods in low - signal problems . in particular , the method presented here can capture arbitrarily small deviations from equilibrium for constant computational cost . more sophisticated techniques with spatially variable underlying equilibrium distribution @xcite are expected to increase computational efficiency by reducing the number of deviational particles required to describe the local state of the gas . one such technique is described in @xcite .

most elementary treatments of reflecting surfaces restrict their attention to the spherical case . in this standard case , and assuming the paraxial approximation ( all angles are small and all rays are close to the optical axis ) , the resulting equation relating the _ axial _ object and image positions and the radius of curvature of the reflecting spherical surface is @xmath0 where all parameters are one dimensional coordinates which locate the image ( @xmath1 ) , object ( @xmath2 ) , and center of curvature ( @xmath3 ) with respect to the vertex ( the intersection of the surface with the optical axis ) @xcite . a convention is typically assumed in which light rays travel from left to right in all figures . the origin of the one dimensional coordinate system employed coincides with the vertex , and locations to the right ( left ) of the vertex are positive ( negative ) . [ ptbh ] the paraxial approximation is equivalent to a first order approximation in the height ( @xmath4 ) of the incidence point ( on the surface ) of a reflecting ray . to higher order , it is found that @xmath5 consequently , spherical mirrors are aberrant at higher order since the image location is not independent of the height , @xmath4 . this paper represents a more general treatment of a mirror than is typically found in the literature . the reflecting surface is assumed to be a conicoid , the surface of revolution generated by a conic . equation ( [ gauss ] ) is then derived as the special case of a spherical surface and to first order in @xmath4 . special cases are analyzed as a function of asphericity , or departure from the spherical , of the reflecting surface . the parabolic surface is shown to be uniquely special in that @xmath6 to all orders for objects at infinity ( @xmath7 ) . [ ptbh ] in fig . [ fig02 ] , a conicoid reflecting surface is depicted with equation @xmath8 where @xmath3 is the radius of curvature of the surface at the vertex , and @xmath9 is the shape factor and is related to the standard eccentricity ( see appendix i or , for example , @xcite ) . for a sphere , @xmath10 , whereas for a paraboloid @xmath11 . note that the @xmath12 coordinate system is set on its side so that @xmath13 coincides with the negative direction on the optical axis ( o.a . ) as defined in fig . [ fig01 ] of the introduction . consequently , the radius of curvature , @xmath3 , at the origin for any concave conicoid ( _ i.e. _ , opening to the left ) will be considered negative . in fig . [ fig02 ] , a representative case is depicted with @xmath14 , the location of the object , and @xmath15 , the location of the image . the figure displays an incident ray , @xmath16 , emanating from the object at @xmath17 and a reflected ray , @xmath18 , passing through the image at @xmath19 . from the figure , the line @xmath16 has equation in the @xmath12-plane @xmath20 similarly , the line @xmath18 has equation @xmath21 consequently , @xmath22 where @xmath23 is the point of reflection , @xmath24 , on the surface . from the figure , it follows that @xmath25 where @xmath26 and @xmath27 therefore @xmath28 substituting for the tangents from above yields @xmath29 -\left ( \frac{1}{uv}\right ) \frac{2y_{0}\left [ 1 + 2\left ( 1-\sigma\right ) ay_{0}\right ] } { \left ( 1 - 2\sigma ay_{0}\right ) ^{2}}=-\frac{4a}{1 - 2\sigma ay_{0 } } \label{eq09a}\]]@xmath30 -\left ( \frac{1}{uv}\right ) & 2y_{0}\left [ 1 + 2\left ( 1-\sigma\right ) ay_{0}\right ] \hspace{0.45in}\nonumber\\ & \hspace{0.6in}=-4a\left ( 1 - 2\sigma ay_{0}\right ) . \label{eq09b}\ ] ] now let @xmath31 be the height of the incidence point @xmath24 for a particular ray from the source object at @xmath17 , then in the paraxial approximation ( @xmath32 ) , @xmath33 equation ( [ eq09b ] ) can then be rewritten to fourth order as @xmath34 h^{2}\nonumber\\ & \hspace{0.5in}+\left [ 4\sigma a^{4}\left ( \frac{1}{v}+\frac{1}{u}\right ) + 2\left ( 3\sigma+2\right ) a^{3}\left ( \frac{1}{uv}\right ) -24\sigma ^{2}a^{5}\right ] h^{4}. \label{eq11}\ ] ] note that there is aberration in imaging a finite axial point since there is no confluence in the rays from @xmath17 . also note that there is no fixed shape factor @xmath35 that eliminates aberration to second order and higher . to first order , all conicoids obey the same relation @xmath36 which coincides , of course , with the gaussian ( first order approximation ) equation for a spherical mirror with focal length @xmath37 . from eq . ( [ eq09b ] ) it follows that for objects at infinity ( @xmath38 ) and a parabolic shape ( @xmath11 ) , the image forms at @xmath39 regardless of the height of the incidence ray , therefore , there is no aberration for such imaging . it is desirable to know to what extend the results of the previous section are pathological to conicoids . with this in mind consider the most general axi - symmetric surface of revolution ( about the y - axis ) as a reflector @xmath40 equation ( [ eq08b ] ) is easily generalized to @xmath41 where @xmath42 . in general , for a given axial object location , the image location ( or intersection point of the reflected ray with the optical axis ) is a function of the object location and the reflection point @xmath43 a reflecting surface is free of aberration if @xmath44 equation ( [ eq14 ] ) can be implicitly differentiated to yield @xmath45 } { y^{\prime}}\right\ } _ { 2}. \label{eq17}\ ] ] the aberration - free surface must satisfy @xmath46 . however , it is evident from eq . ( [ eq17 ] ) that this can not be obtained trivially . for the special case in which the object is at infinity though , the aberration - free surface must only satisfy @xmath47 , and this leads to a defining equation for the surface @xmath48 this is a linear differential equation whose general solution can most easily be found by the reduction in order method to give the general solution @xmath49 . this further reduces to the particular solution of eq . ( [ eq32 ] ) , found by another method , after the two needed boundary conditions are invoked . most elementary treatments of mirrors lack a discussion of the first order equation relating object and image locations in the case of arbitrary mirror shape . the default reflecting surface is always the spherical one . in fact , a simple analysis yields that all axi - symmetric , conic , reflecting surfaces of revolution ( conicoids ) in the first order , paraxial approximation satisfy the same ( gaussian ) equation @xmath50 where @xmath3 is the radius of curvature of the surface at its vertex . aberrations enter at second order and can not be eliminated for finite object locations by any fixed shape . however , for objects at infinity , or specifically , for incoming light parallel to the optical axis , there is a unique reflecting shape that is free of aberration the parabolic one . starting with the general form of a conic section in cartesian coordinates , @xmath51 assume @xmath52-reflection symmetry , so that the equation reduces to @xmath53 next the curve is shifted so the vertex coincides with the origin , @xmath54 with @xmath55 . if the form is further constrained so that the curve lies in @xmath56 half - plane , then the positive root is required , and this yields @xmath57 or in terms of new parameters @xmath58 where @xmath59 . the signed curvature of this curve at the origin is @xmath60 given the optics conventions adopted here as described in the introduction and depicted in figures 1 and 2 , the radius , @xmath3 , of the osculating circle at the origin for a concave conicoid is considered negative . the radius of curvature is therefore related to the parameter @xmath61 @xmath62 and @xmath63 from eq . ( [ eq22 ] ) it follows that @xmath11 corresponds to a parabola . by putting eq . ( [ eq22 ] ) into canonical form @xmath64 it becomes clear that @xmath10 corresponds to a circle with radius @xmath65 . the equation describes a hyperbola when @xmath66 . for @xmath67 , the equation describes an oblate ellipse ( with respect to the y - axis ) , and it describes a prolate ellipse for @xmath68 . in fact , from eq . ( [ eq26 ] ) , the shape factor , @xmath35 , can be related to the standard eccentricity @xmath69 an alternate solution ( to that of section iii ) is presented for the exact conicoid shape in the limit that the object distance approaches infinity ( @xmath70 ) . applying the law of reflection ( based on fermat s principle of stationary optical path ) to a parallel ( to the optical axis ) ray ( from a distant object ) incident on an unknown conicoid surface , results in the optical path displayed in fig . [ fig03 ] . applying eq . ( [ eq04b ] ) to the present special case , it follows that @xmath71 if the notation is changed and the @xmath72 variable is shifted for convenience , @xmath73 , then eq . ( [ eq29 ] ) can be reduced to either a homogeneous nonlinear ordinary differential equation ( ode ) of the form @xmath74 or to a nonlinear clairaut ode @xcite of the form @xmath75 recall that clairaut solutions are of the form @xmath76 and have envelopes that are also exact singularity solutions . solving eq . ( [ eq30 ] ) or ( [ eq31 ] ) yields the final form for the unknown conicoid ( and shifting back @xmath77 ) @xmath78 which is the equation for the ( meridional ) cross section of a paraboloid with focus at @xmath79 . it is also of note that eq . ( [ eq30 ] ) with @xmath80 can be used to model various and sundry airplane , ship , and predator / prey pursuit problems @xcite . foreman , `` the conic sections revisited , '' am . * 59 * , 1002 - 1005 ( 1991 ) ; d.m . watson , _ astronomy 203/403 : astronomical instruments and techniques on - line lecture , _ university of rochester ( 1999 ) , * http://www.pas.rochester.edu/dmw/ast203/lectures.htm . *

the first order equation relating object and image location for a mirror of arbitrary conic - sectional shape is derived . it is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources .

physical models often involve phenomenological parameters or auxiliary fields characterizing the background spacetime or the background media . in most cases , dynamics of the model depend smoothly ( continuously and differentiably ) on the values of the background parameter . a non - smooth functional dependence is a rather rare phenomenon , but if it exists , it usually represents a keystone issue of the model . the examples of such non - smooth behavior are well known in solid state physics as phase transitions at critical points . another similar issue is the scalar higgs model of spontaneous symmetry breaking . in this paper , we present a simple phenomenological model of an electromagnetic medium that allows wave propagation only for a sufficiently big value of the medium parameter . for zero values of the parameter , our medium is the ordinary sr ( or even gr ) vacuum with the standard dispersion relation @xmath0 . however even infinitesimally small variations of the parameter modify the dispersion relation in such a way that it does not have real solutions , i.e. , the medium becomes to be completely opaque . for higher values of the parameter , the dispersion relation is modified once more and once again it has real solutions . it is well known that the dispersion relation can be treated as an effective metric in the phase space . in our model , the vacuum lorentz metric is spontaneously transformed into the euclidean one and returns to be lorentzian for a sufficiently big value of the parameter . we consider the standard electromagnetic system of two antisymmetric fields @xmath1 and @xmath2 that obey the vacuum maxwell system @xmath3}=0\,,\qquad h^{ij}{}_{,j}=0\,.\ ] ] the fields are assumed to be related by the local linear constitutive relation , @xcite,@xcite , @xmath4 due to this definition , the constitutive tensor obeys the symmetries @xmath5 the electromagnetic model ( [ max ] ) with the local linear response ( [ cons ] ) is intensively studied recently , see @xcite , @xcite , @xcite , and especially in @xcite . by using the young diagram technique , a fourth rank tensor with the symmetries ( [ sym ] ) is uniquely irreducible decomposed into the sum of three independent pieces . @xmath6 the first term here is the principal part . in the simplest pure maxwell case it is expressed by the metric tensor of gr @xmath7 in the flat minkowski spacetime with the metric @xmath8 , it reads @xmath9 in quantum field description , this term is related to the photon . the third term in ( [ decomp ] ) is completely skew symmetric . consequently , it can be written as @xmath10 the pseudo - scalar @xmath11 represents the axion copartner of the photon . it influences the wave propagation such that birefringence occurs @xcite , @xcite . in fact , this effect is absent in the geometric optics description and corresponds to the higher order approximation , @xcite , @xcite , @xcite . we turn now to the second part of ( [ decomp ] ) , that is expressed as @xmath12 this tensor has 15 independent components , so it may be represented by a traceless matrix @xcite , @xcite . this matrix reads @xmath13 the traceless condition @xmath14 follows straightforwardly from ( [ skewon - matr ] ) . in order to describe the influence of the skewon on the wave propagation , it is convenient to introduce a covector @xmath15 consider a medium described by a vacuum principal part ( [ princ - part - m ] ) and a generic skewon . the dispersion relation for such a medium takes the form , @xcite , @xcite , @xmath16 here the scalar product @xmath17 and the squares of the covectors @xmath18 and @xmath19 are calculated by the use of the metric tensor . it can be easily checked that eq.([disp ] ) is invariant under the gauge transformation @xmath20 with an arbitrary real parameter @xmath21 . this parameter can even be an arbitrary function of @xmath22 and of the medium parameters @xmath23 . with this gauge freedom , we can apply the lorenz - type gauge condition @xmath24 and obtain the dispersion relation in an even more simple form @xmath25 this expression yields a characteristic fact @xcite : the solutions @xmath26 of the dispersion relation , if they exist , are non - timelike , that is , spacelike or null , @xmath27 we will proceed now with the form ( [ disp ] ) and with the skewon covector expressed as in ( [ skewon - cov ] ) . we can rewrite the dispersion relation as @xmath28 consequently , the real solutions exist only if @xmath29 our crucial observation that the first term here is quartic in the skewon parameters @xmath30 while the second term is only quadratic . under these circumstances , the first term can be small for for sufficiently small skewon parameters and the inequality ( [ ineq ] ) breaks down . for higher values , the first term becomes to be essential and the inequality is reinstated . we now present a model where this possibility is realized , indeed . consider a symmetric traceless matrix with two nonzero entries @xmath31 we denote the components of the wave covector as @xmath32 . the skewon covector has two nonzero components @xmath33 consequently , @xmath34 hence the inequality ( [ ineq ] ) takes the form @xmath35 observe that for every choice of the wave covector this expression is of the form @xmath36 with positive coefficients @xmath37 . quite surprisingly , this functional expression repeats the well known curve of the higgs potential . .,title="fig:",width=245 ] the dispersion relation as it is given in eq.([disp ] ) reads @xmath38 we rewrite it as @xmath39 consequently : * for @xmath40 , we return to the unmodified light cone @xmath41 . * for @xmath42 , except for the trivial solution @xmath43 , there are no real solutions of eq([disp2 ] ) at all . * for @xmath44 , there are two real solutions : @xmath45 for the numerical images of these algebraic cones , see fig . 3 and fig . 4 . ) with @xmath46 and @xmath47 signs respectively . the parameter @xmath48 . @xmath49 is directed as @xmath50-axis , @xmath51 are directed as @xmath52 and @xmath53 axes respectively . @xmath54 . , title="fig:",width=170 ] ) with @xmath46 and @xmath47 signs respectively . the parameter @xmath48 . @xmath49 is directed as @xmath50-axis , @xmath51 are directed as @xmath52 and @xmath53 axes respectively . @xmath54 . , title="fig:",width=170 ] ) with @xmath46 and @xmath47 signs respectively . the parameter @xmath48 . @xmath49 is directed as @xmath50-axis , @xmath55 are directed as @xmath52 and @xmath53 axes , respectively . @xmath56 . , title="fig:",width=170 ] ) with @xmath46 and @xmath47 signs respectively . the parameter @xmath48 . @xmath49 is directed as @xmath50-axis , @xmath55 are directed as @xmath52 and @xmath53 axes , respectively . , title="fig:",width=170 ] in both cones , the skewon interchanges the time axis with the spatial @xmath52-axis . these 3-dimensional cones are tangential to one another when the discriminant in eq . ( [ sym-15 ] ) is zero . it gives a 2-dimensional cone @xmath57 the expressions in eq.([sym-15 ] ) can be treated as finlsler metric elements . due to the fact that they have non - compact 2d - sections as in fig . 2 and compact 2d - sections as in fig . 3 , the corresponding finsler metric tensors are of the lorentz signature type . we construct a model of the electromagnetic vacuum with a skewon field that has the following features : * there is a gap for values of the parameters near zero , where the wave propagation is forbidden . * birefringence of the light propagation . * full interchange between time and spatial direction . * a continuous 2-dimensional variety of optic axes instead of distinct optic axes appearing in anisotropic optics . * the light cones are non - convex . electromagnetic media with an additional skewon field provide a rich class of models of wave propagation with rather unusual features , see @xcite , @xcite . recently the observational restrictions on such models were discussed in @xcite and @xcite . in this paper , we show that higgs - type potential can appear in a simple electromagnetic model by a minimal modification of the vacuum constitutive relation . my acknowledgments to f. hehl ( cologne / columbia , mo ) , yu . obukhov ( cologne / moscow ) , v. perlick ( zarm , bremen ) , c. lmmerzahl ( zarm , bremen ) , and y. friedman ( jct , jerusalem ) for valuable discussions . i acknowledge the gif grant no . 1078 - 107.14/2009 for financial support . y. n. obukhov , t. fukui and g. f. rubilar , phys . rev . d * 62 * , 044050 ( 2000 ) . y. n. obukhov and g. f. rubilar , phys . d * 66 * , 024042 ( 2002 ) . c. lmmerzahl and f. w. hehl , phys . d * 70 * ( 2004 ) 105022 . ni , phys . lett . a * 378 * , 1217 ( 2014 ) . s. di serego alighieri , w .- t . ni and w .- p . pan , `` new constraints on cosmic polarization rotation from b - mode polarization in cosmic microwave background , '' arxiv:1404.1701 .

in the framework of standard electrodynamics with linear local response , we construct a model that provides spontaneously broken transparency . the functional dependence of the medium parameter turns out to be of the higgs type .

the interaction of intense laser pulses with overdense plasmas has attracted much interest for the fast ignitor concept in inertial fusion energy @xcite . the interaction of ultrashort intense laser pulses with thin solid targets have also been of great interest for the application to high energy ion sources @xcite . ultraintense irradiation experiments using an infrared subpicosecond laser , e.g. , nd : glass ( @xmath3 1,053 nm ) or ti : sapphire ( @xmath3800 nm ) lasers , whose powers and focused intensities exceed 100 tw and @xmath4 w/@xmath5 , are possible using chirped pulse amplification techniques @xcite . in these experiments , the classical normalized momentum of electrons @xmath6 , where @xmath7 is the electron mass , @xmath8 is the speed of light , @xmath0 is the laser intensity in w/@xmath5 , and @xmath9 is the wavelength in @xmath10 m . on the other hand , a krf laser ( @xmath3 248 nm ) has an advantage as the fast ignitor in that the critical density is close to the core , and hot electron energies are suitable since the critical density of the krf laser is ten times greater than that of an infrared laser @xcite . the peak intensities of krf laser systems were only the order of @xmath11 w/@xmath5 , namely @xmath12 @xcite . therefore , the dependence of the laser plasma interactions on the laser wavelength was not investigated in @xmath13 . recently , the laser absorption and hot electron generation have been studied by the high intensity krf laser system of which focused intensity is greater than @xmath14 w/@xmath5 @xcite . however , the production of hot electrons by the high intensity krf laser has not been fully understood yet . namely , it has been not clear that the effects of laser wavelength on hot electrons produced by ultrashort intense laser pulse on solid - density targets . the absorption , electron energy spectrum , and hot electron temperature have usually been investigated and scaled using the parameters @xmath1 , @xmath15 , and @xmath16 @xcite , where @xmath17 , @xmath18 , and @xmath19 are the electron density , critical density , and density scale length , respectively . critical density absorption of the laser light converts laser energy into hot electrons having a suprathermal temperature @xmath20 approximately proportional to @xmath21 for @xmath22 , and @xmath23mc^2 $ ] at moderate densities @xcite , where @xmath24 kev , @xmath7 is an electron rest mass . the scaling of the hot electron temperature has been supported by experiments of nd : glass and ti : sapphire lasers @xcite . on the other hand , the results of one - dimensional simulation for normal incidence in the density region @xmath25 and the normalized intensity @xmath26 have shown that @xmath27 mc^2 $ ] , where @xmath28 is the electromagnetic fields at the surface of the overdense plasma , @xmath29 and @xmath30 , which depend weakly on @xmath1 and @xmath15 @xcite . @xmath31 is weakly depend on the angle of incidence , absorption rate , and @xmath32@xcite . the hot electron temperature is scaled by the amplitude of electromagnetic fields at the plasma surface rather than that in vacuum ; namely , the hot electron temperature is slightly dependent on the wavelength . in addition , at the interaction of intense laser pulses with solid density plasma which has a sharp density gradient the hot electron temperature is scaled by @xmath33 rather than @xmath1 @xcite . in the present paper , we study the absorption of ultrashort intense laser pulses on overdense plasmas for different laser wavelengths ( @xmath2 = 0.25 , 0.5 , and 1 @xmath10 m ) using a particle - in - cell ( pic ) simulation . in order to investigate hot electron generation for oblique incidence , we use the relativistic 1 and @xmath34 dimensional pic simulation with the boost frame moving with @xmath35 parallel to the target surface , where @xmath8 and @xmath36 are the speed of light and an angle of incidence@xcite . in the simulation , the target is the fully ionized plastic and the electron density @xmath37 . the density correspond to @xmath38 , @xmath39 , and @xmath40 for @xmath3 0.25 , 0.5 , and @xmath41 m , respectively . the density profile has a sharp density gradient , @xmath42 for @xmath43 and @xmath44 for @xmath45 . in order to clarify the boundary effect , ions are fixed , namely , the boundary does not move all the time . the laser pulse starts at @xmath46 and propagates towards @xmath47 . the laser intensity rises in 5 fs and remains constant after that . the irradiated intensity @xmath48 w/@xmath5 and the angle of incidence @xmath49 and @xmath50 ( p - polarized ) , respectively . @xmath51 2.3 , 9.2 , and 36 for @xmath3 0.25 , 0.5 , and 1.0 @xmath10 m , respectively . however , @xmath52 for all wavelength . normalized electron energy distributions after 50 fs are shown in fig.1(a ) and 1(b ) for @xmath49 and @xmath50 , respectively . the hot electron temperatures are 140 and 340 kev for @xmath49 and @xmath50 , respectively . the hot electron temperatures does not depend on the laser wavelength . the result is well agreement with that of a simple sharp boundary theory . on the other hand , the absorption depends on the laser wavelength , @xmath53 0.9 - 1.8% , 2.2 - 3.0% , and 3.6 - 4.3% and @xmath54 2.6 - 4.1% , 5.3 - 6.7% , and 7.8 - 9.0% for @xmath3 1.0 , 0.5 , and 0.25 @xmath10 m , respectively . the effects of laser wavelength on hot electrons produced by ultrashort intense laser pulse on solid - density targets are studied by the use of a pic simulation . as a result , the dependence to the wavelength of hot electron temperature strongly depend on the boundary condition , even in the one dimensional case , namely , all are not determined only by @xmath1 . the density profiles of both preformed plasma @xcite and multi - dimensional effects such as surface deformation @xcite are very important in the actual experiments . 99 m. tabak _ et al . _ , phys . plasmas * 1 * , 1626 ( 1994 ) ; r. kodama _ et al . _ , nature * 412 * , 798 ( 2001 ) . e.takahashi _ et al . _ , _ proceedings of the third international conference on inertial fusion sciences and applications ( ifsa2003 ) _ , editors : b. a. hammel d. d. meyerhofer j. meyer - ter - vehn h. azechi , p.406 ( american nuclear society , inc . , 2004 ) . _ , _ proc . of the seventh international symposium of the graduate university for advanced studies on science of super - strong field interactions , hayama , japan , 2002 _ , editors : k. nakajima and m. deguchi , p.290 ( american institute of physics , 2002 )

hot electron temperatures and electron energy spectra in the course of interaction between intense laser pulse and overdense plasmas are reexamined from a viewpoint of the difference in laser wavelength . the hot electron temperature measured by a particle - in - cell simulation is scaled by @xmath0 rather than @xmath1 at the interaction with overdense plasmas with fixed ions , where @xmath0 and @xmath2 are the laser intensity and wavelength , respectively .

all authors acknowledge funding from grants erc magreps 267 862 , fp7 grant infernos 308850 , icrea academia 2013 and fis2013 - 47796- p. all data used in this study are included in the main text and in the supplementary materials . j.c .- s . and a.a . equally contributed to this work . [ sec : author ] * ecori binding to dna . * * ( a ) * unfolding / refolding force - distance curves of a dna hairpin in the absence ( magenta / black ) and presence ( blue / cyan ) of ecori protein . the bound ( @xmath9 ) and unfolded ( @xmath10 ) states are discriminated at high force by the presence of two distinct force branches . * ( b ) * cyclic pulling curves classified according to their initial ( blue dot ) and final state ( cyan dot ) that start and end at a high force ( @xmath221 pn ) . work equals the enclosed area between the two curves and is shown in dark / light gray for positive / negative values . * ( c ) * paths of a non - equilibrium cyclic protocol connecting different initial and final states . * ( d ) * partial work distributions of @xmath13 ( green ) and @xmath14 ( magenta ) transitions at different ecori concentrations . * ( e ) * binding energy of ecori ( blue ) and fit to the law of mass action ( red line ) at ( 130 mm @xmath51 , @xmath52c , @xmath53 m ) . * ( f ) * binding energy of ecori at varying [ nacl ] ( 1 nm ecori ) . error bars were obtained from bootstrap using 1000 re - samplings of size n ( n is total number of pulls for each condition shown in tables s1 and s3 ) . * oligo binding to dna . * * ( a ) * scheme of native ( @xmath8 ) , unfolded ( @xmath10 ) and oligo bound ( @xmath9 ) states . * ( b ) * cyclic pulling curves that start and end at low forces ( @xmath26 pn ) classified according to their initial ( blue dot ) and final state ( cyan dot ) . * ( c ) * partial work distributions of @xmath54 ( green ) and @xmath55 ( magenta ) transitions . * ( d ) * binding energy of the 10-base oligo ( blue ) and fit to the law of mass action ( red line ) . the value obtained from hopping equilibrium experiments at [ oligo]=400 nm ( see s1.7 in @xcite ) is shown in cyan . ( inset ) contribution of the ratio @xmath56 to the binding energy . error bars were obtained from bootstrap as described in fig . 1 . * binding specificity , allostery and kinetic stabilization of misfolded states for the peptide echinomycin . * * ( a ) * first rupture force distribution of hairpins sp ( red ) and nsp ( blue ) in the absence ( light ) and presence ( dark ) of echinomycin . * ( b ) * binding energy of echinomycin to a specific ( red ) and nonspecific ( blue ) site , and fit to the law of mass action . * ( c ) * hairpins c and nc contain two specific binding sites ( red boxes ) placed contiguously or separated by 2-bp respectively . binding energy per ligand when one ( blue ) or two ligands ( green ) are bound to hairpins nc or c ( magenta ) ( [ echninomycin]=3 @xmath45 m ) . gaussian distributions are reconstructed from mean and variance of measurements . the wider distribution for the single bound state in hairpin nc ( blue ) is due to the lower number of paths reaching this state at high ligand concentration , increasing measurement error . * ( d ) * pulling cycle of hairpin m in the presence of echinomycin . the unfolding curve ( blue ) shows two force rips at @xmath57 pn corresponding to the unbinding of two ligands bound to specific sites . in the refolding curve ( cyan ) , the hairpin does not fold back to the native state , and misfolds into a kinetically stabilized configuration of longer molecular extension ( @xmath58 of refolding curves at [ echninomycin]=10 @xmath45 m ) . error bars were obtained from bootstrap as described in fig . 1 . the ftlb is derived following the same steps as in @xcite . consider a system with a fluctuating number of particles @xmath8 , which correspond to the ligand molecules . the system evolves under an experimental protocol @xmath59 , where @xmath6 denotes the control parameter and in our case corresponds to the position of the optical trap relative to the pipette . we discretize in time the protocol as @xmath60 , where @xmath61 ( @xmath62 ) denotes the value of @xmath6 at the time of the protocol @xmath63 ( being @xmath64 the time discretization unit ) , and @xmath65 denotes the duration of the protocol . along the protocol @xmath59 the system follows a given trajectory @xmath66 , where a sequence of configurations @xmath67 are sampled . the trajectory can be discretized as @xmath68 . each configuration @xmath69 ( @xmath70 ) is characterized by the number of particles , @xmath71 , and the degrees of freedom of each particle . the equilibrium probability to be in a given configuration @xmath69 at @xmath6 can be written , according to the grand - canonical ensemble , as : @xmath72 where @xmath73 ( being @xmath74 the boltzmann constant and @xmath5 the absolute temperature ) , @xmath75 is the fugacity of the system ( equal to @xmath76 , being @xmath45 the chemical potential of the ligand molecules ) , @xmath77 is the grand canonical partition function , and @xmath78 is the energy of the configuration @xmath69 at @xmath6 . we suppose that the dynamics of the system satisfy the following detailed balance condition : @xmath79 therefore , the probability of the system to follow a given trajectory @xmath66 ( without imposing any initial and final configuration ) , and the probability to follow its time reversed @xmath80 is : [ eq : 1 ] @xmath81 where @xmath82 . we assume that in the forward protocol @xmath59 the system starts in partial equilibrium at @xmath83 , while in the reversed protocol @xmath84 it starts in partial equilibrium at @xmath85 ( and @xmath86 ) . the partial equilibrium probability density function of a given configuration @xmath87 , where @xmath88 is a subset of configurations accessible by the system , can be written as @xcite : suppose that the system starts in non - equilibrium conditions . particularly , the system starts in partial equilibrium at the kinetic state @xmath92 in the forward trajectory and at at the kinetic state @xmath93 in the reversed one . a kinetic state is a partially equilibrated region of configurational space , meaning that during a finite amount of time the system is confined and thermalized within that region . this is mathematically described by a boltzmann - gibbs distribution restricted to configurations contained in that region . then : experiments are performed with a highly stable miniaturized dual - beam optical tweezers described in previous studies @xcite . the dna hairpins are tethered between two beads by using short dsdna handles ( 29-bp ) that are differentially end - labelled with biotin and digoxigenin to attach each handle to a different bead ( see supp . section [ sec : summary of dna hairpins used in this work ] for hairpin sequences and synthesis details ) @xcite . pulling speed is set at 190 nm / s in all the experiments . for the ecori experiments , longer dsdna handles ( @xmath2600-bp ) are used to reduce nonspecific interactions mediated by the protein and beads . for these experiments , the microfluidics chamber was also coated with poly(ethylene glycol ) ( peg ) to avoid protein loss due to nonspecific absorption on the glass surface @xcite . experimental conditions for each interaction were chosen to be comparable to previous ensemble and single - molecule studies : for ecori ( hepes 10 mm ph7.5 , edta 1 mm , nacl 130 mm , bsa 0.1 mg / ml , 100 @xmath45 m , dtt , 0.01% nan@xmath103 ) and salt titrated in the range 60 - 180 mm nacl ; for the oligonucleotide ( tris 10 mm ph7.5 , edta 1 mm , 100 mm nacl , 0.01% nan@xmath103 ) ; and for echinomycin ( tris 10 mm ph7.5 , edta 1 mm , 100 mm nacl , 2% dmso , 0.01% nan@xmath103 ) . all ligands were obtained from commercial sources and used without further purification : ecori ( new england biolabs , 100 u/@xmath45l , @xmath2800 nm dimer ) , oligonucleotide ( eurofins mwg operon , hypur grade ) , echinomycin ( merck millipore ) . concentrations were confirmed using a spectrophotometric analysis for the oligonucleotide ( extinction coefficient 97400 m@xmath104cm@xmath104 at @xmath6=260 nm ) and echinomycin ( extinction coefficient 11500 m@xmath104cm@xmath104 at @xmath6=325 nm ) , whereas for ecori we performed an electrophoretic mobility shift assay using previously described protocols @xcite . all experiments were performed at 25 . in all the cases , the number of cycles obtained per molecule range between 20 and 1300 . a minimum of 2 and a maximum of 10 molecules were pulled in each case ( see tables [ tab : ecori n ] , [ tab : ecori n sal ] , [ tab : oligo n ] , [ tab : echi n ] , [ tab : echins n ] , [ tab : echi c nc n ] [ tab : echi m n ] ) . m. r. shirts , e. bair , g. hooker , & v. s. pande . equilibrium free energies from nonequilibrium measurements using maximum likelihood methods . lett . _ * 91 * , 140601 ( 2003 ) . ultrahigh - resolution optical trap with single - fluorophore sensitivity . methods _ * 8 * , 335340 ( 2011 ) . j. camunas - soler , _ et al_. single - molecule kinetics and footprinting of dna bis - intercalation : the paradigmatic case of thiocoraline . _ nucleic acids res . _ * 43 * , 27672779 ( 2015 ) . a. alemany , & f. ritort . determination of the elastic properties of short ssdna molecules by mechanically folding and unfolding dna hairpins . _ biopolymers _ * 101 * , 11931199 ( 2014 ) .

thermodynamic bulk measurements of binding reactions rely on the validity of the law of mass action and the assumption of a dilute solution . yet important biological systems such as allosteric ligand - receptor binding , macromolecular crowding , or misfolded molecules may not follow these assumptions and require a particular reaction model . here we introduce a fluctuation theorem for ligand binding and an experimental approach using single - molecule force - spectroscopy to determine binding energies , selectivity and allostery of nucleic acids and peptides in a model - independent fashion . a similar approach could be used for proteins . this work extends the use of fluctuation theorems beyond unimolecular folding reactions , bridging the thermodynamics of small systems and the basic laws of chemical equilibrium . binding energies are key quantities determining the fate of intermolecular reactions @xcite . bulk experimental approaches such as surface plasmon resonance , isothermal titration calorimetry and fluorescent ligand binding assays , allow the extraction of binding energies ( @xmath0 ) from measurements of the dissociation constant ( @xmath1 ) with accuracy @xmath21 kcal / mol through the expression : @xmath3~ , \label{eq : masact}\ ] ] where @xmath4 is the boltzmann constant , and @xmath5 the temperature @xcite . however , many ligands such as dna - binding proteins display different binding modes with varying affinities , or require the concerted action of several subunits , making quantitative measurements challenging @xcite . force techniques such as optical tweezers can be used to pull on individual ligand - dna complexes allowing detection of binding events one - at - a - time ( figure 1*a * , inset ) @xcite . however , force - induced ligand unbinding usually takes place in non - equilibrium conditions , and binding energies can not be directly inferred from the measured work values . the crooks fluctuation theorem and the jarzynski equality @xcite are tools to extract equilibrium free energy differences from work distributions obtained far from equilibrium , allowing the measurement of folding free energies of nucleic acids and proteins , both from fully equilibrated @xcite and kinetic states @xcite . however , to date the use of fluctuation theorems remains restricted to unimolecular reactions ( e.g. folding ) . here we introduce a fluctuation theorem for ligand binding ( ftlb ) that allows us to directly extract binding energies of bimolecular or higher - order reactions from irreversible work measurements in pulling experiments ( see s1.1 in @xcite ) . we first show how cyclic protocols allow an unambiguous classification of experimental pathways in relation to the initial and final state , which is an essential step in the application of these theorems . we then apply the ftlb to directly verify the validity of the law of mass action for dilute ligand solutions . next we use the ftlb to accurately measure specific and nonspecific binding energies , as well as allosteric effects due to the cooperative binding of ligand pairs . finally , we show how the ftlb is also applicable to extract binding energies to non - native structures ( e.g. misfolded states , prions , chaperones ) , a measurement inaccesible to most bulk techniques @xcite . as a proof of principle we investigated the binding of the restriction endonuclease ecori to a 30-bp dna hairpin that contains its recognition site ( gaattc ) ( see s1.2,s1.3 in @xcite ) . restriction endonucleases , which bind their cognate sequences with high affinity , are a paradigm of protein - dna interactions @xcite . in a typical experiment , the hairpin is unfolded ( refolded ) by increasing ( decreasing ) the distance ( @xmath6 ) between the optical trap and the micropipette ( figure 1*a * ) . in the absence of ligand , the hairpin folds and unfolds in the force range @xmath7 pn . the binding of ecori increases the stability of the hairpin leading to higher unfolding forces ( @xmath223 pn ) . during a pulling experiment , ecori binds dna when the hairpin is folded . however , since there is no net change in molecular extension upon binding / unbinding , the native ( @xmath8 ) and bound ( @xmath9 ) states can not be distinguished at low forces . in contrast , at forces above @xmath7 pn the bound state ( @xmath9 ) can be unambiguously distinguished from the unfolded state ( @xmath10 ) , as the hairpin remains folded when the protein is bound but unfolds when it is unbound ( figure 1*a * , empty , blue and cyan dots respectively ) . we performed experiments at different ecori concentrations , and determined @xmath23 from the work value ( @xmath24 ) at which the partial work distributions cross ( @xmath25 ) by taking @xmath26 ( figure 1*d * , s1.5 in @xcite ) . the term @xmath23 includes all the energetic contributions involved in going from @xmath9 to @xmath10 ( e.g. binding energy , conformational changes , elastic terms , see s1.6 in @xcite ) . by subtracting the elastic contributions and the energy of formation of the hairpin from the measured @xmath23 value , we extract the binding energy at zero force ( @xmath27 ) at different ecori concentrations ( figure 1*e * and tables s1 , s2 ) . as shown in figure 1*e * , @xmath27 follows the law of mass action ( eq . [ eq : masact ] ) , @xmath28 with @xmath29 @xmath30 , providing a direct test of its validity . this value is independent on the start / end force of the cyclic protocol and relies on a correct classification of paths ( fig . s2-s3 ) . we also performed titration experiments with varying nacl concentration showing that ecori binding energy has a pronounced salt - dependency with slope @xmath31}=-11\pm 2 $ ] @xmath30 ( figure 1 * f * and tables s3 , s4 ) , in agreement with previous bulk experiments @xcite . finally , we repeated experiments with hairpins containing non - cognate dna sequences which did not show binding in the same range of ecori concentrations , proving the specificity of the interaction @xcite . to further test the validity of eq . [ eq : ft ] , we investigated a model system consisting of a short oligonucleotide of 10 bases that binds a dna hairpin . the oligonucleotide can bind the substrate by base - pairing complementarity when the hairpin is in the unfolded ( @xmath10 ) state , thereby inhibiting the refolding of the hairpin at low forces . at forces below the critical force range of the hairpin ( @xmath32 pn ) , the oligo - bound state ( @xmath9 ) competes with the formation of the native hairpin ( @xmath8 ) , and states @xmath9 and @xmath8 can be distinguished due to their different molecular extension ( figure 2*a * ) . to apply eq . [ eq : ft ] , we considered cyclic protocols that start and end at a force lower than the range @xmath33 ( figure 2*b * ) . from the measured partial work distributions and fractions of paths connecting @xmath8 and @xmath9 ( figure 2*c * ) we extracted the binding energies at zero force ( @xmath27 ) ( figure 2*d * and tables s5 , s6 ) . measured binding energies again follow the law of mass action with @xmath34 @xmath30 ( figure 2*d * ) . this agrees with theoretical predictions using the nearest - neighbour model ( @xmath35 @xmath36 ) @xcite and equilibrium experiments performed at the coexistence force of the hairpin , where hopping due to binding / unbinding is observed ( figs . s4-s6 and table s7 ) . the inclusion of the ratio @xmath37 ( figure 2*d * , inset ) is essential to recover the correct binding energies . previous attempts to derive binding energies using unidirectional work measurements and the jarzynski equality did not account for concentration - dependent effects in the chemical potential that are essential in equation [ eq : ft ] @xcite . to prove the general power of the method , we studied echinomycin , a small dna bis - intercalator with selectivity for cg steps @xcite that binds contiguous acgt sites cooperatively @xcite . we performed experiments with a 12-bp dna hairpin containing a single cg - step ( sp hairpin ) that shows rupture forces in the range @xmath38 pn ( figure 3*a * and fig . s7 ) . in the presence of echinomycin the histogram of rupture forces is shifted to higher values and shows a bimodal distribution , indicating two binding modes : a high - affinity binding to the specific cg - site ( high - force peak , @xmath39 pn ) , and a low - affinity binding to other non - specific sites ( low - force peak , @xmath40 pn ) . to confirm this , we pulled a hairpin in which we removed the specific binding site by inverting the cg - motif ( nsp hairpin ) . in the presence of ligand only the low affinity peak is observed ( figure 3*a * ) . to extract the binding energy of each mode , we performed cyclic protocols that start at a force high enough to discriminate both binding modes : we used @xmath39 pn ( @xmath41 pn ) for the sp ( nsp ) hairpin in order to extract both the specific and nonspecific binding energy of the ligand . in this way , we obtained paths connecting states @xmath9 and @xmath10 , and extracted the binding energy of the specific and nonspecific modes ( tables s8-s11 ) . for both binding modes , @xmath42 follows the law of mass action with @xmath43 @xmath30 and @xmath44 @xmath30 ( figure 3*b * ) , which give affinities of 2 nm and 1.8 @xmath45 m respectively ( eq . [ eq : masact ] ) . this measurement of an affinity in the nm range for the specific binding is compatible with quasi - equilibrium experiments ( fig . s8 ) and improves previous studies where accurate measurements could not be obtained due to the concurrent action of both modes @xcite . the ftlb allows us to go beyond free - energy measurements of single ligands , and measure allosteric effects between ligands binding at nearby positions @xcite . for this , we designed hairpin @xmath46 which contains two acgt sites separated by 2 bp ( figure 3*c * ) . the simultaneous binding of two ligands can be distinguished from the binding of a single ligand from the force rips observed in the force - distance curve ( fig . s9 ) . by applying the ftlb we extracted the binding energy per ligand in the single and double bound states , and found that binding is favoured by the presence of a neighbouring ligand . the ftlb allows us to quantitatively test the distance - dependence of this allosteric effect by performing a differential measurement of binding energies with hairpin @xmath47 , which contains two contiguous sites ( figure 3*c * , tables s12-s14 ) . the binding energy per ligand we obtain in the double bound state in hairpin @xmath47 is @xmath48 @xmath30 higher than in hairpin @xmath46 , providing a direct experimental measurement of cooperativity effects in ligand pairs as a function of their distance . single - molecule manipulation is particularly suited to observe the formation of misfolded structures ( e.g. prions , amyloids ) @xcite , but methods to characterize binding to these species are currently lacking . by applying the ftlb it is possible to extract the binding energy to these kinetically stabilized non - native structures . by using a dna hairpin with two binding sites separated by 4bp , we observe the formation of a misfolded structure consisting of two short ( 4bp ) hairpins in series ( figure 3*d * , hairpin m ) . such an off - pathway kinetic state is unobservable in the absence of ligand due to its low energy of formation , however it is kinetically stabilized by the binding of the ligand . we applied eq . [ eq : ft ] by choosing a starting point of the cyclic protocol where the native - bound and misfolded - bound conformations are distinguishable ( @xmath49 pn ) , and found that the energy of binding to both configurations are equal ( @xmath50 @xmath30 , fig . s10 and tab . s15 , s16 ) . in this work , we have introduced a fluctuation theorem for ligand binding ( ftlb ) to directly determine binding energies as a function of ligand concentration in single - molecule experiments . using different biomolecular systems of increasing complexity we provide a single - molecule verification of the law of mass action , and show how the ftlb can account for mass exchange between a molecular system and the environment . we can resolve binding energies to specific and non - specific sites with affinities spanning six orders of magnitude . the ftlb provides a direct experimental measurement of binding energies without assuming any model or reaction scheme , which is particularly useful in cases where the law of mass action does not hold . to show this , we applied the ftlb in two situations where this may happen : the cooperative binding of multiple ligands to the same substrate and the stabilization of kinetic structures through ligand binding - both measurements inaccessible to bulk methods and relevant to many interactions between proteins and ligands . the use of an inherently non - equilibrium method to obtain equilibrium binding energies also grants access to molecular interactions that equilibrate over very long timescales ( e.g. nucleosome assembly ) and that can only be currently measured by indirect techniques such as competition assays @xcite . the ftlb relates work measurements to binding energies without making any assumption on reaction kinetics or the ideal solution limit . therefore it might be also used to test the explicit breakdown of the law of mass action in conditions where it is not applicable , for instance in crowded environments , where ligands exhibit compartmentalized dynamics due to steric hindrance interactions @xcite . lastly , the applicabilty of the ftlb is not restricted to biomolecular reactions , and might be directly applied to other interacting systems that can only be explored through non - equilibrium methods .

to compile the sample , image fields from the vla - first survey ( becker et al . 1995 ) containing components bright and extended enough to judge the source morphologies were inspected by - eye . this gave an initial 100 candidates with extended winged emission ( fig . 1 ; cheung 2006 ) . compared to previously known examples ( e.g. , lal & rao 2006 ) , the new candidates are systematically fainter ( @xmath010@xmath1 ) and more distant ( @xmath2@xmath30.3 ) . new optical spectroscopic observations are identifying many of the fainter , more distant optical hosts . most candidates have clear winged emission and higher resolution vla observations of initially @xmath040 sources have been obtained to confirm the morphological identifications . of the candidates , enough are legitimate x - shaped sources ( conventionally , those with wing to lobe extents of @xmath40.8:1 ) to more than double the number known . lower frequency gmrt observations of selected objects are being pursued to map any spectral structure to estimate the particle ages in the wings to test formation scenarios ( e.g. , dennett - thorpe et al . 2002 ) . we examined the host galaxies of about a dozen new and previously known examples with available sdss images ( 54 sec exposures ) to quantify any asymmetry in the surrounding medium as required by hydrodynamic wing formation models ( e.g. , capetti et al . most of the galaxies are highly elliptical with the minor axes roughly aligned with the wings , consistent with the findings of capetti et al . for a similarly sized sample . however , we found smaller ellipticities ( @xmath5@xmath60.1 ) in at least two examples , 3c192 and b2 0828 + 32 , confirming previous studies of these hosts ( smith & heckman 1989 ; ulrich & r " onnback 1996 ) . round " hosts are not necessarily incompatible with the hydrodynamic picture as observed @xmath5 values can be lowered by projection . this should be investigated more thoroughly with a dedicated host galaxy imaging program . becker , r.h . , white , r.l . , & helfand , d.j . 1995 , apj , 450 , 559 capetti , a. , et al . 2002 , a&a , 394 , 39 cheung , c.c . 2006 , aj , submitted dennett - thorpe , j. et al . 2002 , mnras , 330 , 609 lal , d.v . , & rao , a.p . 2006 , mnras , in press ( astro - ph/0610678 ) merritt , d. , & ekers , r.d . 2002 , science , 297 , 1310 smith , e.p . , & heckman , t.m . 1989 , apjs , 69 , 365 ulrich , m .- h . , & r " onnback , j. 1996 , a&a , 313 , 750

a small number of double - lobed radio galaxies are found with an additional pair of extended low surface brightness ` wings ' of emission giving them a distinctive ` x'-shaped appearance . one popular explanation for the unusual morphologies posits that the central supermassive black hole ( smbh)/accretion disk system underwent a recent realignment ; in a merger scenario , the active lobes mark the post - merger axis of the resultant system ( e.g. , merritt & ekers 2002 ) . however , this and other interpretations are not well tested on the few ( about one dozen ) known examples . in part to remedy this deficiency , a large sample of winged and x - shaped radio sources is being compiled for a systematic study . an initial sample of 100 new candidates is described as well as some of the follow - up work being pursued to test the different scenarios .

we would like to thank bruce reed for introducing us to the classical version of the locker puzzle and richard cleve for pointing out the perfect quantum search of @xcite . this work was partially supported by an an nserc discovery grant and an nserc postdoctoral fellowship .

the _ locker puzzle _ is a game played by multiple players against a referee . it has been previously shown that the best strategy that exists can not succeed with probability greater than , no matter how many players are involved . our contribution is to show that quantum players can do much better they can succeed with . by making the rules of the game significantly stricter , we show a scenario where the quantum players still succeed perfectly , while the classical players win with vanishing probability . other variants of the locker puzzle are considered , as well as a cheating referee . * keywords : quantum complexity , grover search , locker puzzle * 10000 10000 grover s quantum algorithm @xcite provides a quadratic speedup over the best possible classical algorithm for the problem of unsorted searching in the query model . while grover s search method has been shown to be optimal @xcite , our results reveal that in the context of multi - player query games , applying grover s algorithm yields success probabilities that are much better than the success probabilities of classical optimal protocols . specifically , we show that in the case of the _ locker puzzle _ , quantum players succeed with probability 1 while the known optimal classical success probability is bounded above by . in order to amplify this separation , we prove that a significantly stricter version of the locker puzzle has vanishing classical success probability , while still admitting a perfect quantum strategy . we also consider the empty locker and the coloured slips versions of the locker puzzle , and the possibility of a cheating referee . [ sec : locker puzzle ] the _ _ locker puzzle _ _ is a cooperative game between a team of @xmath0 players numbered @xmath1 and a referee . in the initial phase of the game , the referee chooses a random permutation @xmath2 of @xmath3 , and for each player @xmath4 she places number @xmath4 in locker @xmath5 . in the following phase , each player is individually admitted into the locker room . once in the room , each player is allowed to open @xmath6 lockers , one at a time , and look at their contents ( for simplicity , we ll take @xmath0 to be even ) . after the player leaves the room , all lockers are closed . the players are initially allowed to discuss strategy , but once the game starts , they are separated and can not communicate . an individual player @xmath4 _ wins _ if he opens a locker containing number @xmath4 , while the team of @xmath0 players _ wins _ if all individual players win . we would like to know what is the best strategy for the team of @xmath0 players . a nave approach is for each player to independently choose @xmath6 lockers to open . each players wins independently with probability @xmath7 , hence the team wins with probability @xmath8 . surprisingly , it is known that the players can do much , much better ! we will review in section [ section : optimal - classical - locker ] an optimum strategy by which , for any @xmath0 , the players can win with probability at least @xmath9 . the locker puzzle was originally considered by peter bro miltersen , and was first published in @xcite ; a journal version appears in @xcite . sven skylum is credited for the pointer - following strategy that we will give in the next section . a proof of optimality for this strategy is given by eugene curtin and max warshauer @xcite . our presentation of the classical puzzle and its solution follows along the lines of their article . many variations have been proposed @xcite . we will consider the variations of _ empty lockers _ in section [ section : empty - lockers ] , _ coloured slips _ in section [ section : coloured - slips ] ( to be accurate , the locker and the coloured slips puzzles are variants of the empty locker puzzle ) , and a _ cheating referee _ in section [ sec : cheating ] . [ section : optimal - classical - locker ] we saw that a nave solution allows the players to win with an exponentially small probability . how can we devise a strategy that does better ? the reader avid to search for a solution on his or her own is encouraged to do so now . the key is to find a solution where the individual success probabilities are not independent . consider the following strategy : when first entering the locker room , player @xmath4 opens locker number @xmath4 . a number is revealed ; this is used to indicate which locker to open next ( i.e. if number @xmath10 is revealed , the next locker opened is locker @xmath10 ) . each player executes this pointer - following strategy until @xmath6 lockers are opened . to analyze the success probability , note that the team will win provided that the _ permutation _ that corresponds to the placement of numbers in lockers by the referee does not contain a cycle of length longer than @xmath6 . the probability of such a long cycle occurring is : @xmath11 it can be shown that as @xmath12 , @xmath13 and that the sum increases with @xmath0 . hence the probability that the team wins is decreasing to @xmath14 . using a reduction to another game , this strategy can be shown to be optimal @xcite . [ sec : quantum solution ] we now present our first contribution : a quantum solution to the locker puzzle , which performs better than the classical solution . as before the referee chooses a random permutation @xmath2 and she places numbers in the lockers according to this permutation . in the quantum solution , we allow the players to open locker doors in _ superposition _ , each player working with his own quantum register . this is analogous to the quantum query model . for the quantum case , we need to modify the goal of the game which , for player @xmath4 , becomes to _ correctly guess _ the locker containing number @xmath4 after @xmath6 queries , and _ not _ to open locker containing number @xmath4 , because this would be too easy to do in superposition ! we show that quantum players can always win at the locker game . in fact , our results are stronger : we give a stricter version of the locker puzzle for which the optimal classical solution succeeds with vanishing probability , while a quantum strategy always succeeds ! [ imp ] the main idea is to apply grover s quantum search algorithm to the locker puzzle . for player @xmath4 , we consider the action of opening a locker as a query to the oracle which when input locker number @xmath15 , @xmath16 , outputs the following : @xmath17 note that this oracle is weaker than the oracle in the original puzzle which would output @xmath18 . we discuss this further in section [ subsection : optimality ] and in the conclusion . grover s search algorithm @xcite was thoroughly analyzed in @xcite , where it was shown that in a black - box search scenario where it is known that a single solution exists , @xmath19 queries yield a failure probability no greater than @xmath20 , where @xmath0 is the number of elements in the search space ( here , @xmath0 is assumed to be large ) . this was further improved in @xcite , where is was shown that the same amount of queries is sufficient to find a solution with _ certainty_. applying this directly to the quantum players of the locker puzzle yields the following : 1 . [ step : groverquery]each player performs @xmath19 queries ( this is less than the @xmath21 queries in the classical solution ) . 2 . each player wins independently with certainty , implying that the team wins with certainty . [ sec : reducing - number - queries ] we ve seen that quantum players of the locker game can succeed with probability 1 . our solution only requires @xmath19 oracle queries per player . hence , we now consider the asymptotically stricter version of the locker puzzle , where players are allowed to open at most @xmath22 lockers . the next theorem state that the success probability for classical players goes quickly to 0 . [ thm : classic ] in the locker puzzle with @xmath22 queries , classical players win with probability at most @xmath23 . let @xmath24 . we upper bound the success probability of the first @xmath25 players , when each player is allowed to open @xmath26 lockers . since @xmath27 , this upper bounds the success probability of all @xmath0 players . consider a new game where the first player opens exactly @xmath26 lockers and publicly reveals all of their contents . if the first player s number is not revealed the players lose and the game is over . otherwise the @xmath26 revealed players have successfully located their lockers . these @xmath26 lockers and players are now removed from the game . the first player has success probability at most @xmath28 . in successive rounds , a player is chosen from amongst those not yet removed from the game . he continues in the same way by choosing @xmath26 of the remaining lockers and revealing their contents . if he finds his label , again @xmath26 lockers and players are removed from the game . the game stops whenever a chosen player does not find his label . otherwise it continues for @xmath26 rounds and terminates with a win for the players . the success probability of the new game is at most @xmath29 the original game with no revealing of numbers can not do better . [ subsection : optimality ] in the quantum query model with oracle ( [ eq : oracle ] ) the total number of queries required to obtain a success probability of one for the players is in @xmath30 . first consider a variation of the quantum game where the players act sequentially in the order @xmath31 and are allowed to announce their results to the other players . the number of queries performed by player 1 must be in @xmath32 or he will not succeed with probability one . this follows from the analysis of grover s algorithm , see @xcite . the only information given by the oracle @xmath33 is the location of the locker containing label @xmath34 . suppose player 2 is allowed to receive this information and remove that locker from consideration . the permutation @xmath2 induces a random permutation on the remaining @xmath35 lockers . player 2 s success probability is then one only if his number of queries is in @xmath36 . continuing , the @xmath4-th player must ask a number of queries in @xmath37 . the total number of queries is therefore in @xmath30 . in the modified game we share all information available to all players that have not already played . so this shows a lower bound of the same order for the original version of the quantum game where no information is shared . let us now compare the strength of oracle ( [ eq : oracle ] ) with the stronger oracle where @xmath38 . in the classical setup , the weaker oracle ( [ eq : oracle ] ) merely tells a given player whether or not his label is in a requested locker . there are an even number @xmath0 of lockers and he can ask @xmath39 queries . again we consider a sequential version of the game as described above , where each player reveals his results . if he succeeds , he reveals the locker with his number and that locker is removed . for the other lockers he queried , the only information he has is that they did not contain his label . therefore after his locker is removed , the other players have no further information . the success probability of this variation of the locker game is : @xmath40 where we have used stirling s formula twice . this is exponentially small and provides an upper bound on the success probability of the classical locker game with the weak oracle ( [ eq : oracle ] ) . by comparison , as we saw in section [ section : optimal - classical - locker ] the players can win with constant probability using the stronger oracle . an open question is whether the quantum algorithm can be improved by using this stronger oracle . the original motivation for the locker puzzle came from the study of time - space tradeoffs for the substring search problem in the context of _ bit probe complexity _ @xcite . there , a version with both _ empty lockers _ and _ coloured slips _ was presented . we now examine these two variations separately and consider the quantum case . [ section : empty - lockers ] suppose there are a total of @xmath41 lockers . the referee selects an unordered subset @xmath2 of @xmath42 with cardinality @xmath0 and she puts label @xmath4 into locker @xmath43 for @xmath44 . the remaining @xmath45 lockers are empty . assume @xmath46 is even , and we allow the players to open up to @xmath47 lockers . an optimum winning strategy for this more general situation is unknown : the pointer algorithm fails if an empty locker is opened . even for the case @xmath48 , where half of the lockers are empty , it is still unknown if there is a classical strategy with success probability bounded away from zero @xcite . however , the quantum strategy given in section [ sec : quantum solution ] still succeeds with probability one with a number of queries in @xmath49 per player , for a total of @xmath50 queries . it suffices to modify the oracle ( [ eq : oracle ] ) so that @xmath15 runs over the range @xmath51 , and query it @xmath52 times . if it turns out that for these same parameters , the classical success probability vanishes , then the power of the quantum world would be once more confirmed , as in section [ sec : reducing - number - queries ] . and section [ subsection : optimality ] . [ section : coloured - slips ] consider the empty lockers game with @xmath41 lockers , again with @xmath0 players and @xmath0 slips of paper , each labelled @xmath53 . this time the referee colours each slip either red or blue as she chooses , and places them in a randomly selected subset of @xmath0 lockers . as before , each player @xmath4 may open @xmath47 lockers using any adaptive strategy , and based on this , must make a guess about the colour of the slip labelled @xmath4 . the players win if every player correctly announces the colour of his slip . with @xmath54 , this can be solved with the pointer - following algorithm and the players have success probability about 0.31 . in the quantum setting , the players can win with probability one at the colour guessing game also , by changing the oracle ( [ eq : oracle ] ) . let @xmath55 be the colour of the slip for player @xmath4 . define for @xmath51 and @xmath56 : @xmath57 now we use the protocol described in section [ imp ] with each player querying this new oracle @xmath52 times . if for player @xmath4 @xmath58 , then there is exactly one @xmath15 for which @xmath59 and grover s algorithm returns @xmath60 with probability one . otherwise , if @xmath61 then @xmath62 is identically zero and grover s algorithm may return any value @xmath15 . the player now makes one further call to oracle ( [ eq : oracle1 ] ) with the returned value @xmath15 and guesses red if the oracle returns one and blue otherwise . [ sec : cheating ] a cheating referee can obviously beat the players in the locker game . she simply has to omit the label of one of the players . this could be easily exposed by requiring that all the lockers be opened and checked at the end of the game . a more subtle way of cheating is if the referee can somehow choose the permutation @xmath2 . in the original locker game , let @xmath63 , and let @xmath64 be a random unordered subset of @xmath65 players . she may set @xmath66 , @xmath67 , and fill out the rest of @xmath2 at random from the remaining players . it is easy to verify that , using the pointer algorithm , player @xmath68 opens @xmath6 lockers @xmath69 and does not find his label . he has to guess and loses with probability about @xmath70 . the same thing happens for each of the players @xmath71 . ( incidentally , the reason for not choosing @xmath72 is that the players not finding their label may guess the locker number they see in the last locker they open , winning the game with probability one ! ) . using variants of this idea the referee may cheat successfully for some time before the players catch on . if the players have access to shared randomness ( which is unknown to the referee ) , they can circumvent this problem by first applying their own permutation on the lockers before opening any of them . interestingly , our quantum protocol is impervious to a referee who maliciously chooses the permutation , and does not require shared randomness . [ sec : conclusion ] it was previously known that the locker puzzle has an intriguing classical optimal solution . now we know that the locker puzzle and its variants also have interesting quantum solutions which perform significantly better than the classical ones . we have given a quantum solution in the black - box query complexity model that _ does not use the pointer - following technique that is crucial to the classical optimal solution_. it would be interesting to see if using the stronger classical oracle could lead to a quantum solution that works with a reasonable probability of success using @xmath73 total queries . with this stronger oracle , perhaps shared entanglement could help the players ? it would also be interesting to see if , analogous to the classical case , our results have any consequences for time - space tradeoffs for data structures @xcite .

in our single source model ( updated version is in @xcite ) we explained the knee as the effect of a local , recent supernova , the remnant from which accelerated mainly oxygen and iron . these nuclei form the intensity peaks which perturb the total background intensity . the comprehensive analysis of the world s data gives as our datum the plots given in the figure 1 ; these are deviations from the running mean for both the energy spectrum mostly from cherenkov data and the summarised electron size spectrum . it is against these datum plots that our comparison will be made . in the present work we endeavour to push the subject forward by examining a number of aspects . they are examined , as follows : + ( i ) can we decide whether the solar system is inside the supernova shock or outside it ? + ( ii ) is the identification of oxygen and iron in the peaks correct ? + ( iii ) can both the peaks be due to protons rather than nuclei ? in view of claims from a few experiments ( dice , blanca ) that the mean mass is low in the pev region , it is wise to examine this possibility . the appreciation that the frequency of sn in the local region of the interstellar medium ( ism ) has been higher than the galactic average , over the past million years , has improved the prospects for the ssm being valid @xcite and thereby increases the probability that we are close to the surface of a remnant . it is doubtlessly possible for particles to escape from an snr shock and propagate ahead . such a situation has been considered in the berezhko - model. the problem concerns uncertainties in the diffusion coefficient for the ism ; however , estimates have been made @xcite and figure 1 shows the result for the sun being outside the shock at the distance of 1.5@xmath0 for the center of snr ( @xmath0 is the radius of the remnant ) . it is seen that the result does not fit well the datum points at all . the model tested must be rejected in its given form . it is possible to restore it by taking an energy spectrum of more nearly the form for the inside snr location or at the position outside , but very close to the shell . the corresponding cureves are shown in figure 1 by full lines . a tolerable astrophysical case could be made for helium and oxygen rather than oxygen and iron , and the direct measurements at lower energies than the knee region do not really rule it out . figure 2 shows the @xmath1-values for the corresponding spectra . the separation of the he and o peaks is a little greater than for o and fe ( 8/2 compared with 26/8 ) and this causes the he , o pattern to be displaced somewhat . although the fit to the datum points is not as good as for o , fe , the he , o combination can not be ruled out on the basis of the @xmath1-plots alone . the absence of the preferred - by - us nuclei between the two peaks is a worry , though ( incertion of carbon does not help to fill the gap between two peaks ) . the fe peak would then be expected at log(@xmath2 ) = 1.1 . calculations have been made for the case of two proton peaks , the proton spectra having been taken to be the standard interior - to - the snr form . the result is also shown in figure 2 . an interesting situation develops here . although it is possible to tune either the energy spectrum or the size spectrum to fit the @xmath1-results , it is not possible to choose an energy spectrum which fits both . this arises because of the sensitivity of the number of electrons at the detection level to the primary mass . in figure 2 the separation of the proton peaks in the energy spectrum was chosen such that the @xmath1-distribution for shower size was a reasonable fit to the data . however , the separation of the peaks in the energy spectrum necessary for the shower size fit is less than that for o , fe by 0.15 ; the result is that after the necessary binning ( 0.2 in @xmath3 units ) for the energy spectrum there is no agreement there . it is evident from the foregoing that the two - proton peak model is unacceptable . this result cast doubt on the analyses of eas data which conclude that the mean primary mass is low ( @xmath4 ) in the pev region . as mentioned already , it is our view that some , at least , of the models used in the mass analyses are inappropriate for the interactions of nuclei , particularly for the production and longitudinal development of the electromagnetic component . it is interesting to know , in connection with mean mass estimates , that the recent work using the tibet eas array @xcite has given strong support for the result - favoured by us - in which the average cosmic ray mass increases with energy . in fact , their mass is even higher than ours : @xmath5 , compared with our 2.4 , at 1 pev , and 3.3 , compared with 3.0 at 10 pev . equally significant is the fact that the sharpness of the iron component that they need to fit the overall data is quite considerable : @xmath6 = 1.4 . it will be remembered that straightforward galactic diffusion - the conventional model - gives @xmath7 for any one mass component and @xmath8 for the whole spectrum @xcite . returning to the question of our location with respect to the snr it seems difficult to account for the @xmath1-distribution if we are some distance outside the shell , unless the diffusion coefficient for cosmic ray propagation in the ism is almost energy - independent . we appear to be inside , or only just outside . finally , concerning the nature of the peaks : o , fe or he , o , it is difficult to rule out the latter from the @xmath1-plots alone , although the lack of an iron peak is surprising . however , there is some evidence from the tunka-25 cherenkov experiment for a further peak at roughly the correct energy for the third ( fe ) peak @xcite . there is also a hint of a peak in kascade spectrum , which is observed at an even higher energy than in tunka-25 @xcite . most other experiments - but not all - do not have the sensitivity to detect a further peak so the situation here is still open . we still prefer our original suggestion , viz . that the peaks are due to o and fe , and their shape is the consequence of the sharp cut - off in the energy spectrum of particles accelerated by snr . the main reason for the preference is the fact that o and fe spectra extrapolate and fit direct measurements of those components rather well @xcite and there are good astrophysical reasons favouring these nuclei . the single source model , with its explanation of the knee in the cosmic ray energy spectrum in terms of particles ( probably principally nuclei of oxygen and iron ) from a recent , local sn , has been examined further . it is true that the identity of the nuclei is not completely secure and it is just possible that rather than o , fe , the combination is he , o : however , we still prefer the original explanation . the question of the nature of the particles responsible for the knee is , therefore , still somewhat uncertain ; 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an analysis is made of the masses and spectral features for cosmic rays in the pev region , insofar as they have a bearing on the problem of the interaction of cosmic ray particles . in our single source model we identified two peaks seen in a summary of the world s data on primary spectra , and claimed that they are probably due to oxygen and iron nuclei from a local , recent supernova . in the present work we examine other possible mass assignments . we conclude that of the other possibilities only helium and oxygen ( instead of o and fe ) has much chance of success ; the original suggestion is still preferred , however . concerning our location with respect to the snr shell , the analysis suggests that we are close to it - probably just inside .

type ia supernovae ( sne ia ) , characterized by no @xmath1 but strong si lines in the spectra at the maximum brightness , are brighter than most of sne classified into the other types and exhibit uniform light curves . thus they are used as a standard candle to measure distances to remote galaxies . a plausible explosion model for sne ia is the accreting white dwarf ( wd ) model , in which a white dwarf in a binary system accretes material from the companion star , increases its mass , usually up to the chandrasekhar mass limit ( @xmath2 ) , and then explodes ( e.g. , * ? ? ? . there have been significant progresses in the accreting wd model since @xcite introduced the stellar wind from the wd while it accretes materials from the companion . their model succeeded in sustaining a stable mass transfer in the progenitor systems of sne ia . according to their model , there are two main evolutionary paths leading to sne ia , the super soft x - ray source ( sss ) channel and the symbiotic channel @xcite . accordingly their model predicts which companion stars lead to sne ia . the above evolutionary scenario for sne ia has not been confirmed by observations , which will require the identification of the companion star that should remain in the vicinity of the explosion site . @xcite argued that their group identified a g2iv star as the companion of tycho brahe s supernova remnant ( snr ) by measuring the velocities and distances of stars in the vicinity of the center of the snr . they concluded that this g2iv star was moving much faster than the other neighbor stars and that the distance to this star seemed consistent with the distance to tycho s snr . although @xcite has argued that the observed velocity of tycho g might correspond to the velocity of stars belonging to the thick disk population , the expected stellar mass in thick disk stars within the cone with 2.87 arcsec radius ( which corresponds to the angular distance from the center of tycho s snr to the tycho g star ) , at 3 kpc from earth , is only 2 @xmath3 , which makes the thick disk star alternative very unlikely . for this estimate we use the density in the vicinity of tycho s snr @xcite . although the coincidence of the kinematic characteristics of tycho g with its being at the position and distance of the snr appears significant , confirmation by other means would nonetheless be very useful . in this paper we propose a direct method to prove that the companion star is located inside the sn ejecta . a hint was dropped by observations for a star called s - m star discovered by @xcite near a type ia snr 1006 . @xcite proved that the s - m star was not the companion of this supernova by investigating features of fe ii absorption lines in the ultraviolet ( uv ) spectrum . very broad wings were observed in both blue and red sides of the absorption lines . the line width was a few thousand km / s much larger than the thermal velocity of stellar atmosphere , which is thought to be @xmath410 km / s . the broad wings are likely to be formed by fe ii in the ejecta of snr 1006 ; photons in the blue wing are absorbed by the matter ejected toward us , and those in the red wing away from us . thus it was proved that the s - m star is located behind the snr 1006 ejecta . when a star is inside the ejecta of sne ia , photons emitted from the star are absorbed only by the ejecta moving toward us . hence the broad wing must be present only in the blue side . the absorption line with only blue wing enables us to identify companion stars of sne ia . @xcite used the uv range to observe the s - m star with the faint object spectrograph on the hubble space telescope . however , in addition to difficulties in uv observations from the ground , companion stars on the evolutionary paths suggested by the above mentioned scenario @xcite may not be bright in the uv range . then we will focus on absorption lines in the visible range . furthermore the corresponding transitions need to be from the ground state because most fe ions in the ejecta are expected to be in the ground state . thus only fe i can produce such absorption lines in sne ia ejecta . in this paper , we estimate the amount of fe i in the ejecta of tycho s snr by taking account of collisional processes in non - equilibrium and ionizations by photons emitted from the shocked ejecta , and calculate spectra of a star located at the center of a snr and discuss whether we can identify the feature of fe i absorption lines in the spectrum of the companion star . [ cols="^,^,^,^,^,^ " , ] [ tbl : ew ] even when we find a star that exhibits the absorption feature discussed in this paper , there is a chance that a star other than the companion star happens to be inside the ejecta . a star existing in the vicinity of a sn ia gets a fraction of the explosion energy and is accelerated . if the companion star similar to tycho g star with the mass of @xmath5 1.2 @xmath6 and the radius of @xmath7 2 @xmath8 is located at the distance of @xmath9 5.5 @xmath8 from the progenitor , the size of the roche lobe is comparable to the size of the companion . thus the star in this situation will get the maximum velocity after the explosion . then the orbital velocity before the explosion is @xmath10 km / s . in a 3-d hydrodynamical simulation of sne ia by @xcite , they obtain a plausible kick velocity @xmath11 km / s . therefore , including the orbital velocity , the velocity of the companion star becomes @xmath12 km / s . if the companion star has been moving away from the explosion site at that speed , the companion star is now at the distance of @xmath130.08 pc from the center . the stellar mass density in the neighborhood of tycho s snr estimated from a model of the galaxy @xcite is less than 0.03 @xmath14 . thus the expected stellar mass inside this volume is only @xmath15 . therefore if we find a star showing absorption lines with broad blue wings in the spectrum , it is likely that the star is the companion star . as a consequence , we have demonstrated that there exhibit very deep absorption lines with unique shapes in the spectrum of the companion star located at the center of a young snr such as tycho s snr . there are , however , a few factors that might reduce or even erase these distinct absorption features . first , the number of fe i in the freely expanding ejecta is very sensitive to the number of ionizing photons emitted from the shocked ejecta . an increase in the number of ionizing photons by a few factors might decrease the number of fe i by a few orders of magnitude or more . since the main source of ionizing photons is o in the outer ejecta , the distributions of o and density in the outer ejecta need to be known precisely . unfortunately , these regions in w7 have some problems to reproduce the observed optical spectra ( * ? ? ? * and references therein ) . due to this uncertainty in the explosion model , it is not conclusive if the companion star of tycho s sn will exhibit unique fe i absorption features discussed in this paper . nevertheless , it is true that every sn ia has a period during which the companion star has the distinct absorption features discussed above because the ejecta become cool enough to have plenty of fe i for a time after the optical brightening . second , it is assumed in our calculations that ions in the shocked region are ionized to fe@xmath16 , si@xmath17 , o@xmath18 , c@xmath19 immediately after the shock passes following the procedure taken by @xcite . since ions in lower ionization stages are a strong source of ionizing photons , ionization may be more advanced in real young snrs . arnaud , m. rothenflug , r. 1985 , a&as , 60 , 425 branch , d. 1998 , , 36 , 17 colella , p. , woodward , p. 1984 , jcoph , 54 , 174 decourchelle , a. , et al . 2001 , a&as , 365 , l218 dehnen , w. , binney , j. , 1998 , mnras , 294 , 429 engstrom , l. , et al . 1992 , jphb , 25 , 2459 fuhrmann , k. 2005 , mnras , 359 , l35 hachisu , i. , kato , m. , nomoto , k. 1996 , apj , 470 , l97 hachisu , i. , kato , m. , nomoto , k. , umeda , h. 1999 , apj , 519 , 314 hachisu , i. , kato , m. , nomoto , k. 1999 , apj , 522 , 487 hamilton , a. , sarazin , c. 1984 , apj , 287 , 282 hamilton , a. , fesen , r. 1988 , apj , 327 , 178 itoh , h. , masai , k. , nomoto , k. 1988 , apj , 334 , 279 kato , t. 1976 , apjs , 30 , 397 reinecke , m. , hillebrandt , w. , & niemeyer , j. c. 2002 , , 391 , 1167 lotz , w. 1967 , apjs , 14 , 207l marietta , e. , burrows , a. , fryxell , b. 2000 , apjs , 128 , 615 mihalas , d. , 1978 , stellar atmospheres . nomoto , k. 1982 , , 253 , 798 nomoto , k , thielemann , f. , yokoi , k. 1984 , apj , 286 , 644 ruiz - lapuente , p. , et al . 2004 , nature , 431 , 1069 schweizer , f. middleditch , j. 1980 , apj , 241 , 1039 sorokina , e. i. , et al . 2004 , astl , 30 , 737 spitzer , l. 1978 , physical processes in the interstellar medium . tunklev , m. , et al . 1997 , phys , 55 , 707 verner , d. , et al . 1996 , apj , 465 , 487 vink , j. , et al . 2003 , apjl , 587 , l31 wang , l. , baade , d. , hflich , p. , wheeler , j. c. , kawabata , k. , & nomoto , k. 2004 , , 604 , l53 woosley , s. e. , & weaver , t. a. 1986 , lecture notes in physics , berlin springer verlag , 255 , 91 wu , c. , et al . 1993 , apj , 416 , 247

we propose a method to identify the companion stars of type ia supernovae ( sne ia ) in young supernova remnants ( snrs ) by recognizing distinct features of absorption lines due to fe i appearing in the spectrum . if a sufficient amount of fe i remains in the ejecta , fe i atoms moving toward us absorb photons by transitions from the ground state to imprint broad absorption lines exclusively with the blue - shifted components in the spectrum of the companion star . to investigate the time evolution of column depth of fe i in the ejecta , we have performed hydrodynamical calculations for snrs expanding into the uniform ambient media , taking into account collisional ionizations , excitations , and photo - ionizations of heavy elements . as a result , it is found that the companion star in tycho s snr will exhibit observable features in absorption lines due to fe i at @xmath0 nm and 385.9911 nm if a carbon deflagration sn model @xcite is taken . however , these features may disappear by taking another model that emits a few times more intense ionizing photons from the shocked outer layers . to further explore the ionization states in the freely expanding ejecta , we need a reliable model to describe the structure of the outer layers .

we note that linear stability analysis can not be used to probe the stability of the synchronization , as we can not perform a valid taylor expansion when @xmath81 , where @xmath82 . for equal driving force profiles that we linearize , @xmath182 , @xmath183 , if we were to taylor expand , then the linearized expression for @xmath184 would be @xmath185 which has a singularity at @xmath81 . the apparent singularity actually occurs at @xmath186 and at @xmath187 in the full expression , but the choice of constraining force ensures this zero in the denominator is canceled by the numerator . however , when we expand in @xmath37 and shift the singularity so that it occurs at @xmath81 , then the numerator is no longer zero at this point . the reason we have this zero in the denominator is the following : the torque free condition ( [ eq : forcetorquefree ] ) is @xmath188 along with equations ( [ eq : rl]-[eq : rb],[eq : rld]-[eq : rbd ] ) , we use ( [ eq : torquefree ] ) to solve for the constraining forces @xmath189 , @xmath24 . however , at @xmath190 , @xmath189 is multiplied by a term which vanishes , so the torque free condition can be satisfied without specifying @xmath189 . we over - constrain the system when we divide by zero and specify @xmath189 at @xmath190 . geometrically , @xmath191 corresponds to the phase where @xmath192 is parallel to @xmath193 . our numerical analysis of the full expression avoids this singularity .

the green alga _ chlamydomonas _ swims with synchronized beating of its two flagella , and is experimentally observed to exhibit run - and - tumble behaviour similar to bacteria . recently we studied a simple hydrodynamic three - sphere model of _ chlamydomonas _ with a phase dependent driving force which can produce run - and - tumble behaviour when intrinsic noise is added , due to the non - linear mechanics of the system . here , we consider the noiseless case and explore numerically the parameter space in the driving force profiles , which determine whether or not the synchronized state evolves from a given initial condition , as well as the stability of the synchronized state . we find that phase dependent forcing , or a beat pattern , is necessary for stable synchronization in the geometry we work with . introduction microorganisms swim in the low reynolds number regime where viscous forces dominate , inertia is negligible and the familiar propulsion methods of larger organisms become ineffective @xcite . fluid flow is governed by the stokes equation , which is time reversible . a necessary condition on a periodic swimming stroke in order to achieve net propulsion is that it is non - time reversible @xcite . inspired by sperm cells , which achieve propulsion by propagation of bending waves through their flagellum , taylor demonstrated that propulsion is possible in a viscous environment by studying the propagation of waves on an infinite sheet @xcite . purcell showed that a swimmer needs at least two compact degrees of freedom to break the time reversal symmetry and achieve net propulsion @xcite . many microorganisms swim using flagella @xcite ; there are two fundamentally different types of flagella : bacterial flagella and eukaryotic flagella ( or cilia ) . eukaryotic flagella form bends when microtubules on one side of the flagella ` walk ' or ` slide ' along the microtubules on the other side @xcite . the propagation of bends allows the flagella to form beat patterns that can break the time reversal symmetry . for example , the first half of an individual cilium s beat cycle , called the _ power stroke _ , has the cilium sticking out and pushing the fluid , while the second half , called the _ recovery stroke _ , has the cilium bent as it returns to its original position @xcite . our understanding of propulsion at low reynolds number has been developed by theoretical model microswimmers . lighthill demonstrated a model that can achieve net propulsion by studying periodic shape deformations of a nearly spherical swimmer , showing that the swimming velocity is at most of the order of the square of the amplitude of the deformations @xcite . purcell s three - link swimmer was studied by becker _ et al . _ , who determined the swimming direction and velocity for different angle amplitudes and relative link lengths @xcite . a useful one - dimensional model is the linear three - sphere swimmer , where three beads are connected by two rods that change length with a non - reciprocal pattern @xcite . dreyfus _ et al . _ studied a rotational analogue of the three - sphere swimmer @xcite . avron _ et al . _ presented a more efficient swimmer consisting of a pair of bladders which exchange their volume and vary the distance between them @xcite . there have been several experimental realisations of artificial low reynolds number swimmers @xcite . when two sperms swim close to each other , their tails beat in synchrony @xcite and taylor studied this using his waving sheet model with hydrodynamic interactions @xcite . coordinated beating of flagella or cilia is important for a range of processes including motility , efficient pumping of fluid and symmetry breaking in developing embryos @xcite . theoretical and experimental models have been studied to show that synchronization can occur through hydrodynamic interaction and that it is relevant to bacterial swimming and pumping by arrays @xcite . flagellar synchronization is observed in _ chlamydomonas _ , a unicellular green alga that swims using two flagella that beat with a breaststroke pattern @xcite . the cell has diameter @xmath0 and swims with velocity @xmath1 so the reynolds number is @xmath2 and inertia is negligible . during normal swimming , the flagella beat in synchrony . these periods of synchrony are interrupted by periods of asynchronous beating and during these asynchronies , there is a large change in the cell s orientation @xcite . this is analogous to run - and - tumble behaviour observed in bacteria . simple models have helped us understand better the intricacies of low reynolds number swimming and hydrodynamic synchronization , and a recent development has been to combine these two effects in the context of a simple three - sphere model for the swimming of _ chlamydomonas _ @xcite . this simple model captures some of the important features of _ chlamydomonas _ , namely , the ability to swim , the exact role of hydrodynamic interactions @xcite , the existence of stable synchronized states and an emergent run - and - tumble behaviour which is observed when we add white noise to the driving force @xcite . here , we consider the model without added noise and explore its phase diagram and full parameter space to see when the model evolves into the synchronized state . we also investigate the stability of the synchronized state under various conditions , and the different types of behaviour that can be obtained form the model . these studies have revealed a number of intriguing features . the model we arrange three beads in the @xmath3 plane , each of radius @xmath4 , on a frictionless scaffold , as shown in figure [ fig : model ] . in a lab frame , but it does not interact with the fluid . the green underlay is a schematic of a _ chlamydomonas _ cell . ] we refer to the left , right and back beads with the subscripts ` @xmath5 ' , ` @xmath6 ' and ` @xmath7 ' , respectively . let @xmath8 be the origin of the cell reference frame with respect to a lab frame . the cell axes @xmath9 make an angle @xmath10 with the lab axes @xmath11 . the left and right beads model the flagella and move on circular trajectories in the cell frame of radius @xmath7 in opposite directions and with phases @xmath12 and @xmath13 ; the back bead models the cell body and is fixed with respect to the cell frame . the positions and velocities of the beads are @xmath14 where the unit vectors @xmath15 and @xmath16 are in the normal and tangent directions of the circular trajectory of @xmath17 . the left and right beads are driven by tangential forces @xmath18 and @xmath19 respectively . normal forces @xmath20 and @xmath21 are exerted by the beads in order to be constrained to the circular trajectories . the force on the back bead is such that the swimmer is force free and torque free : @xmath22 where @xmath23 for @xmath24 and @xmath25 for @xmath26 . the forces and velocities are related through hydrodynamic interactions between the beads : @xmath27 where @xmath28 is the friction coefficient of each bead ( @xmath29 is viscosity of the ambient fluid ) . in the limit when @xmath4 is small compared with all other length scales , the hydrodynamic interaction is described by the oseen tensor @xmath30 with @xmath31 @xcite . the phase difference @xmath32 evolves according to @xmath33 , \label{eq : deltadot}\end{aligned}\ ] ] where @xmath34 and @xmath35 . \label{eq : thetadot}\end{aligned}\ ] ] we solve equation [ eq : deltadot ] numerically for a choice of stroke pattern ( driving forces ) @xmath36 , @xmath24 . the long term behaviour of @xmath37 depends on the stroke pattern and in many cases the initial condition . we compute @xmath38 and @xmath39 to leading order in @xmath40 , since we do not require hydrodynamic interactions for synchronization @xcite , but we include the next order hydrodynamic term when computing the velocities , since we need this second order affect to achieve a net swimming velocity . swimming velocity in the synchronized state first we consider the synchronized state where @xmath41 and @xmath42 , so that @xmath43 . we do not worry about the stability of the synchronized state , which we consider in the next section , and assume that the swimmer stays in this state . since the reynolds number is low , we need to ask ` does the model achieve net propulsion ? ' if hydrodynamic interactions are not included , then the cell just moves forwards and backwards and there is no net motion . however , if we include hydrodynamic interactions , which vary in strength around the cycle , then the symmetry in the swimming stroke is broken and net propulsion is achieved . the magnitude and direction of the net swimming velocity depends on the ratios @xmath44 and @xmath45 . figure [ fig : hlvel ] shows the net swimming velocity in the @xmath46 direction for a range of @xmath47 and constant driving force @xmath48 . for @xmath49 , swimming is in the positive direction , otherwise the cell swims in the negative direction . polotzek and friedrich in reference @xcite give the following explanation of why the cell may swim in either direction . the instantaneous velocity @xmath50 is the ratio of the force @xmath51 , which has to be applied to the back bead to prevent it from moving , and the friction coefficient @xmath52 associated with towing the swimmer in the @xmath46 direction . the force @xmath53 oscillates during a stroke cycle and the hydrodynamic interactions , which reduce the magnitude of @xmath53 , are strongest when the beads are closest together . on the other hand , the friction coefficient is largest when the beads are furthest apart and smallest when the beads are close together . the geometry of the swimmer determines which effect dominates and therefore whether the net swimming is in the positive or negative direction . . the zero contour lies approximately on the line @xmath54 for sufficiently large @xmath44 . ] ( 10,10)(0,0 ) ( 327,13 ) ( 88,246 ) ( 142,180 ) ( 312,180 ) ( 218,174 ) ( 218,96 ) ( 117,115 ) ( 314,115 ) ( 117,85 ) ( 314,85 ) ( 117,62 ) ( 314,62 ) herein we fix the values @xmath55 and @xmath56 , which results in forwards swimming for @xmath57 . the the net velocity is also affected by the force profile and we consider driving forces @xmath58 such that @xmath59 , where @xmath60 is a fixed average force . the net velocity @xmath61 can be written as @xmath62 , where @xmath63 , @xmath64 is the period , and we can write @xmath65 . in the synchronized state the force dependence cancels in the ratio @xmath66 , so the force only enters the net velocity expression through the @xmath67 term . in order to maximise the net velocity , we must minimise the period @xmath68 , where we can write @xmath69 . minimising @xmath70 with the constraint @xmath59 tells us that a constant force profile @xmath71 maximises the net velocity . clearly , increasing @xmath60 increases the net velocity . however as we shall see in the next section , the synchronized state is not stable when we choose a constant force profile . friedrich _ et al . _ showed that a constant driving force can give a stable synchronized state if we change the direction of rotation of the beads , so @xmath72 @xcite , which is equivalent to changing the sign of @xmath73 , but here we choose to work with @xmath57 and @xmath74 . synchronization and stability we consider force profiles of the forms @xmath75 and @xmath76 , where @xmath77 and @xmath24 . the definition of the synchronized state that we use here is zero ( or integer multiple of @xmath78 ) phase difference between the two flagella , i.e. when @xmath79 , @xmath80 . initially we tried to analyst the the synchronization stability by linear stability analysis , but we are unable to do this because we can not perform a valid taylor expansion when @xmath81 , where @xmath82 . we work numerically to avoid this taylor expansion ; for further details see the appendix . we identify five main types of stability of the synchronized state by looking at the evolution of @xmath37 from different initial conditions @xmath83 for a number of @xmath84 equally spaced in the range @xmath85 : ( i ) all the initial conditions @xmath83 evolve into the synchronized state for all @xmath84 ( the synchronized state is stable ) . ( ii ) some choices of @xmath84 evolve into the synchronized state and others choices evolve into an oscillating state , but there is a larger number of @xmath84 that lead to synchronization than the number of @xmath84 that leads to oscillations . ( iii ) some choices of @xmath84 evolve into the synchronized state and others choices evolve into an oscillating state ; the numbers of @xmath84 that lead to each type of behaviour are similar . ( iv ) some choices of @xmath84 evolve into the synchronized state and others choices evolve into an oscillating state , but there is a larger number of @xmath84 that lead to oscillations than the number of @xmath84 that leads to synchronization . ( v ) all choices of @xmath84 evolve into the oscillating state , ( the synchronized state is unstable ) . although the choice of initial condition @xmath86 is arbitrary , we want to know how likely it is that a small perturbation from the synchronized state will decay back to synchronization , or whether it is likely to evolve into an oscillating state . this choice of @xmath87 is suitable for this purpose . for type ( v ) stability , if we start in the synchronized state , then it is likely that some numerical noise will kick @xmath37 into an oscillating state . it is possible for a small amount of noise to kick the synchronized state into an oscillating state for types ( ii ) , ( iii ) , ( iv ) , with low probability for type ( ii ) , then increasing probability for type ( iii ) and then type ( iv ) . first we consider the case where @xmath88 . for each choice of coefficient and initial condition , @xmath37 evolves either to an integer multiple of @xmath78 and remains at this value ( synchronization ) ; or it reaches a state where it oscillates about @xmath89 sinusoidally ; or it reaches a periodic state near zero , but never reaching zero . figure [ fig : devolutions1 ] shows examples of these three cases and the corresponding orientation @xmath90 . for driving force @xmath91 and initial condition @xmath92 with ( a ) @xmath93 , ( b ) @xmath94 , ( c ) @xmath95 . the insets show a small part of the plot in more detail . the bottom axis @xmath96 shows the number of cycles which increases monotonically with time . bottom row : corresponding @xmath97.,title="fig : " ] for driving force @xmath91 and initial condition @xmath92 with ( a ) @xmath93 , ( b ) @xmath94 , ( c ) @xmath95 . the insets show a small part of the plot in more detail . the bottom axis @xmath96 shows the number of cycles which increases monotonically with time . bottom row : corresponding @xmath97.,title="fig : " ] for driving force @xmath91 and initial condition @xmath92 with ( a ) @xmath93 , ( b ) @xmath94 , ( c ) @xmath95 . the insets show a small part of the plot in more detail . the bottom axis @xmath96 shows the number of cycles which increases monotonically with time . bottom row : corresponding @xmath97.,title="fig : " ] + for driving force @xmath91 and initial condition @xmath92 with ( a ) @xmath93 , ( b ) @xmath94 , ( c ) @xmath95 . the insets show a small part of the plot in more detail . the bottom axis @xmath96 shows the number of cycles which increases monotonically with time . bottom row : corresponding @xmath97.,title="fig : " ] for driving force @xmath91 and initial condition @xmath92 with ( a ) @xmath93 , ( b ) @xmath94 , ( c ) @xmath95 . the insets show a small part of the plot in more detail . the bottom axis @xmath96 shows the number of cycles which increases monotonically with time . bottom row : corresponding @xmath97.,title="fig : " ] for driving force @xmath91 and initial condition @xmath92 with ( a ) @xmath93 , ( b ) @xmath94 , ( c ) @xmath95 . the insets show a small part of the plot in more detail . the bottom axis @xmath96 shows the number of cycles which increases monotonically with time . bottom row : corresponding @xmath97.,title="fig : " ] ( 10,10)(0,0 ) ( 145,127 ) ( 290,126 ) ( 434,126 ) ( 8,192 ) ( 154,192 ) ( 300,192 ) ( 14,88 ) ( 147,93 ) ( 159,79 ) ( 289,82 ) ( 306,99 ) ( 435,59 ) ( 80,110 ) ( 80,10 ) ( 225,110 ) ( 225,10 ) ( 370,110 ) ( 370,10 ) when @xmath37 oscillates about @xmath89 , then the orientation oscillates about some fixed value . the cycle averaged motion is in a straight line , but the cell jiggles from side to side as well as backwards and forwards as it moves along . when @xmath94 and the oscillations are near zero , there is a net drift in the orientation so the net motion of the cell is along a curved trajectory . for many choices of @xmath58 , the initial condition determines whether @xmath37 evolves into the synchronized state or the oscillating state . figure [ fig : icphasediagram ] shows the the dependence of @xmath37 evolution on initial condition for @xmath98 . a 63 @xmath99 69 grid is shown where each square represents an initial condition @xmath100 . a black square represents an initial condition for which @xmath101 after a sufficiently long time ; a white square represents an initial condition for which @xmath37 continues to oscillate periodically as @xmath102 . evolves for different initial conditions for @xmath103 with ( a ) @xmath104 , ( b ) @xmath105 , ( c ) @xmath106 . black squares represent initial conditions which lead to the synchronized state and white squares represent initial conditions which lead to a periodic oscillating state . the stability of the synchronized state is : ( a ) type ( v ) unstable ; ( b ) type ( i ) stable ; ( c ) type ( ii).,title="fig : " ] evolves for different initial conditions for @xmath103 with ( a ) @xmath104 , ( b ) @xmath105 , ( c ) @xmath106 . black squares represent initial conditions which lead to the synchronized state and white squares represent initial conditions which lead to a periodic oscillating state . the stability of the synchronized state is : ( a ) type ( v ) unstable ; ( b ) type ( i ) stable ; ( c ) type ( ii).,title="fig : " ] evolves for different initial conditions for @xmath103 with ( a ) @xmath104 , ( b ) @xmath105 , ( c ) @xmath106 . black squares represent initial conditions which lead to the synchronized state and white squares represent initial conditions which lead to a periodic oscillating state . the stability of the synchronized state is : ( a ) type ( v ) unstable ; ( b ) type ( i ) stable ; ( c ) type ( ii).,title="fig : " ] ( 10,10)(0,0 ) ( 120,10 ) ( 0,130 ) ( 268,10 ) ( 147,130 ) ( 418,10 ) ( 298,130 ) ( 70,4 ) ( 218,4 ) ( 369,4 ) for @xmath104 , all initial conditions lead to an oscillating state and the synchronized state is unstable ( type ( v ) ) . the black squares in figure [ fig : icphasediagram ] are initially in the synchronized state . many squares along the line @xmath42 are white because a small amount of numerical noise drives the system away from the synchronized state . for @xmath105 , initial conditions close to @xmath42 lead to the synchronized state , but initial conditions far from @xmath42 lead to an oscillating state . the synchronized state is stable ( type ( i ) ) . for @xmath106 , most initial conditions close to @xmath42 lead to the synchronized state , but a few initial conditions close to @xmath42 lead to an oscillating state and we have type ( ii ) stability ; if @xmath37 starts close to the synchronized state , it is likely to evolve into the synchronized state and it will stay in the synchronized state if there is no noise , but it is also possible for the cell to start close to the synchronized state and move away into an oscillating state . in an oscillating state the cell can still swim , but there will be more side to side movement . there appear to be a few white squares on the line @xmath107 , however this is because the grid does not lie exactly on the @xmath78 line , the grid contains points @xmath108 and @xmath109 and this small deviation from the synchronized state @xmath110 is enough for evolution into an oscillating state for a few choices of @xmath84 . similar behaviour is observed for other harmonics , but with different ranges of coefficients giving the different stability types for the synchronized state . for example , figure [ fig : harm4 ] shows the 4th harmonic for three different coefficients of cosine and initial condition @xmath111 . figure [ fig : harm4](a ) shows that @xmath37 oscillate about @xmath89 for @xmath112 , oscillations are close to zero for @xmath113 ( it is interesting to note the 4 peaks in every cycle ) , and @xmath37 evolves into the synchronized state for @xmath114 . for the 4th harmonic with initial condition @xmath111 and coefficient ( a ) @xmath112 , ( b ) @xmath113 , ( c ) @xmath114 . ( a ) , ( b ) @xmath37 evolves into different oscillating states . ( c ) @xmath37 evolves into the synchronized state . the insets show a small part of the plot in more detail.,title="fig : " ] for the 4th harmonic with initial condition @xmath111 and coefficient ( a ) @xmath112 , ( b ) @xmath113 , ( c ) @xmath114 . ( a ) , ( b ) @xmath37 evolves into different oscillating states . ( c ) @xmath37 evolves into the synchronized state . the insets show a small part of the plot in more detail.,title="fig : " ] for the 4th harmonic with initial condition @xmath111 and coefficient ( a ) @xmath112 , ( b ) @xmath113 , ( c ) @xmath114 . ( a ) , ( b ) @xmath37 evolves into different oscillating states . ( c ) @xmath37 evolves into the synchronized state . the insets show a small part of the plot in more detail.,title="fig : " ] ( 10,10)(0,0 ) ( 81,7 ) ( 222,7 ) ( 370,7 ) ( 10,88 ) ( 144,26 ) ( 151,88 ) ( 286,26 ) ( 291,86 ) ( 424,28 ) figure [ fig : harmstab ] shows the stability of the synchronized state for the first 10 harmonics for a discrete range of coefficients when we choose the cosine term , i.e. @xmath115 . . orange blocks represent stability ( i ) ; dark blue blocks represent stability ( ii ) ; pale blue blocks represent stability ( iii ) ; pale green blocks represent stability ( iv ) ; and bright green blocks represent stability ( v ) . ] ( 10,10)(0,0 ) ( 96,147 ) ( 225,12 ) we see that there are more type ( i ) and ( ii ) force profiles for negative coefficients than for positive , showing that we are more likely to end up in the synchronized state when the coefficient is negative than when the coefficient is positive , for an arbitrary choice of harmonic . we see that for @xmath116 there is no type ( i ) behaviour , so we can not guarantee that we will reach the synchronized states for these higher harmonics . the unstable type ( v ) band around @xmath117 gets narrower as @xmath118 increases , so we only need weak phase dependence to reach a synchronized state for higher harmonics , but the region of initial conditions which does lead to the synchronized state is very small . even after reaching the synchronized state , it is likely that noise will drive @xmath37 away from the synchronized state . usually the stability moves towards the lower types of stability ( more stable types ) as @xmath119 increases for each harmonic , although there are some exceptions . for example , when @xmath120 we can start in a type ( i ) region , then as @xmath121 increases we move into a type ( ii ) region . we also see a type ( iii ) region surrounded by type ( iv ) regions on both sides for @xmath122 and @xmath123 . for each type of stability shown in figure [ fig : harmstab ] , we select an arbitrary force profile and show the full initial condition phase diagram in figure [ fig : icselection ] . in the type ( i ) stable case , we see that oscillating states can still evolve ( see also figure [ fig : icphasediagram ] ) , but the initial conditions for an oscillating state are not close to the synchronized case . in a few cases when we replace the cosine with sine , all initial conditions lead to the synchronized state , for example , the force profile @xmath124 for @xmath125 , except for a very thin dotted white curve through the middle of the phase diagram indicating an unstable oscillating state . however , if we look at this oscillating state for long enough , after some time the numerical noise causes it to move into the synchronized state . . ( a ) type ( i ) stable diagrams for @xmath126 and @xmath127 . ( b ) type ( ii ) stability for @xmath128 and @xmath129 . ( c ) type ( iii ) stability for @xmath128 and @xmath130 . ( d ) type ( iv ) stability for @xmath131 and @xmath132 . ( e ) type ( v ) stability for @xmath133 and @xmath134.,title="fig : " ] . ( a ) type ( i ) stable diagrams for @xmath126 and @xmath127 . ( b ) type ( ii ) stability for @xmath128 and @xmath129 . ( c ) type ( iii ) stability for @xmath128 and @xmath130 . ( d ) type ( iv ) stability for @xmath131 and @xmath132 . ( e ) type ( v ) stability for @xmath133 and @xmath134.,title="fig : " ] . ( a ) type ( i ) stable diagrams for @xmath126 and @xmath127 . ( b ) type ( ii ) stability for @xmath128 and @xmath129 . ( c ) type ( iii ) stability for @xmath128 and @xmath130 . ( d ) type ( iv ) stability for @xmath131 and @xmath132 . ( e ) type ( v ) stability for @xmath133 and @xmath134.,title="fig : " ] + . ( a ) type ( i ) stable diagrams for @xmath126 and @xmath127 . ( b ) type ( ii ) stability for @xmath128 and @xmath129 . ( c ) type ( iii ) stability for @xmath128 and @xmath130 . ( d ) type ( iv ) stability for @xmath131 and @xmath132 . ( e ) type ( v ) stability for @xmath133 and @xmath134.,title="fig : " ] . ( a ) type ( i ) stable diagrams for @xmath126 and @xmath127 . ( b ) type ( ii ) stability for @xmath128 and @xmath129 . ( c ) type ( iii ) stability for @xmath128 and @xmath130 . ( d ) type ( iv ) stability for @xmath131 and @xmath132 . ( e ) type ( v ) stability for @xmath133 and @xmath134.,title="fig : " ] ( 10,10)(0,0 ) ( 73,161 ) ( 219,161 ) ( 367,161 ) ( 143,2 ) ( 297,2 ) ( 0,288 ) ( 122,169 ) ( 148,288 ) ( 269,169 ) ( 295,288 ) ( 416,169 ) ( 71,134 ) ( 192,12 ) ( 225,134 ) ( 345,12 ) we see from the bright green band down the center of figure [ fig : harmstab ] that we need some form of phase dependence in order to achieve synchronization . if we choose a constant driving force then @xmath37 evolves into an oscillating state for all initial conditions . the synchronized state is unstable , so even if we start in the synchronized state , a small amount of numerical noise can drive the system into the oscillating state . friedrich _ et al . _ showed that synchronization can occur with constant forcing when the direction of rotation of the beads is reversed ( equivalent to @xmath135 and reversing swimming direction ) but here we focus on the case @xmath136 and @xmath74 . the inspiration for our run - and - tumble model in reference @xcite came from the initial condition phase diagrams . to see run - and - tumble we want to start in a stable synchronized state , then allow noise to move us temporarily into a white region of the phase diagram , before moving back into a black region . in reference @xcite , we allowed noise to vary the coefficients @xmath137 , so that a black square in the noiseless phase diagram can change to a white square when the instantaneous effect of the noise changes the value of @xmath137 , then changes back to a black square when the instantaneous effect of the noise is smaller . this allows us to start in the synchronized state ( with fluctuations due to the noise ) , then move away from the synchronized state when the instantaneous noise is large and we are at a suitable point in the phase diagram , then move back into the fluctuating synchronized state when the instantaneous noise is small . in reference @xcite , we chose to work with the first harmonic and use @xmath138 , where @xmath139 is the noise term . we chose the value 0.7 because it is in the stability type ( i ) region , but lies close to the type ( ii ) region . in the fluctuating synchronized state , when we move through the values of @xmath140 which are surrounded by white squares in the type ( ii ) phase diagram , there is the possibility to move into an oscillating state , but there are still plenty of black squares surrounding the line @xmath42 , so we can have long periods in the _ run _ phase . the noise causes fluctuations of the position in the phase diagram , and this could also be a cause of run - and - tumble behaviour . for example , consider the phase diagram in figure [ fig : icselection](a ) . if we are in the synchronized state and noise is small enough such that fluctuations in @xmath37 are within the black region , then tumbles will not occur . if the noise is larger , so @xmath37 fluctuations move into the white region , then the cell could begin to move into the oscillating state , and after a few oscillations noise could kick the oscillations into the black region and the cell would move back towards a synchronized state . elsewhere , we will consider the effects of adding noise to @xmath39 and @xmath141 , without any noise in the coefficient , to see if we obtain run - and - tumble behaviour this way and compare the statistics to the run - and - tumble obtained when noise is added to the coefficient . if we start in the synchronized state , then @xmath142 which is non - zero for @xmath143 , so the system does not stay in the synchronized state . we focus on the first harmonic and consider the case @xmath144 and @xmath145 where @xmath146 ( and we have dropped the upper index on the coefficient ) . when @xmath147 and @xmath148 , synchronization is frustrated and @xmath37 oscillates about @xmath149 , @xmath80 , shown in figure [ fig : mc](a ) for @xmath150 . the orientation of the cell drifts , shown in figure [ fig : mc](b ) so the cell swims along a curved trajectory . for @xmath151 , the centre of @xmath37 oscillations drifts away from the synchronized state , but remains close to @xmath152 . swapping the signs of the coefficients swaps the direction of the orientation drift . when the coefficients have the same sign but different magnitudes , @xmath37 oscillates about @xmath153 and the orientation oscillates about some fixed value . figure [ fig : mc](c ) shows the evolution of @xmath37 for @xmath154 . this type of behaviour is also seen for some choices of equal coefficients , for example , in figure [ fig : devolutions1](e ) , ( f ) where @xmath155 . choices of coefficients which give this type of behaviour can be used to model a mutant of _ chlamydomonas _ which swims with antiphase synchrony @xcite . when the model swims with antiphase beating , the beat frequency is higher than when it swims with in phase beating , which has been observed in real _ chlamydomonas _ cells @xcite . and ( b ) , ( d ) , ( f ) corresponding orientation @xmath90 for force profiles @xmath156 and initial conditions @xmath157 , @xmath158 and with ( a ) , ( b ) @xmath150 ; ( c ) , ( d ) @xmath154 ; ( e ) , ( f ) @xmath159 . each inset shows a small part of the main plot in more detail.,title="fig : " ] and ( b ) , ( d ) , ( f ) corresponding orientation @xmath90 for force profiles @xmath156 and initial conditions @xmath157 , @xmath158 and with ( a ) , ( b ) @xmath150 ; ( c ) , ( d ) @xmath154 ; ( e ) , ( f ) @xmath159 . each inset shows a small part of the main plot in more detail.,title="fig : " ] and ( b ) , ( d ) , ( f ) corresponding orientation @xmath90 for force profiles @xmath156 and initial conditions @xmath157 , @xmath158 and with ( a ) , ( b ) @xmath150 ; ( c ) , ( d ) @xmath154 ; ( e ) , ( f ) @xmath159 . each inset shows a small part of the main plot in more detail.,title="fig : " ] + and ( b ) , ( d ) , ( f ) corresponding orientation @xmath90 for force profiles @xmath156 and initial conditions @xmath157 , @xmath158 and with ( a ) , ( b ) @xmath150 ; ( c ) , ( d ) @xmath154 ; ( e ) , ( f ) @xmath159 . each inset shows a small part of the main plot in more detail.,title="fig : " ] and ( b ) , ( d ) , ( f ) corresponding orientation @xmath90 for force profiles @xmath156 and initial conditions @xmath157 , @xmath158 and with ( a ) , ( b ) @xmath150 ; ( c ) , ( d ) @xmath154 ; ( e ) , ( f ) @xmath159 . each inset shows a small part of the main plot in more detail.,title="fig : " ] and ( b ) , ( d ) , ( f ) corresponding orientation @xmath90 for force profiles @xmath156 and initial conditions @xmath157 , @xmath158 and with ( a ) , ( b ) @xmath150 ; ( c ) , ( d ) @xmath154 ; ( e ) , ( f ) @xmath159 . each inset shows a small part of the main plot in more detail.,title="fig : " ] ( 10,10)(0,0 ) ( 83,107 ) ( 83,9 ) ( 226,107 ) ( 226,9 ) ( 368,107 ) ( 368,9 ) ( 12,188 ) ( 148,125 ) ( 16,84 ) ( 149,80 ) ( 155,188 ) ( 288,125 ) ( 165,94 ) ( 290,41 ) ( 295,182 ) ( 430,159 ) ( 304,85 ) ( 431,78 ) when the coefficients have opposite signs and different magnitudes , there are two main types of behaviour that occur . for @xmath160 and @xmath161 or @xmath162 and @xmath163 , then @xmath37 oscillates periodically and the corresponding orientation drifts in the negative direction in the former case and in the positive direction in the latter case . this is shown in figure [ fig : mc](e ) , ( f ) for @xmath159 . for @xmath160 and @xmath164 or @xmath162 and @xmath165 , then oscillations in phase difference , @xmath37 , drift in the negative ( positive ) direction and the orientation drifts in the positive ( negative ) direction in the former ( latter ) case . figure [ fig : deldrift ] shows examples of this this case where one bead completes more cycles than the other bead . there is a difference in the mean angular velocity of the two beads without choosing a different @xmath60 for each bead . and corresponding orientation for ( a ) , ( b ) @xmath166 and @xmath167 ; ( c ) , ( d ) @xmath168 and @xmath169 . the insets show a small part of the plot in more detail.,title="fig : " ] and corresponding orientation for ( a ) , ( b ) @xmath166 and @xmath167 ; ( c ) , ( d ) @xmath168 and @xmath169 . the insets show a small part of the plot in more detail.,title="fig : " ] + and corresponding orientation for ( a ) , ( b ) @xmath166 and @xmath167 ; ( c ) , ( d ) @xmath168 and @xmath169 . the insets show a small part of the plot in more detail.,title="fig : " ] and corresponding orientation for ( a ) , ( b ) @xmath166 and @xmath167 ; ( c ) , ( d ) @xmath168 and @xmath169 . the insets show a small part of the plot in more detail.,title="fig : " ] ( 10,10)(0,0 ) ( 128,136 ) ( 128,6 ) ( 325,136 ) ( 325,6 ) ( 40,234 ) ( 207,236 ) ( 32,108 ) ( 209,65 ) ( 239,239 ) ( 406,154 ) ( 228,109 ) ( 408,80 ) so far we have considered force profiles with only one harmonic term . now we consider driving forces with contributions from two harmonics . for simplicity we choose equal profiles for the left and right beads , @xmath170 , and of the form @xmath171 , @xmath172 and with the @xmath173 s chosen such that @xmath174 for all real @xmath140 . figure [ fig : harm12 ] shows the stability of the synchronized state for @xmath175 and @xmath176 . each grid square represents a choice of driving force with coefficients @xmath177 , @xmath178 and the colour represents the stability of the synchronized state for that particular driving force . , ( b ) @xmath179 . the colour of each square represents the following stability : orange represents type ( i ) ; dark blue represents type ( ii ) ; pale blue represents type ( iii ) ; pale green represents type ( iv ) ; bright green represents type ( v).,title="fig : " ] , ( b ) @xmath179 . the colour of each square represents the following stability : orange represents type ( i ) ; dark blue represents type ( ii ) ; pale blue represents type ( iii ) ; pale green represents type ( iv ) ; bright green represents type ( v).,title="fig : " ] ( 10,10)(0,0 ) ( 125,4 ) ( 322,4 ) ( 193,16 ) ( 392,16 ) ( 34,170 ) ( 232,170 ) we see that there are large regions for which the synchronized state is type ( i ) stable . conclusion this simple mechanical model is able to evolve into a stable synchronized state for certain choices of parameters in the driving force when the initial condition is within some region of the synchronized state . we do not need hydrodynamic interactions to achieve stable synchronization ; we include hydrodynamic friction on each bead , with force free and torque free conditions and a phase dependent driving force , which can be constructed with a suitable combination of harmonic terms . for many choices of force profile , some initial conditions allow the model to evolve into the synchronized state , while other initial conditions that are very close to the synchronized state lead to an oscillating state . there are some force profiles , including constant forcing , where there are no initial conditions that evolve into the synchronized state , and if the system starts in the synchronized state when the driving forces are equal , even a small amount of numerical noise can drive the system into an oscillating state . there are different types of periodic behaviour for different choices of parameters in the driving force ; often the phase difference oscillates about @xmath89 , but sometimes the oscillations can occur close to zero with multiple peaks per cycle . when the parameter in the driving force is different for the left and right beads , we can get periodic oscillating states about a range of values , or we can get a drifting oscillating state , where one bead has a higher average angular velocity than the other . when the coefficients have equal magnitude and opposite sign , this can lead to oscillations about the synchronized state . this frustrated synchronization is interesting when we add intrinsic noise to the driving force , because then the behaviour of @xmath37 is very similar for both opposite coefficients and equal coefficients , although the behaviour in the orientation is different in the two cases . the nonlinear mechanics of the system make it difficult to study analytically and it is not easy to predict the parameter ranges which give stable synchronization . our numerical results have highlighted some of the main types of behaviour of the model . an important feature is that it is necessary to have some sort of phase dependent driving force in order to have a stable type ( i ) or type ( ii ) synchronized state . when the phase dependence is only weak , then the synchronized state is unstable , which we see from figure [ fig : harmstab ] when the coefficient is small . the value of the coefficient at which the phase dependence becomes strong enough to give synchronization depends on the harmonic , whether we choose a positive or negative coefficient , and whether we choose sine or cosine . these latter choices are equivalent to adding a constant phase @xmath180 , @xmath89 or @xmath181 in the harmonic term . this simple mechanical model shows a wide range of behaviour when we vary the parameter in the driving forces . the variety of stabilities suggests possibilities for developing run - and - tumble models , where noise can be used to to jump between regions of a phase diagram that lead to synchronization or oscillations , or jump between phase diagrams as we did in reference @xcite . we would like to thank nariya uchida for fruitful discussions and the epsrc for financial support .

the emergence of non trivial collective behaviour in multidimensional systems has been analized in the last years by many authors @xcite @xcite @xcite . those important class of systems are the ones that present global interactions . a basic model extensively analized by kaneko is an unidimensional array of @xmath0 elements : @xmath1 where @xmath2 , is an index identifying the elements of the array , @xmath3 a temporal discret variable , @xmath4 is the coupling parameter and @xmath5 describes the local dynamic and taken as the logistic map . in this work , we consider @xmath5 as a cubic map given by : @xmath6 where @xmath7 $ ] is a control parameter and @xmath8 $ ] . the map dynamic has been extensively studied by testa et.al.@xcite , and many applications come up from artificial neural networks where the cubic map , as local dynamic , is taken into account for modelizing an associative memory system . @xcite proposed a gcm model to modelize this system optimazing the hopfield s model . the subarmonic cascade , showed on fig-[fig:2 ] prove the coexistence of two equal volume stable attractors . the later is verified even as the gcm given by eq.[eq : sist ] has @xmath9 . janosi et . @xcite studied a globally coupled multiattractor quartic map with different volume basin attractors , which is as simple second iterate of the map proposed by kaneko , emphazasing their analysis on the control parameter of the local dynamic . they showed that for these systems the mean field dynamic is controlled by the number of elements in the initial partition of each basin of attraction . this behaviour is also present in the map used in this work . in order to study the coherent - ordered phase transition of the kaneko s gcm model , cerdeira et . @xcite analized the mechanism of the on - off intermitency appearing in the onset of this transition . since the cubic map is characterized by a dynamic with multiple attractors , the first step to determine the differences with the well known cuadratic map given by kaneko is to obtain the phase diagram of eq.[eq : sist ] and to study the the coherent - ordered dynamical transition for a fixed value of the control parameter @xmath10 . the later is done near an internal crisis of the cubic map , as a function of the number of elements @xmath11 with initial conditions in one basin and the values of the coupling parameter @xmath4 , setting @xmath0 equal to 256 . after that , the existence of an inverse period doubling bifurcation as function of @xmath4 and @xmath11 is analized . the dynamical analysis process breaks the phase space in sets formed by synchronized elements which are called clusters . this is so , even when , there are identical interactions between identical elements . the system is labeled as _ 1-cluster _ , _ 2-cluster _ , etc . state if the @xmath12 values fall into one , two or more sets of synchronized elements of the phase space . two different elements @xmath13 and @xmath14 belong to the same cluster within a precision @xmath15 ( we consider @xmath16 ) only if @xmath17 thus the system of eq.[eq : sist ] , shows the existence of different phases with clustering ( coherent , ordered , partially ordered , turbulent ) . this phenomena appearing in gcm was studied by kaneko for logistic coupled maps when the control and coupling parameters vary . a rough phase diagram for an array of 256 elements is determined for the number of clusters calculated from 500 randomly sets of initial conditions within the precision specified above . this diagram displayed in fig-[fig:1 ] , was obtained following the criteria established by this author . therefore , the @xmath18 number of clusters and the number of elements that build them are relevant magnitudes to characterize the system behaviour . in order to study phase transition , the two greatest lyapunov exponents are shown in fig-[fig:4 ] and fig-[fig:5 ] . they are depicted for a=3.34 as a function of @xmath4 and for three different values of initial elements @xmath11 . in the coherent phase , as soon as @xmath4 decrease , the maximum lyapunov exponent changes steeply from a positive to a negative value when the two cluster state is reached . a sudden change in the attractor phase space occurs for a critical value of the coupling parameter @xmath19 in the analysis of the transition from two to one cluster state . besides that , in the same transition for the same @xmath19 , a metastable transient state of two cluster to one cluster chaotic state is observed , due to the existence of an unstable orbit inside of the chaotic basin of attraction , as is shown in fig-[fig:3 ] the characteristic time @xmath20 in which the system is entertained in the metastable transient is depicted in fig-[fig:6 ] , for values of @xmath4 near and above @xmath19 . for a given set of initial conditions , it is possible to fit this transient as : @xmath21 this fitting exponent @xmath22 , depends upon the number of elements with initial conditions in each basin as is shown in the next table for three @xmath11 values and setting @xmath23 . [ cols="<,<,<",options="header " , ] it is worth noting from the table that @xmath22 increases with @xmath11 up to @xmath24 , and for @xmath11 due to the basins symmetry . in order to analize the existence of period doubling bifurcations , the maxima lyapunov exponent @xmath25 is calculated as function of @xmath11 and @xmath4 . for each @xmath11 , critical values of the coupling parameter , called @xmath26 , are observed when a negative @xmath25 reaches a zero value without changing sign . this behaviour is related to inverse period doubling bifurcations of the gcm . fitting all these critical pair of values @xmath27 , a rough @xmath11 vs @xmath26 graph is shown in fig-[fig:7 ] , and different curves appears as boundary regions of the parameter space where the system displays @xmath28 ( @xmath29 ) periods states . this is obtained without taking into accout the number of final clusters . it is clear that greater values of @xmath11 , correspond to smaller @xmath26 for the occurrence of the bifurcation . evidence of period 16 appears for values of @xmath30 smaller than 30 . in fig-[fig:7 ] t=2(symmetric ) means period two orbit , with clusters oscillating with equal amplitud around zero , t=2(asymmetric ) means period two orbit , with clusters oscillating with different amplitud . the study of systems with coexistence of multiple attractors gives a much richer dynamics and a new control parameter must necessarily be added . although the dimensionality in the parameter space is increased by one , the dynamics is rather simple to characterize . some of the relevant aspects of this kind of systems are shown in this work . the phase diagram that was obtained shows the existence of similar phases to those using the cuadratic and quartic map , this behaviour suggests some kind of universality in the dynamics of the gcm . another interesting issue found , concerns the metastable transition between two to one cluster state , along with a sudden jump in the maximum lyapunov exponent , as it was displayed in fig.[fig:7 ] . the characteristic time given by eq.[eq:1 ] also correspond to the above transition where the critical exponent @xmath31 and the critical coupling parameter @xmath32 shows a strong dependence on the number of initial elements in each basin . an inverse bifurcation cascade appears when the system is in two or more clusters state where @xmath32 and @xmath30 are the critical parameters of the bifurcation , which means the maximum lyapunov exponent is equal to zero . this work is partially supported by conicet ( grant pip 4210 ) . mfc and lr also express their acknowledgment to the ictp where the initial discussion of the work was performed .

a system of n unidimensional global coupled maps ( gcm ) , which support multiattractors is studied . we analize the phase diagram and some special features of the transitions ( volumen ratios and characteristic exponents ) , by controlling the number of elements of the initial partition that are in each basin of attraction . it was found important differences with widely known coupled systems with a single attractor .

it is an extrapolation of 18 orders of magnitude from the neutron radius of a heavy nucleus such as @xmath1pb with a neutron radius of @xmath2 fm to the approximately 10 km radius of a neutron star . yet both radii depend on our incomplete knowledge of the equation of state of neutron - rich matter . that strong correlations arise among objects of such disparate sizes is not difficult to understand . heavy nuclei develop a neutron - rich skin as a result of its large neutron excess ( _ e.g. , _ @xmath3 in @xmath1pb ) and because the large coulomb barrier reduces the proton density at the surface of the nucleus . thus the thickness of the neutron skin depends on the pressure that pushes neutrons out against surface tension . as a result , the greater the pressure , the thicker the neutron skin @xcite . yet it is this same pressure that supports a neutron star against gravitational collapse @xcite . thus models with thicker neutron skins often produce neutron stars with larger radii @xcite . the above discussion suggests that an accurate and model - independent measurement of the neutron skin of even a single heavy nucleus may have important implications for neutron - star properties . attempts at mapping the neutron distribution have traditionally relied on strongly - interacting probes . while highly mature and successful , it is unlikely that the hadronic program will ever attain the precision status that the electroweak program enjoys . this is due to the large and controversial uncertainties in the reaction mechanism @xcite . the mismatch in our knowledge of the proton radius in @xmath0pb relative to that of the neutron radius provides a striking example of the current situation : while the charge radius of @xmath0pb is known to better than 0.001 fm @xcite , realistic estimates place the uncertainty in the neutron radius at about 0.2 fm @xcite . the enormously successful parity - violating program at the jefferson laboratory @xcite provides an attractive electroweak alternative to the hadronic program . indeed , the parity radius experiment ( prex ) at the jefferson laboratory aims to measure the neutron radius of @xmath1pb accurately ( to within @xmath4 fm ) and model independently via parity - violating electron scattering @xcite . parity violation at low momentum transfers is particularly sensitive to the neutron density because the @xmath5 boson couples primarily to neutrons . moreover , the parity - violating asymmetry , while small , can be interpreted with as much confidence as conventional electromagnetic scattering experiments . prex will provide a unique observational constraint on the thickness of the neutron skin of a heavy nucleus . we note that since first proposed in 1999 , many of the technical difficulties intrinsic to such a challenging experiment have been met . for example , during the recent activity at the hall a proton parity experiment ( happex ) , significant progress was made in controlling helicity correlated errors @xcite . other technical problems are currently being solved such as the designed of a new septum magnet and a specific timeline has been provided to solve all remaining problems within the next two years @xcite . our aim in this contribution is to report on some of our recent results that examine the correlation between the neutron skin of @xmath0pb and various neutron - star properties @xcite . in particular , we examine the consequences of a `` softer '' equation of state that is based on a new accurately calibrated relativistic parameter set that has been constrained by both the ground state properties of finite nuclei and their linear response . further , results obtained with this new parameter set dubbed `` fsugold '' @xcite will be compared against the nl3 parameter set of lalazissis , konig , and ring @xcite that , while highly successful , predicts a significantly stiffer equation of state . the starting point for the calculation of the properties of finite nuclei and neutron stars is an effective field - theory model based on the following lagrangian density : @xmath6\psi \nonumber \\ & & - \frac{\kappa}{3 ! } ( g_{\rm s}\phi)^3 \!-\ ! \frac{\lambda}{4!}(g_{\rm s}\phi)^4 \!+\ ! \frac{\zeta}{4 ! } \big(g_{\rm v}^2 v_{\mu}v^\mu\big)^2 \!+\ ! \lambda_{\rm v } \big(g_{\rho}^{2}\,{\bf b}_{\mu}\cdot{\bf b}^{\mu}\big ) \big(g_{\rm v}^2v_{\mu}v^\mu\big ) \;. \label{lagrangian}\end{aligned}\ ] ] the lagrangian density includes an isodoublet nucleon field ( @xmath7 ) interacting via the exchange of two isoscalar mesons a scalar ( @xmath8 ) and a vector ( @xmath9 ) one isovector meson ( @xmath10 ) , and the photon ( @xmath11 ) @xcite . in addition to meson - nucleon interactions , the lagrangian density is supplemented by four nonlinear meson interactions , with coupling constants denoted by @xmath12 , @xmath13 , @xmath14 , and @xmath15 . the first three of these terms are responsible for a softening of the equation of state of symmetric nuclear matter at both normal and high densities @xcite . in particular , the cubic ( @xmath12 ) and quartic ( @xmath13 ) scalar self - energy terms are needed to reduce the compression modulus of symmetric nuclear matter , in accordance to measurements of the giant monopole resonance in medium to heavy nuclei @xcite . in turn , @xmath16-meson self - interactions ( @xmath14 ) are instrumental for the softening of the equation of state at high density thereby affecting primarily the limiting masses of neutron stars @xcite . finally , the last of the coupling constants ( @xmath15 ) induces isoscalar - isovector mixing and has been added to tune the poorly - known density dependence of the symmetry energy @xcite . as a result of the strong correlation between the neutron radius of heavy nuclei and the pressure of neutron - rich matter @xcite , the neutron skin of a heavy nucleus is highly sensitive to changes in @xmath15 . [ cols="<,^,^,^,^,^,^,^,^",options="header " , ] in conclusion , a new accurately calibrated relativistic model ( `` fsugold '' ) has been fitted to the binding energies and charge radii of a variety of magic nuclei . in this regard , the new parametrization is as successful as the nl3 set which has been used here as a useful paradigm . in particular , symmetric nuclear matter saturates at a fermi momentum of @xmath17 ( corresponding to a baryon density of @xmath18 ) with a binding energy per nucleon of @xmath19 mev . further , by constraining the fsugold parameter set by a few nuclear collective modes , we obtain a nuclear - matter incompressibility of @xmath20 mev and a neutron skin thickness in @xmath0pb of @xmath21 fm . while the description of the various collective modes imposes additional constraints on the eos at densities around saturation density , the high - density component of the eos remains largely unconstrained . thus , we made no attempts at constraining the eos at the supranuclear densities of relevance to neutron - star physics . rather , we simply explored the consequences of the new parametrization on a variety of neutron star observables and eagerly await high - quality data that will constrain the high - density component of the eos . in particular , we found a limiting neutron - star mass of @xmath22 , a radius of @xmath23 km for a @xmath24 neutron star , and no direct urca cooling in neutron stars with masses below @xmath25 . it is interesting to note that recent observations of pulsar - white dwarf binaries at the arecibo observatory suggest a pulsar mass for psrj0751 + 1807 of @xmath26 at a 95% confidence level @xcite . if this observation could be refined , not only would it redefine the high - density behavior of this ( and many other ) eos , but it could provide us with a precious boost in our quest for the equation of state .

the nucleus of @xmath0pb a system that is 18 order of magnitudes smaller and 55 orders of magnitude lighter than a neutron star may be used as a miniature surrogate to establish important correlations between its neutron skin and several neutron - star properties . indeed , a nearly model - independent correlation develops between the neutron skin of @xmath1pb and the liquid - to - solid transition density in a neutron star . further , we illustrate how a measurement of the neutron skin in @xmath0pb may be used to place important constraints on the cooling mechanism operating in neutron stars and may help elucidate the existence of quarks stars .

it is by now standard to parameterize transverse momentum distributions with functions having a power law behaviour at high momenta . this has been done by the star @xcite and phenix @xcite collaborations at rhic and by the alice @xcite , atlas @xcite and cms @xcite collaborations at the lhc . in this talk we would like to pursue the use of the tsallis distribution to describe transverse momentum distributions at the highest beam energies . + in the framework of tsallis statistics @xcite the entropy @xmath1 , the particle number , @xmath2 , the energy density @xmath3 and the pressure @xmath4 are given by corresponding integrals over the tsallis distribution : @xmath5^{-\frac{1}{q-1 } } .\label{tsallis}\ ] ] it can be shown ( see e.g. @xcite ) that the relevant thermodynamic quantities are given by : @xmath6 , \label{entropy } \\ n & = & gv\int\frac{d^3p}{(2\pi)^3 } f^q , \label{number } \\ \epsilon & = & g\int\frac{d^3p}{(2\pi)^3}e f^q , \label{epsilon}\\ p & = & g\int\frac{d^3p}{(2\pi)^3}\frac{p^2}{3e } f^q\label{pressure } .\end{aligned}\ ] ] where @xmath7 and @xmath8 are the temperature and the chemical potential , @xmath9 is the volume and @xmath10 is the degeneracy factor . we have used the short - hand notation @xmath11 often referred to as q - logarithm . it is straightforward to show that the relation @xmath12 ( where @xmath13 refer to the densities of the corresponding quantities ) is satisfied . the first law of thermodynamics gives rise to the following differential relations : @xmath14 since these are total differentials , thermodynamic consistency requires the following maxwell relations to be satisfied : @xmath15 this is indeed the case , e.g. for eq . this follows from @xmath16^{-\frac{q}{q-1 } } \nonumber \\ & = & - g\int\frac{d^3p}{(2\pi)^3}\frac{p^2}{3 } \frac{d}{pdp}\left [ 1 + ( q-1 ) \frac{e-\mu}{t}\right]^{-\frac{q}{q-1 } } \nonumber \\ & = & g\int\frac{d\cos\theta d\phi dp}{(2\pi)^3 } \left [ 1 + ( q-1 ) \frac{e-\mu}{t}\right]^{-\frac{q}{q-1 } } \frac{d}{dp}\frac{p^3}{3 } \nonumber \\ & = & n \nonumber\end{aligned}\ ] ] after an integration by parts and using @xmath17 . + following from eq . , the momentum distribution is given by : @xmath18^{-q/(q-1 ) } , \label{tsallismu}\ ] ] or , expressed in terms of transverse momentum , @xmath19 , the transverse mass , @xmath20 , and the rapidity @xmath21 @xmath22^{-q/(q-1 ) } . \label{tsallismu1}\ ] ] at mid - rapidity , @xmath23 , and for zero chemical potential , as is relevant at the lhc , this reduces to @xmath24^{-q/(q-1)}. \label{tsallisfit1}\ ] ] in the limit where the parameter @xmath0 goes to 1 it is well - known that this reduces to the standard boltzmann distribution : @xmath25 the parameterization given in eq . is close to the one used by various collaborations @xcite : @xmath26^{-n } , \label{alice}\ ] ] where @xmath27 and @xmath28 are fit parameters . this corresponds to substituting @xcite @xmath29 and @xmath30 after this substitution eq . becomes @xmath31^{-q/(q-1)}\nonumber\\ & & \left [ 1 + ( q-1)\frac{m_t}{t } \right]^{-q/(q-1 ) } . \label{alice2}\end{aligned}\ ] ] at mid - rapidity @xmath32 and zero chemical potential , this has the same dependence on the transverse momentum as eq . apart from an additional factor @xmath33 on the right - hand side of eq . . however , the inclusion of the rest mass in the substitution eq . is not in agreement with the tsallis distribution as it breaks @xmath33 scaling which is present in eq . but not in eq . . the inclusion of the factor @xmath33 leads to a more consistent interpretation of the variables @xmath0 and @xmath7 . + a very good description of transverse momenta distributions at rhic has been obtained in refs @xcite on the basis of a coalescence model where the tsallis distribution is used for quarks . tsallis fits have also been considered in ref . @xcite but with a different power law leading to smaller values of the tsallis parameter @xmath0 . + interesting results were obtained in refs . @xcite where spectra for identified particles were analyzed and the resulting values for the parameters @xmath0 and @xmath7 were considered . + the transverse momentum distributions of identified particles , as obtained by the alice collaboration at 900 gev in @xmath34 collisions , are shown in figure fig : positive . the fit for positive pions was made using @xmath35^{-q/(q-1)}. \label{tsallisfitpi}\ ] ] with @xmath0 , @xmath7 and @xmath9 as free parameters . + + in figure strange we show fits to the transverse momentum distributions of strange particles obtained by the alice collaboration @xcite in @xmath34 collisions at 900 gev . + similarly we show fits to the transverse momentum distributions obtained by the cms collaboration @xcite in figure cms and by the atlas collaboration in figure chargedatlas . + the transverse momentum distributions of charged particles were fitted using a sum of three tsallis distributions , the first one for @xmath36 , the second one for @xmath37 and the third one for protons @xmath38 . the relative weights between these were determined by the corresponding degeneracy factors , i.e. 1 for for @xmath36 and @xmath37 and 2 for protons . the fit was taken at mid - rapidity and for @xmath39 using the following expression was used @xmath40^{-\frac{q}{q-1}},\ ] ] where @xmath41 and @xmath42 , @xmath43 and @xmath44 . the factor @xmath45 in front of the right hand side of this equation takes into account the contributions of the antiparticles @xmath46 . the tsallis distribution also describes the transverse momentum distributions of charged particles in @xmath47 collisions in all pseudorapidity intervals as shown in figure ppb . + collisions obtained by the alice collaboration @xcite using the tsallis distribution.,height=377 ] collisions obtained by the alice collaboration @xcite using the tsallis distribution.,height=377 ] obtained from fits to transverse momentum spectra described in the text.,height=377 ] obtained from fits to transverse momentum spectra described in the text.,height=377 ] the tsallis distribution described here in eq . leads to excellent fits to the transverse momentum distributions in high energy @xmath34 and @xmath47 collisions . the values obtained for the tsallis parameter @xmath0 are truly remarkably consistent , a feature which does not become apparent when using the parametrization of eq . . 90 b. i. abelev et al . 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( 2013 ) 082302 . atlas collaboration , new j. phys . * 13 * ( 2011 ) 053033 . cms collaboration , phys . * 105 * ( 2010 ) 022002 ; eur . j. c * 72 * ( 2012 ) 2164 . c. tsallis , j. statist . phys . * 52 * , 479 ( 1988 ) . t.bir , g. purcsel , k. rmssy , eur . j. a * 40 * ( 2009 ) 325 . j. m. conroy , h. g. miller , a. r. plastino , phys . a * 374 * , 4581 ( 2010 ) . j. cleymans and d. worku , j. phys . g * 39 * ( 2012 ) 025006 . j. cleymans and d. worku , eur . j. a * 48 * ( 2012 ) 160 . k. rmssy , t.s . bir , phys . b * 689 * ( 2010 ) 14 . k. rmssy , t.s . bir , j. phys . g * 36 * ( 2009 ) 064044 . cheuk - yin wong , g. wilk , acta physica polonica , 43 ( 2012 ) 2047 . t. wibig , j. phys . g : nucl . part . phys . * 37 * 115009 ( 2010 ) . t. wibig , i. kurp , jhep * 0312 * 039 ( 2003 ) . l. marques , e.andrade-ii , a. deppman , arxiv:1210.1725[hep - ph ] i. sena , a. deppman , eur . j. a 49 ( 2013 ) 17 ; arxiv:1209.2367[hep - ph ] k. rmssy , arxiv:1212.0260[hep - ph ] . j. cleymans , g.i . lykasov , a.s . parvan , a.s . sorin , o.v . teryaev , d. worku phys . b * 723 * ( 2013 ) 351 . [ arxiv:1104.0620 [ hep - ph ] ] .

an overview is presented of transverse momentum distributions of particles at the lhc using the tsallis distribution . the use of a thermodynamically consistent form of this distribution leads to an excellent description of charged and identified particles . the values of the tsallis parameter @xmath0 are truly remarkably consistent . = by -1

hera is an @xmath0 collider which has especially high sensitivity to new particles coupling to lepton - quark pairs . in 1994 - 97 hera collided 27.5 gev positrons on 820 gev protons . in 1998 the proton energy was raised to 920 gev increasing the center - of - mass energy @xmath1 from 300 gev to 318 gev . in 1998 and in the first months of 1999 , hera ran with electrons . in may 1999 hera switched back to @xmath2 collisions . the three main colliding periods as well as the corresponding luminosities for each experiment are summarized in table [ tab : lumit ] . * * . _ _ luminosities collected by h1 and zeus for each colliding period . _ _ [ cols="^,^,^,^,^",options="header " , ] hera resulting limits on @xmath3 coupling are the following : * h1 : @xmath4 * zeus : @xmath5 figure [ fig : final ] summarizes the limits on the anomalous coulings @xmath6 ( @xmath7 vectorial coupling ) and @xmath8 ( @xmath3 magnetic coupling ) obtained at hera , lep and tevatron . hera sensitivity to @xmath8 is competitive with other colliders . hera is the unique collider to test direct @xmath10 interactions . about @xmath11 of @xmath2 data and @xmath12 of @xmath13 data have been collected per experiment at hera-1 . no evidence of new physics has been observed in various models in inclusive analyses ( contact interactions , extra - dimensions , leptoquarks ) and exclusive analyses ( lepton - flavour violation , @xmath14-violating susy , excited fermions ) , therefore new constraints have been set . hera limits are seen to be competitive with and complementary to the lep and tevatron searches . the status of isolated lepton events with missing @xmath15 is still intriguing and will become clearer with the new hera-2 data . hera has been shutdown since fall 2000 for a general upgrade : new focussing magnets have been installed in order to increase the luminosity and many improvements have been performed in the detectors in order to increase their sensitivity . moreover , the lepton beam will be longitudinally polarised in the h1 and zeus interaction regions . the first luminosity runs are predicted for beginning 2002 and hera-2 is expected to accumulate 1 @xmath16 in the next 5 years . the anticipated factor of ten increase in the integrated luminosity will give an outstanding discovery potential for hera . i which to thank my h1 and zeus colleagues who contributed to the results presented here as well as people who helped me in preparing this talk .

recent results on searches for physics beyond the standard model obtained by the h1 and zeus experiments are reported here . after a brief introduction to the hera collider , indirect searches for contact interactions and extra - dimensions are presented as well as direct searches for new physics including leptoquarks , lepton - flavour violation , squarks produced by r - parity violation and excited fermions . new results from isolated lepton events and single top searches are also presented . finally the future prospects of hera-2 are shown . * search for new particles at hera * + mireille schneider + cppm , 163 , avenue de luminy , case 907 , + 13288 marseille cedex 9 , france

since its discovery by kageyama _ et al_.@xcite , the spin dimer compound srcu@xmath4(bo@xmath5)@xmath4 has attracted much attention as a suitable material for frustrated spin systems in low dimension . srcu@xmath4(bo@xmath5)@xmath4 exhibits various interesting phenomena , such as a quantum disordered ground state @xcite and a complex shape of magnetization curve@xcite , because of its unique crystal structure . in consideration of the structure , miyahara and ueda suggested that the magnetic properties of the spin dimer compound srcu@xmath4(bo@xmath5)@xmath4 can be described as a spin-@xmath6 two - dimensional ( 2d ) orthogonal - dimer model @xcite , equivalent to the shastry - sutherland model on square lattice with some diagonal bonds @xcite . the ground state of the shastry - sutherland model in dimer phase is exactly represented by a direct product of singlets . the low - energy dispersions possess six - fold degeneracy and are almost flat reflecting that the triplet tends to localize on vertical or horizontal bonds . recent experiments by esr @xcite and neutron inelastic scattering ( nis ) have observed splitting of degenerate dispersions of srcu@xmath4(bo@xmath5)@xmath4 , which can not be explained by the _ isotropic _ shastry - sutherland model . hence c ' epas _ et al . _ pointed out that the dzyaloshinski - moriya ( dm ) interaction @xcite must be added between vertical and horizontal dimers in the isotropic shastry - sutherland model in order to explain the splitting . @xcite in this paper , as a simple model to clarify effects of the dm interaction to low - energy excitations in orthogonal - dimer systems , one - dimensional ( 1d ) orthogonal - dimer model with the dm interaction is studied by using the perturbation theory and the numerical exact - diagonalization method . in the absence of the dm interactions , properties of ground state , low - energy excitations , and magnetization processes of the 1d orthogonal dimer model has been studied by several authors . the hamiltonian of the 1d orthogonal - dimer model with the dm interaction is given by @xmath7 where @xmath8 here @xmath9 is the number of unit cells in the system , as shown by a broken rectangle in fig . the unit cell includes two dimers along vertical and horizontal direction , which are designated by the index , @xmath10 and @xmath11 , respectively . @xmath12 ( @xmath13 and @xmath14 ) denotes a spin-@xmath6 operator on @xmath15-spin in @xmath10-th dimer . @xmath16 and @xmath17 severally indicate the exchange coupling in intra - dimer and in inter - dimer . due to the structure of system , the dm exchange interaction , @xmath18 , exists only on inter - dimer bonds and has only a component perpendicular to two kinds of dimer in the unit cell . the periodic boundary condition is imposed to the system . , that is @xmath19 . the unit cell includes a vertical and horizontal dimer . the former dimers are at @xmath10-site and the latter at @xmath20-site.,width=283 ] in this section , let us discuss the ground state and low - energy excitations of the 1d orthogonal dimer model with the dm interaction . we can expect that the ground state is in the dimer phase in the limit of strong intra - dimer coupling ( @xmath21 ) , even when the dm interaction is switched on the isotropic system . therefore , it is reasonable to treat the intra - dimer hamiltonian ( [ eq : intra ] ) as an unperturbated one and the others as perturbation . the inter - dimer interaction @xmath17 creates two adjacent triplets from a pair of a singlet and triplet and vice versa , and besides shows scatterings between two triplets . the dm interaction not only causes the former process but also creates or annihilates two adjacent singlets . therefore the dm interaction can play a crucial role in the ground state and the low - energy excitations in the dimer phase . first , we discuss the ground - state energy of hamiltonian ( [ eq : hamiltonian ] ) . in the absence of the dm interaction , the ground state is exactly represented by a direct product of singlets and its energy is given as @xmath22 . on the other hands , the ground - state energy of total hamiltonian ( [ eq : hamiltonian ] ) is estimated as @xmath23 from the perturbation expansion up to the third order in @xmath24 and @xmath25 . the result means that the ground state can not be exactly described by the direct product of singlets owing to the dm interaction . next , we argue the low - energy excitations in the system . since the ground state belongs to the dimer phase in the region of strong-@xmath16 , the lowest excited states will be well described by @xmath26 here , @xmath27 and @xmath28 are the total magnetization and the wave number , respectivery . @xmath29 and @xmath30 in ket severally denote a singlet and a triplet with @xmath31 at @xmath10-site and , @xmath32 ( @xmath33 ) is defined as an operator to create a triplet propagating on vertical ( horizontal ) dimers . by using two states of eqs . ( [ eq : vfourier ] ) and ( [ eq : pfourier ] ) , the hamiltonian ( 1 ) is projected on following ( @xmath34)-matrix : @xmath35 where @xmath36,~ { \mbox{\boldmath $ v$}}_m(k)\equiv \left [ \begin{array}{c } t_{m , k}^{\rm ver } \\ t_{m , k}^{\rm hor } \\ \end{array } \right].\end{aligned}\ ] ] the eq . ( [ eq : hm ] ) for @xmath1 has no off - diagonal elements within perturbation up to the third order . therefore the excitation energies for @xmath1 are given by @xmath37 in contrast to the 2d orthogonal dimer model , two excitation energies , @xmath38 and @xmath39 , split in the case of 1d system . it is also interesting to note that the curvature of @xmath39 appears in the third ordered correction in eq . ( [ eq : excitede1 ] ) . on the other hand , the projected hamiltonian with @xmath40 has an off - diagonal element . the perturbation calculation up to the third order leads to the matrix : @xmath41 , \label{eq : apm1}\end{aligned}\ ] ] where @xmath42 by diagonalizing eq . ( [ eq : apm1 ] ) , the excitation energies with @xmath40 are obtained as @xmath43 the curvature of @xmath44 is dominant by the first ordered correction with regard to @xmath25 in the off - diagonal element @xmath45 . the correction derives from the scattering between a singlet and a triplet with @xmath2 due to the dm interaction . subtracting the ground - state energy of eq . ( [ eq : grounde ] ) from excited - state energies of eq . ( [ eq : excitede0 ] ) , ( [ eq : excitede1 ] ) , and ( [ eq : excitede3 ] ) , the low - energy dispersions , @xmath46 , are estimated as @xmath47 figure 2 shows the low - energy dispersions for @xmath48 and @xmath49 . the low energy spectra @xmath50 and @xmath51 are severally represented by the lower and upper solid lines , and then the upper and lower dotted lines denote @xmath52 and @xmath53 in eqs . ( [ eq : omega2 ] ) . the full and open circles represent the low - energy spectra with @xmath1 and @xmath2 . the perturbation theory is in agreement with the numerical diagonalization , as to low - energy excitations . the dispersions with same @xmath31 are not degenerate , which happens even if the dm interaction is not taken account of . therefore the inter - dime coupling @xmath17 is also important for splitting of the low - energy dispersions with same @xmath31 . this is because the parity on the vertical dimer is conserved in the one - dimension system without the dm interaction . the dm interaction not only splits into branches with @xmath1 and @xmath2 , but also makes triplets move more easily . and @xmath49 . the solid and dotted curves are of @xmath1 and @xmath40 , respectively . the full ( open ) circles indicates the excitation energies for @xmath1 ( @xmath2 ) calculated by numerical diagonalizations.,width=264 ] we investigated the low - energy excitations in the 1d orthogonal - dimer model with the dm interaction using the perturbation theory and numerical exact - diagonalization method . the dm interaction allows a triplet to propagate in singlet sea as seen in the 2d system @xcite , while the triplet is localized on vertical or horizontal dimer in the absence of the dm interaction . this curvature effect happens in a two - dimensional orthogonal - dimer model , but the splitting of spectra reflects a stringent constraint for the motion of a triplet due to one dimensionality as well as the dm interaction . we gratefully acknowledge helpful discussions and comments with tetsuro nikuni , masaaki nakamura , and takahiro yamamoto on several points in this work . we would also like to thank k@xmath54ichir@xmath54 ide for valuable advice on numerical techniques . 9 h. kageyama , et al . * 82 * ( 1999 ) 3168 . k. onizuka , et al . : j. phys . * 69 * ( 2000 ) 1016 . s. miyahara and k. ueda : phys . 87 * ( 2001 ) 3701 . b. s. shastry and b. sutherland : physica b * 108 * ( 1981 ) 1089 . h. nojiri , et al . : j. phys . * 68 * ( 1999 ) 2906 . i. dzyaloshinski : j. phys . solids * 4 * ( 1958 ) 241 ; + t. moriya : phys . rev . * 120 * ( 1960 ) 91 . o. cpas , et al . : phys . rev . lett . * 87 * ( 2001 ) 167205 . a. koga , k. okunishi and n. kawakami : phys . b. * 62 * ( 2000 ) 5558 . n. b. ivanov and j. richter : phys . a * 232 * ( 1997 ) 308 . j. richter , n. b. ivanov and j. shulenburg : phys . * 88 * ( 2002 ) 201601 . s. miyahara and k. ueda : j. phys . ( _ suppl . _ ) b * 70 * ( 2001 ) 180 .

effects of the dzyaloshinski - moriya ( dm ) interaction on low - energy excitations in a one - dimensional orthogonal - dimer model are studied by using the perturbation expansions and the numerical diagonalization method . in the absence of the dm interaction , the triplet excitations show two flat spectra with three - fold degeneracy , which are labeled by magnetization @xmath0 . these spectra split into two branches with @xmath1 and with @xmath2 by switching - on of the dm interaction and besides the curvature appears in the triplet excitations with @xmath3 more strongly than those of @xmath1 . , , quantum spin ; low - energy excitation ; dzyaloshinski - moriya interaction ;

we consider the grassmannian @xmath0 , the set of two - planes inside @xmath1 . a plane @xmath2 is given by two linearly independent vectors or by any two linear combinations of them that are independent , so @xmath3 there is a transitive action of @xmath4 ( or @xmath5 ) on @xmath0 . @xmath6 if we consider a particular point @xmath7 @xmath8 @xmath9 we notice that the conformal group of space time , @xmath10 , has spin group @xmath11 . its complexification , @xmath12 , has spin group @xmath13 . how to extract the minkowski space from @xmath0 ? notice that since the two vectors are independent , @xmath14 at least one of the @xmath15 determinants in this matrix is @xmath16 . the space is covered by the atlas @xmath17 @xmath18 is the _ big cell _ , and using the @xmath19 freedom , a plane in @xmath18 can be represented by @xmath20 with the entries of @xmath21 totally arbitrary . so @xmath22 , and it is a good candidate for the minkowski space . what about the group action ? @xmath18 is left invariant by the _ lower parabolic _ subgroup of @xmath23 , @xmath24 and it acts on @xmath21 as @xmath25 the group is @xmath26 so it is the poincar group where instead of the lorentz group we have put its double cover . @xmath21 belongs to the _ twistor space _ associated to spacetime . using the pauli matrices , we can revert to the spacetime notation and obtain the standard action of the poincar group on minkowski spacetime @xmath27 also the spacetime metric has an interpretation in the twistor formalism , @xmath28 quantization of spacetime means to deform the commutative algebra of functions ( can be polynomials or smooth functions ) to a non commutative algebra . other properties that we want to consider in the quantum setting have to be first defined in the algebraic formalism and then quantized. this is the case of the group actions . the respective algebras are @xmath29/ ( \det g-1),\qquad a , b=1,\dots , 4.\ ] ] @xmath30/ ( \det x\cdot \det y -1 ) , \qquad i , j=1,2,\quad a , b=3,4.\ ] ] @xmath31.\ ] ] the group law is expressed in terms of a _ coproduct _ @xmath32with the property @xmath33 the action on the minkowski space is a _ coaction _ @xmath34 in refs . @xcite one substitutes the group @xmath13 by @xmath35 in the twistor construction . all the scheme of coaction and big cell can be repeated in the quantum case , which gives a quantization for the minkowski space as a big cell inside a quantum conformal space ( a quantum grassmannian ) . we just state the result : the quantum minkowski space is a quantum matrix algebra with the rows interchanged . the correspondence @xmath36 is given in terms of the respective generators : @xmath37 this means that the commutation relations among the quantum generators are the following @xmath38 what happened to the groups ? they have become _ quantum groups _ with a non commutative product and a coproduct that is _ the same _ than the one we had before . this means that the group law has not changed , nor the coaction on the grassmannian and the minkowski space . the only change is that all these varieties have become non commutative . it is a remarkable property of matrix quantum groups that the coproduct is compatible with both , the commutative product and the non commutative one . in the quantum version @xmath39 , the sets of generators @xmath40 , @xmath41 and @xmath42 are separately isomorphic to @xmath15 matrix algebras , but while @xmath40 and @xmath41 commute among them , @xmath43 does not commute with the rest of the generators . a quantum matrix algebra is an algebra over @xmath44 $ ] , where @xmath45 is a parameter . moreover , as a module over @xmath46 , it is a free module , which means that it has a basis . it is well known that there is at least one _ ordering _ among the generators such that the standard monomials associated to this ordering are a basis of the quantum matrix algebra . ( this is a non trivial property ) . the ordering is the following @xmath47 and then there is an isomorphism ( _ ordering rule _ or _ quantization map _ ) between @xmath48 and @xmath49 $ ] : @xmath50@ > q_{\mathrm{m}}>>{\mathcal{o}}_q({\mathrm{m}})\\t_{41}^a t_{42}^b t_{31}^c t_{32}^d @ > > > { \hat{t}}_{41}^a { \hat{t}}_{42}^b { \hat{t}}_{31}^c { \hat{t}}_{32}^d\end{cd}.\ ] ] with the quantization map we can pull back the non commutative product to @xmath49 $ ] . this defines a _ star product _ , @xmath51,\ ] ] which can be computed _ explicitly _ @xmath52 @xmath53 are numerical factors defined recursively . we recover the semiclassical interpretation of the algebra being an algebra of functions , but with a star product . the previous formula for the star product is nice and compact , but can only be computed on polynomials . can we extend it to smooth functions ? not obvious . we prove that there exists a ( unique ) differential star product that coincides with the one given above on polynomials . change of the parameter : @xmath54 . we expand in powers of @xmath55 so we obtain a star product of the form @xmath56 with @xmath57 at each order , we have contributions from each of the terms with different @xmath58 @xmath59 we want to write @xmath60 as a bidifferential operator . but this is not trivial because all the dependence in the exponents should cancel . @xmath61 antisymmetrizing and changing variables we obtain the poisson bracket @xmath62 notice that if the @xmath40 s are real , then the poisson bracket is pure imaginary . also , it is quadratic . we have computed explicitly up to the order @xmath63 , but the expression is already too big to display it here . we looked for an argument to show it at arbitrary order . this can be done by careful inspection . the proof that it is differential at each order is rather technical and we do not reproduce it here @xcite but having the explicit formula for the polynomials is essential to apply the argument . an example of the possible difficulty : suppose that we want to reproduce @xmath64 as the result of applying a differential operator to @xmath65 . we have several choices , @xmath66 but none of them is both , independent on the exponent @xmath67 and polynomial in the variable . so the right combination of coefficients should appear in order to cancel the factors that appear when differentiating . for example , if the result were @xmath68 , then we have a differential operator @xmath69 since we have recovered the interpretation of functions for the non commutative algebra , we can try to express the coaction as an action of this space of functions . remember that , formally , for the generators the coaction is the same than in the commutative algebra . we just need to pull it back to the star product algebra . we define the transformed variables ( no translations are considered here ) @xmath70 @xmath71 one just has to expand the star products in the right hand side . up to order @xmath55 we have computed it in terms of a differential operator , @xmath72 and the coefficients are polynomials of order 6 in the variables @xmath73 . let @xmath74 be a commutative algebra over @xmath75 . an involution @xmath76 of @xmath74 is an antilinear map satisfying , for @xmath77 and @xmath78 @xmath79 let us consider the set of fixed points of @xmath76 , @xmath80 it is easy to see that this is a real algebra whose complexification is @xmath74 . @xmath81 is a _ real form _ of @xmath74 . _ classical minkowski space _ : @xmath82 the combinations @xmath83 are fixed points of the involution . one has @xmath84.\ ] ] _ classical euclidean space _ : @xmath85 the commbinations @xmath86 are fixed points of @xmath87 , and as before , @xmath88.\ ] ] formally , the same expressions on the generators as in the classical case are involutions in the quantum algebra . a few things change : * checking with the commutation relations they are antiautomorphisms , this is @xmath89 * this discards the interpretation of the real form of the non commutative algebra as the set of fixed points of the involution . * when pulling back to the star product algebra , the poisson bracket is purely imaginary . finally one finds also the corresponding involutions in the group , @xmath90 it is not difficult to realize that in the minkowskian case the real form of the lorentz group ( corresponding to the generators @xmath40 and @xmath41 ) is @xmath91 and in the euclidean case is @xmath92 . d. cervantes wants to thank the departament de fsica terica , universitat de valncia for the hospitality during the elaboration of this work .

we present a deformation of the minkowski space as embedded into the conformal space ( in the formalism of twistors ) based in the quantum versions of the corresponding kinematic groups . we compute explicitly the star product , whose poisson bracket is quadratic . we show that the star product although defined on the polynomials can be extended differentiably . finally we compute the eucliden and minkowskian real forms of the deformation .

in astrophysics , the observation of a splitting of spectral lines in the visible and uv ranges for a few white dwarfs @xcite confirmed the existence of intense magnetic fields ( 0.1 - 10@xmath2 mg ) as predicted by blackett @xcite . the influence of a magnetic field on an atom modifies its emission or absorption lines . thanks to this property , known as zeeman effect , the detection of magnetic fields is possible at large distances , through the measured radiation . the linear and quadratic zeeman effects @xcite explain the separation of spectral lines and enable one to determine a value of the magnetic field . in the same way , pulsars and neutron stars having an even more intense magnetic field ( 10@xmath3 - 10@xmath4 mg ) have been discovered through their spectrum in the range of radio - frequencies and x - rays . there are numerous astrophysical applications , either direct or indirect , and requiring sometimes a sophisticated theoretical modeling . the methods differ according to the nature of the objects studied ( see table [ tab1 ] ) , the magnitude and the geometry of the magnetic fields , and to the quality of the observation in terms of sensitivity and spectral resolution . moreover , the variations of the magnetic field of stars during their rotation bring some information about their global geometry . the `` spectro - polarimetric '' methods exploit the additional recording of the circular polarization with respect to the wavelength . this enables one to obtain a detailed map of the field @xcite through a separation of its components parallel or perpendicular to the line of sight . strong magnetic fields are also encountered , for instance , in magneto - inertial fusion @xcite . inserting a magnetic field into inertial - confinement - fusion capsules before compressing them @xcite presents the advantages to suppress the electron thermal - conduction losses and to better control the @xmath5-particle energy deposition . the magnetic fields generated inside a hohlraum can reach a few mg . .orders of magnitude of magnetic fields encountered in astrophysics ( 1 mg=10@xmath6 g=100 t ) . [ cols="^,^",options="header " , ] if needed , the evaluation of @xmath7 can be refined . for instance , it is possible to calculate an average value of @xmath8 depending only on @xmath9 . this can be achieved using the sum rule @xcite @xmath10 which states that the sum of the land factors for any given @xmath9 is independent of the coupling conditions . such a property stems from the fact that the trace of a matrix is invariant under an orthogonal transformation . one can thus define an average land factor associated to a given value of @xmath9 : @xmath11 where @xmath12 is the number of levels having angular momentum @xmath9 @xcite , which can be evaluated recursively @xcite , in a similar manner to @xmath13 ( see eq . ( [ recsl ] ) ) . the same methodology can be applied in order to determine analytically the moments of the hyperfine components of a line . the hyperfine operator in the subspace corresponding to the relevant nucleus and atomic level reads : @xmath14 where @xmath15 is the magnetic hyperfine - structure constant of the level @xmath16 . the @xmath17-order moment of the hyperfine components is provided by the expression @xmath18^n\nonumber\\ & & \times\langle\gamma jifm|\mathcal{z}_q^{(1)}|\gamma jifm\rangle^2,\end{aligned}\ ] ] where @xmath19 is the @xmath20-component of the dipole operator @xmath21 . the @xmath9-file sum rule @xcite enables one to simplify the expression of the strength : @xmath22=\frac{1}{3}[i , j],\end{aligned}\ ] ] and therefore @xmath23}\sum_{f , f'}\left(a_jx_{fij}-a_{j'}x_{f'ij'}\right)^n\nonumber\\ & & \times\langle f||\mathcal{z}^{(1)}||f'\rangle^2,\end{aligned}\ ] ] where @xmath24 . equation ( [ mn0 ] ) can be written @xmath25}\sum_{f , f'}[f , f']\left(a_jx_{fij}-a_{j'}x_{f'ij'}\right)^n\nonumber\\ & & \times\langle ( ij)f||\mathcal{z}^{(1)}||(ij)f'\rangle^2,\end{aligned}\ ] ] or @xmath26}\sum_{f , f'}[f , f']\left(a_jx_{fij}-a_{j'}x_{f'ij'}\right)^n\nonumber\\ & & \times{\left\{\begin{array}{ccc}f & 1 & f ' \\ j ' & i & j \end{array}\right\}}^2.\end{aligned}\ ] ] in the case where @xmath27 or @xmath28 is equal to 0 , the calculation is very simple @xcite . in the general case , using @xmath29}{\left\{\begin{array}{ccc}f & j & i \\ 1 & i & j \end{array}\right\}},\ ] ] one has to calculate : @xmath30{\left\{\begin{array}{ccc}f & j & i \\ 1 & i & j \end{array}\right\}}^{k_1}\nonumber\\ & & \times{\left\{\begin{array}{ccc}f ' & j ' & i \\ 1 & i & j ' \end{array}\right\}}^{k_2}{\left\{\begin{array}{ccc}f & 1 & f ' \\ j ' & i & j \end{array}\right\}}^2,\end{aligned}\ ] ] which can be done using graphical methods @xcite . another approach consists in adopting another point of view , leading to the evaluation of quantities of the type : @xmath31(\bar{f}-a)^n\ ] ] where @xmath32 is a constant ( depending on other quantum numbers ) . such a quantity can be expressed , as for the zeeman effect , in terms of bernoulli numbers ( see appendix b ) : @xmath33 the splitting of @xmath27 components in a weak magnetic field @xcite is in every way similar to the splitting of @xmath9 levels . the scale of the splitting is determined by the factor @xmath34 , which is defined by @xmath35 and connected with the land factor by @xmath36 in this work , a statistical modeling of electric dipolar lines in the presence of an intense magnetic field was proposed . the formalism requires the moments of the zeeman components of a line @xmath37 , which can be obtained analytically in terms of the quantum numbers and land factors . it was found that the fourth - order a - type gram - charlier expansion series provides better results than the usual development in powers of the magnetic field often used in radiative - transfer models . using our recently published recursive method for the numbering of ls - terms of an arbitrary configuration , a simple approach to estimate the contribution of a magnetic field to the width ( and higher - order moments ) of a transition array of e1 lines was presented . we hope that such results will be useful for the interpretation of z - pinch absorption or emission spectra , for the study of laser - induced magnetic fields in inertial - fusion studies , for the modeling of magnetized stars as well as for any application involving magnetic fields in spectroscopic studies of atomic and molecular systems . the authors would like to thank c. bauche - arnoult , j. bauche and r. karazija for helpful discussions . @xmath40=(2a+1)(2b+1)(2c+1)\cdots\ ] ] @xmath41 @xmath42 @xmath43{\left(\begin{array}{ccc}1 & j '' & 1 \\ 0 & 0 & 0 \end{array}\right)}{\left(\begin{array}{ccc}1 & j '' & 1 \\ -q & 0 & q \end{array}\right ) } & & \nonumber\\ \times{\left\{\begin{array}{ccc}j & j & 1 \\ j '' & 1 & j \end{array}\right\}}{\left\{\begin{array}{ccc}j ' & j & 1 \\ j '' & 1 & j \end{array}\right\}}.\nonumber\\ & & \end{aligned}\ ] ] @xmath44 @xmath45 @xmath46}}.\ ] ] @xmath47\bar{j}}}.\ ] ] @xmath48(2j-1)(2j+3)\bar{j}}}.\ ] ] @xmath49\bar{j}}}.\ ] ] the bernoulli polynomials can be obtained by successive derivation of a generating function : @xmath50 one can write @xmath51 where @xmath52 is the @xmath53-order bernoulli number , which is non - zero only if @xmath53 is even and which can be obtained from the relation : @xmath54 the first bernoulli polynomials are @xmath55 @xmath56 @xmath57 @xmath58 and @xmath59 the bernoulli polynomials obey the following identity : @xmath60 and the bernoulli numbers have the explicit laplace s determinantal formula @xcite : @xmath61 using second - order ts expansion ( [ iq2 ] ) and assuming the knowledge of the variance @xmath62 of the other broadening mechanisms , it becomes possible to estimate the magnitude of the magnetic field from the measurement of the full width at half maximum ( fwhm ) of the line @xmath63 . this simple formula ( [ est ] ) can provide an estimation of the magnetic field , even if the other broadening mechanisms ( stark , electron collisions , doppler , autoionization ) are dominant . however , it is not as efficient as the method proposed by stambulchik _ @xcite , which is applicable in situations where the magnetic field has various directions and amplitudes ( or if they vary in time ) . n. zeldes , arch . exact sci . * 63 * , 289 ( 2009 ) . g. racah developed a method for fitting by least squares to the theoretical formulas the measured g - factors of atomic levels together with the energy values ( see [ n. zeldes , arch . exact sci . * 63 * , 289 ( 2009 ) ] and references therein ) . unfortunately , the work was never presented ( g. racah died in august 1965 , before the conference ) .

the modeling of complex atomic spectra is a difficult task , due to the huge number of levels and lines involved . in the presence of a magnetic field , the computation becomes even more difficult . the anomalous zeeman pattern is a superposition of many absorption or emission profiles with different zeeman relative strengths , shifts , widths , asymmetries and sharpnesses . we propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra . in this model , the @xmath0 and @xmath1 profiles are described using the moments of the zeeman components , which depend on quantum numbers and land factors . a graphical calculation of these moments , together with a statistical modeling of zeeman profiles as expansions in terms of hermite polynomials are presented . it is shown that the procedure is more efficient , in terms of convergence and validity range , than the taylor - series expansion in powers of the magnetic field which was suggested in the past . finally , a simple approximate method to estimate the contribution of a magnetic field to the width of transition arrays is proposed . it relies on our recently published recursive technique for the numbering of ls - terms of an arbitrary configuration . characterization of anomalous zeeman patterns in complex atomic spectra jean - christophe pain and franck gilleron cea , dam , dif , f-91297 arpajon , france

this work was supported by the us national science foundation grant phy-1520976 . inspection of fig . 1 ( b ) shows that there are two phase shift extrema as a function of @xmath9 . the one we do not use , between the spectator and line resonances , is less sensitive to detuning , but it would increase the rate of unintentional transfer out of the qubit basis . this is partly because there are many more spectator atoms than targets ; the small amount of off - resonant transfer would get multiplied by a much larger number . in addition , there can be atoms that see a fraction of the intensity that most line atoms see , due to misalignment of beams relative to the lattice or beam profile imperfections ; this can put their resonances closer to the phase shifting microwaves . to ensure operation near the phase shift extremum , we find it necessary to adjust the intensities of the addressing beam in a target specific way . this corrects for beam profile distortion by the mems mirror steering system and for the finite rayleigh range of the addressing beams near their foci . the deviation of the cross atom resonance , 1.8@xmath6 , from 2@xmath6 ( see fig . 1 ( a ) ) occurs because the zeeman shift due to the bias b - field is not very much larger than the addressing beams vector light shifts . thus when there is only one addressing beam , the quantization axis tilts slightly toward its propagation direction . our rb building block . these are the microwave pulses corresponding to a pg / cg pair . the red pulse is the pg . the cg is inside the dashed rectangle : the blue pulses are @xmath59 , the black pulses form the spin - echo type structure and the purple pulses are off - resonant microwaves that induce phase shifts . all the pulses have a blackman profile . ] we choose randomized benchmarking ( rb ) to characterize the performance of our gate instead of quantum state tomography for several reasons : it can distinguish gate errors from spam errors ; it has less resource overhead and is easily scaled to multi - qubit systems ; and it reflects the fidelity of a group of operations that is not biased by a particular kind of gate . the basic building block of an rb sequence is a pg - cg pair executed on two target atoms . a cg is a @xmath84 rotation about the @xmath85 or @xmath86axis on the bloch sphere . it contains one phase gate @xmath37 sandwiched by two global @xmath87 rotations . a pg is implemented as a global @xmath88 rotation ( about the @xmath85 or @xmath86axis ) or the absence of one ( for the identity or a rotation about @xmath89 ) . for the @xmath90 rotation , we frame - shift all successive microwave pulses . we extend the spin - echo type structure to include the pauli pulses , as shown in supplementary fig . 1 . the @xmath59 and the pauli pulses are at the rephasing points in this spin - echo type structure . while the main purpose of the echo @xmath3 pulses is to cancel the crosstalk due to addressing beams and microwave pulses , they also serve to preserve the qubit in the face of inhomogeneous broadening . moreover , their phases can be adapted to mitigate microwave power errors , as described in the next section . we have used separate measurements to isolate the factors that contribute to the spam error : collisions with background gas atoms ( 3@xmath34 ) , imperfect state transfer from @xmath91 to @xmath20 ( 2@xmath34 ) , and imperfect clearing ( @xmath92 ) . the sum of these expected terms matches the measured @xmath81 from rb . generally , there are two types of microwave transition imperfections : power and frequency errors . our passively stabilized microwave source limits our power stability . we effectively measure it by driving atoms with up to 65 @xmath3-pulses and find the average fractional error to be @xmath93 . the source of frequency errors in our system is the inhomogeneous broadening of the ensemble of atoms ( @xmath23130 hz ) due to vibrational excitation . although , this is too small to affect the fidelity of individual microwave pulses at the @xmath83 level , state evolution between pulses affects our error cancellation scheme . various techniques have been developed in nmr for dealing with such errors , including composite pulses @xcite , and dynamical decoupling@xcite . composite pulses from the bb1 family can be made insensitive to imperfect pulse amplitude and pulses from the corpse families can be made insensitive to frequency errors . since neither does both , and they come at the cost of considerably longer pulse durations , they are not suitable for our purpose . we instead implement phase cycling schemes in which the errors introduced by microwave pulses are cancelled by subsequent pulses . before tackling the more complicated case of a random sequence of clifford and pauli gates , let us consider a simple spin echo sequence , a repeating sub - cycle of torque vector directions given by : \{@xmath94 } on the bloch sphere . dephasing from any initial state is controlled , unlike with simpler schemes or the widely used xy class of pulses @xcite , which do nt have a perfect cancellation in the absence of inhomogeneous broadening . inhomogeneous broadening compromises error cancellation , but phase cycling still greatly improves the performance . in supplementary fig . 2 we demonstrate the performance of this pulse scheme . supplementary fig . 2 ( a ) plots the spin echo fringe with 100 @xmath3 pulses with phase cycling , with the dashed lines marking the maximum population . the almost lossless fringe contrast confirms the high fidelity of this spin - echo type structure . supplementary fig . 2 ( b ) plots this contrast versus microwave rabi frequency . it is clear that this pulse scheme is quite robust against power fluctuation . while this pulse scheme works nearly perfectly in a set of four , its implementation in an rb sequence is interrupted when there is a @xmath59 pulse or a pauli pulse ( see supplementary fig . 1 ) . we have empirically determined the following rules for choosing the right phase when the `` phase flow '' is interrupted : 1 . the spin echo @xmath3 pulses around successive pauli pulses ( see supplementary fig . 1 ) should follow the cycle : \{@xmath95}. 2 . if the pg preceding a cg has a torque vector along the same axis as the cg s @xmath59 pulse , then the torque vector of the first @xmath3 pulse inside the cg should be opposite that of pg . otherwise , it can have the same phase as the @xmath59 pulse . 3 . the final four @xmath3 pulses in a cg should follow the cycle : \{@xmath94}. these rules are based on experimental testing with many randomized benchmarking sequences and phase schemes , but they may not be optimal . the fidelity for data in fig . 2 . is calculated as follows . the qubit state takes the form of @xmath96 @xmath97 , where @xmath98 and @xmath99 are the polar and azimuth angles on a bloch sphere , and @xmath100 represents a spherically symmetric shrinkage of the bloch sphere . we measure the population in @xmath12 . after a detection @xmath101 pulse with a phase @xmath102 scanned , the population has a sinusoidal dependence on @xmath102 : @xmath103 . we first normalize the results by the maximum / minimum population ( 0.95/0.01 ) , which is set by the spam error , and then fit the curve to the above functional form , enabling us to reconstruct the qubit state after the gate operation . the fidelity in the fig . inset is determined as follows . we fix all the qubit state parameters to the theoretically perfect values ( @xmath104 , @xmath105 ) , except for @xmath99 , which is determined by the @xmath106 gate . since both the fidelity @xmath51 and the population in @xmath12 are a function of @xmath99 , a relation between @xmath51 and @xmath107 can be established : @xmath108 . we normalize @xmath107 as before , and then calculate @xmath51 and its associated uncertainties . this approach is less mathematically rigorous than rb , but it is sufficient to illustrate the insensitivity of the gate to addressing beam alignment and intensity noise .

although the quality of quantum bits ( qubits ) and quantum gates has been steadily improving , the available quantity of qubits has increased quite slowly . to address this important issue in quantum computing , we have demonstrated arbitrary single qubit gates based on targeted phase shifts , an approach that can be applied to atom , ion or other atom - like systems . these gates are highly insensitive to addressing beam imperfections and have little crosstalk , allowing for a dramatic scaling up of qubit number . we have performed gates in series on 48 individually targeted sites in a 40% full @xmath0 3d array created by an optical lattice . using randomized benchmarking , we demonstrate an average gate fidelity of 0.9962(16 ) , with an average crosstalk fidelity of 0.9979(2 ) . pacs numbers : : the performance of isolated quantum gates has recently been improved for several types of qubits , including trapped ions @xcite , josephson junctions @xcite , quantum dots @xcite , and neutral atoms @xcite . single qubit gate errors now approach or , in the case of ions , surpass the commonly accepted error - threshold @xcite ( error per gate @xmath1 ) , for fault - tolerant quantum computation @xcite . it remains a challenge in all these systems to execute targeted gates on many qubits with fidelities comparable to those for isolated qubits @xcite . neutral atom and ion experiments have to date demonstrated the most qubits in the same system , 50 and 18 respectively @xcite . the highest fidelity gates in these systems are based on microwave transitions , but addressing schemes typically depend on either addressing light beams @xcite which are difficult to make as stable as microwaves , or magnetic field gradients @xcite which limit the number of addressed qubits . in this report , we present a way to induce phase shifts on atoms at targeted sites in a @xmath2 optical lattice that is highly insensitive to addressing laser beam fluctuations . we further show how to convert targeted phase shifts into arbitrary single qubit gates . these high fidelity gates are only sensitive to laser fluctuations at second order in intensity and fourth order in beam pointing . we demonstrate average single gate errors across our array that are below 0.004 , and present a path towards reaching the fault - tolerant threshold . in previous work @xcite we performed single site addressing in a 3d lattice using crossed laser beams to selectively ac stark shift target atoms , and microwaves to temporarily map quantum states from a field insensitive storage basis to the stark - shifted computational basis . while we use most of the same physical elements here , the crucial difference is that these new gates are based on phase shifts in the storage basis , and do not require transitions out of it . non - resonant microwaves are applied that give opposite - sign ac zeeman shifts for different atoms . a specific series of non - resonant pulses and global @xmath3-pulses on the qubit transition gives a zero net phase shift for non - target atoms and a controllable net phase shift for target atoms . the resultant gate fidelity is much better than our previous gate because of this gate s extreme insensitivity to the addressing beam alignment and power , the insensitivity of the storage basis to magnetic fields and vector light shifts , and the independence on the phase of the non - resonant microwave pulses . the principle of this phase gate , where optical addressing does not compromise fidelity , can be adapted to other atom and ion qubit geometries . addressing spectrum , phase shift and timing sequence . ( a ) spectra of the @xmath4 transition . we plot the ratio of the number of detected @xmath5 atoms to the initial number of atoms as a function of the detuning from the unshifted resonance . the green diamonds are due to spectators , the blue triangles are due to line atoms and the orange circles are due to cross atoms . the solid lines are fits to gaussians . the resonance frequencies of line atoms and cross atoms are marked by @xmath6 and @xmath7 . ( b ) exact calculation of the cumulative phase shift ( @xmath8 ) on a target atom as a function of the microwave detuning from the unshifted resonance . the optimum operation point is marked by @xmath9 . ( c ) addressing pulse sequence . first row : blackman - profiled microwave pulse sequence . the black pulses ( 80 @xmath10s ) are resonant on the @xmath11 to @xmath12 transition and affect all atoms . the purple pulses ( 120 @xmath10s ) are addressing pulses detuned from the @xmath13 to @xmath14 transitions by @xmath9 . second row : the addressing light intensity . the addressing light barely affects the trapping potential , so a linear ramp is optimal . it is effectively at full power for 252 @xmath10s . third and fourth rows : schematic of addressing beams in two planes . the atom color codes are as in ( a ) . , width=302 ] detailed descriptions of our apparatus can be found in refs 15 , 21 and 22 . we optically trap and reliably image neutral @xmath15cs atoms in a 5 @xmath16 spaced cubic optical lattice . the atoms are cooled to @xmath17 ground vibrational state occupancy and then microwave transferred into the qubit basis , the @xmath18 , @xmath19 and @xmath20 hyperfine sublevels , which we will call @xmath12 and @xmath11 , respectively . lattice light spontaneous emission is the largest source of decoherence , with a 7 s coherence time ( @xmath21 ) that is much longer than the typical microwave pulse time of 80 @xmath22 . we detect the qubit states by clearing atoms in the @xmath20 states and imaging the @xmath19 atoms that remain . to target an atom , we cross two circularly polarized , 880.250 nm addressing beams ( beam waist @xmath23 2.7 @xmath16 , rayleigh range @xmath23 26 @xmath16 ) . the addressing beams can be directed to a new target in @xmath24 5 @xmath22 using micro - electro - mechanical - system ( mems ) mirrors @xcite . the addressing beams ac stark shift the @xmath25 levels of the atom at their intersection by about twice as much as any other atom . this is illustrated in fig . 1(a ) , for which atoms are prepared in @xmath20 and a microwave near the @xmath26 transition is scanned . the resonances are visible for atoms at the intersection ( orange , termed `` cross '' atoms ) , atoms in one addressing beam path ( blue , termed `` line '' atoms ) , and the rest of the atoms ( green , termed `` spectator '' atoms ) . the ac stark shift for the line atoms , @xmath6 , is chosen so that there is a region between the blue and orange peaks in which only a small fraction ( @xmath27 ) of atoms in any class ( cross , line or spectator ) makes the transition . when a microwave pulse is applied in that frequency range , atoms experience different ac zeeman shifts depending on their class . the addressing pulse sequence for a pair of target atoms in two planes , shown in fig 1 . ( c ) , consists of four stages @xcite . the qubit - resonant spin - echo pulses ( the black pulses on the microwave line in fig 1 . ( c ) ) reverse the sign of the phase shifts , so whatever phase shifts ( ac zeeman or ac stark ) a non - target atom gets during the cross stages ( the first and third ) are exactly canceled by the shifts it gets during the dummy stages ( the second and fourth ) , where there is no cross atom . in contrast , the first ( second ) target atom spends stage 1 ( 3 ) as a cross , stage 3 ( 1 ) as a spectator , and stages 2 and 4 ( 2 and 4 ) as a line atom . when the microwave frequency is chosen to be between the line and cross resonances , the change in the target atom s status from cross to line changes the sign of the ac zeeman shift . away from the resonances , the net phase shift for the target atoms is : @xmath28 where @xmath9 is the microwave detuning from the spectator resonance , @xmath29 is the shift of cross atoms in units of @xmath6 ( see supplementary materials ) , @xmath30 is the microwave rabi frequency and @xmath31 is the pulse duration . successive terms correspond to the integrated ac zeeman shift on the first target atom during successive stages . the overall phase shift can be directly controlled by changing the power of the microwave field . the black curve in fig . 1(b ) shows the result of an exact calculation of the target atom s phase shift as a function of @xmath9 . the phase shift minimum at @xmath32 khz is the preferred operating point for the gate , since the shift then quadratically depends on the change in @xmath9 and thus also on the addressing beams ac stark shift , with the coefficient of 21 @xmath33 . for example , a 2@xmath34 change in @xmath6 gives a 8 mrad phase shift , which in turn leads to only a @xmath35 gate error . since the intensity changes quadratically with beam alignment , the gate is sensitive to beam pointing only at fourth order . the phase shift on target sites amounts to a rotation about the @xmath36axis ( an @xmath37 gate ) , but a universal gate requires arbitrary rotations about any arbitrary axis . we can make an @xmath38 gate by combining the @xmath37 gate with global @xmath39 rotations : @xmath40 for non - target atoms , which see the global microwave pulses but experience no @xmath37 , @xmath41 clearly has no net effect . it is straightforward to generalize this formula to obtain arbitrary rotations on a bloch sphere for target atoms . the corresponding complete set of single qubit gates on target atoms all leave the non - target atoms unchanged . interference fringe of one @xmath42 phase gate applied to 48 randomly chosen sites . the black dots correspond to the target atoms , and the green dots correspond to non - target atoms . solid lines are fits to data . dashed lines mark the maximum and minimum possible populations . after all these gates , the net @xmath43 for target atoms is @xmath44 , and for the non - target atoms it is @xmath45 . the average error per gate for both target and non - target atoms is @xmath46 . , width=340 ] we have demonstrated one @xmath47 gate on 48 randomly chosen sites ( in 24 gate pairs ) within a @xmath48 array . given the average initial site occupancy of @xmath49 , an average of 20 qubits experience the phase gate during each implementation . we probe the coherence by closing the spin echo sequence with a global @xmath50 pulse whose phase we scan , as shown in fig . 2 . the green points are due to non - target atoms , and the black points are due to atoms at the 48 target sites . the corresponding curves are sinusoidal fits to the data . the dashed lines mark the maximum and minimum populations one expects given perfect gate fidelity , @xmath51 , defined as the square of the projection of the measured state onto the intended state , in the face of state preparation and measurement ( spam ) errors ( see supplementary materials ) . from these curves we determine that the error per gate pair , @xmath52 , is @xmath53 for both target and non - target atoms on average . at least for this particular gate , most of the error is clearly common to target and non - target atoms . the good contrast of the target atom fringe illustrates the homogeneity of the phase shifts across the ensemble . the error per gate , @xmath54 , is thus @xmath55 on average . to graphically illustrate the flexibility of our gates , we have performed an @xmath56 rotation on a 32 site pattern ( see fig . 3 ) . we rotate the superposition of target atoms from @xmath57 to @xmath58 , and then use a @xmath59 detection pulse with phase of @xmath3 to return spectator atoms to @xmath11 and target atoms to @xmath12 . fig . 3 shows images from 5 planes summed over 50 implementations . ! h @xmath56 gates performed in a specific pattern . ( 1 - 5 ) : fluorescent images of 5 successive planes . each image is the sum of 50 implementations . for clarity , the contrast is enhanced using the same set of dark / bright thresholds on all pictures to account for the shot noise . note that there are no targeted sites in planes 2 and 4 ; the light collected there is from atoms in the adjacent planes . the drawing to the lower right marks the targeted sites in blue , with plane shading and blue lines to guide the eye.,title="fig:",width=340 ] to confirm the robustness of this gate , we applied an @xmath47 gate to 24 targets , and measured the probability that atoms return to @xmath12 after a @xmath59 pulse as a function of the fractional change in addressing beam intensity ( see the fig . 4 inset and supplementary materials ) . the data confirms the theoretical prediction ( solid line ) of extreme insensitivity to addressing beam intensity ( see fig . 1(b ) ) . semi - log plot of fidelity from a randomized benchmarking sequence . we plot the probability of returning the two target atoms to @xmath12 after a randomized benchmarking sequence versus the sequence length . at each length we employ 3 randomized cg sequences , each of which is combined with 3 sets of randomized pg sequences , for a total of 9 points . each data point is averaged over @xmath23100 implementations . a least squares fit using the @xmath60 determined from the auxiliary rb measurement on non - target atoms gives @xmath61 = @xmath62 . inset : fidelity of an @xmath47 gate as a function of the fractional change of the addressing ac stark shift . the points are experimental data and the curve is from the exact calculation . , width=340 ] to fully characterize gate performance we employ the standard randomized benchmarking ( rb ) protocol @xcite , which has been used in nuclear magnetic resonance @xcite , quantum dots @xcite , ion systems @xcite and neutral atoms systems @xcite . we implement rb by choosing computation gates ( cg ) at random from \{@xmath39 , @xmath63 } and pauli gates ( pg ) at random from \{@xmath64 } where @xmath65 is the identity @xcite . following each randomized sequence , a detection gate is applied that in the absence of errors would return either the target qubits or the non - target qubits to @xmath12 . for the targets , the average value of @xmath51 decays exponentially with the length of the randomized sequence : @xmath66 where @xmath67 is the spam error and @xmath68 is the number of cg - pg operations applied to the pair of target atoms . a similar expression yields @xmath69 and @xmath70 for the spectator and line atoms respectively , the unwanted changes wrought on the non - target atoms when a random series of gates is executed on the targets . in this way we can characterize crosstalk and extract errors per gate from errors per gate pair . for target atoms , @xmath71 , for spectator atoms , @xmath72 , and for line atoms , @xmath73 . first analyzing the non - target data ( see supplementary fig . 3 ) , we determine that @xmath74 , @xmath75 , and @xmath76 . the crosstalk , defined as the average error per gate for non - target atoms , is @xmath77 . only global microwave pulse imperfections contribute to @xmath78 . their contribution to @xmath79 may differ since the microwave sequence is optimized for spectators . spontaneous emission from the addressing beams adds to @xmath79 , with a calculable contribution of @xmath80 . fig . 4 shows the rb data for the two target atoms . using the @xmath81 from the non - targets , the fit of eq . 3 to the data yields @xmath82 . a summary of the errors for the target and non - target atoms is shown in table 1 . the errors can mostly be traced to microwave power stability . we expect that reaching the state of the art @xcite , and perhaps tweaking our spin echo infrastructure @xcite ( see supplementary fig . 1 ) , can bring it below @xmath83 . the next largest contribution is from the readily calculable spontaneous emission of addressing light . its contribution is invariant with gate times , since @xmath6 must be changed inversely with gate time . addressing with light between the d1 and d2 lines , as we do , locally minimizes spontaneous emission , but an eight - fold reduction could be obtained by doubling the wavelength , which would not dramatically compromise site addressing . the required powerful addressing beams would exert a significant force on line atoms , but deeper lattices and adiabatic addressing beam turn - on would make the associated heating negligible . in our current experiment we need to wait 70 @xmath22 after the addressing beams are turned on for our intensity lock to settle . technical improvement there could halve the time the light is on , ultimately leaving the spontaneous emission contribution to the error just below @xmath83 per gate . that limit is based on addressing with a differential light shift . it would disappear were the same basic scheme to be employed on a 3-level system , where only one of the qubit states is strongly ac stark shifted by the addressing light . in that case the phase shifting microwaves ( or light ) would simply be off - resonant from the qubit transition , and the error due to spontaneous emission would decrease proportional to the detuning . since the dominant target errors have the same sources as the non - target errors , improvements to the gate will correspondingly improve the crosstalk . adapting this method to more common 1d and 2d geometries is straightforward . only a single addressing beam is needed , and the dummy stages would be executed with half - intensity addressing beams . the same insensitivity to addressing beam power and alignment would follow . in summary , we report on a universal single qubit gate based on targeted phase shifts . the gate is robust to addressing light fluctuations , and can be applied to large arrays of qubits , including our demanding 3d lattice geometry . scalable addressing is an important step towards a scalable quantum computer . 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in the first place , we note that all the time - evolution free - propagators in eq.(2 ) are retarded , @xmath130 with @xmath131 . this is so because the time - order prescription on the time integrals implies @xmath132 , hence @xmath133 holds in all the @xmath130 oparators of eq.(2 ) . it is the time - ordering together with the heaviside function @xmath134 in the integrand of eq.([laeq ] ) that guarantee causality . substituting in eq.([laeq ] ) the expressions of the operators @xmath135 as sums over normal modes , and making use of the identities @xcite @xmath136 and @xmath137,\label{sm1}\end{aligned}\ ] ] that we will denote by @xmath138 , we can write eq.([laeq ] ) as @xmath139,\nonumber\end{aligned}\ ] ] where the integrand of the time - ordered integrals is the product of the retarded time - evolution free - propagators , @xmath140 is the fine - structure constant and @xmath141 is the electron charge . next , integrating in time we end up with @xmath142}}{(k - k_{a})(k - k_{b})(k'-k)}\nonumber\\&+&\frac{\cos{[(\omega'-\omega_{a})t]}}{(k'-k_{a})(k'-k_{b})(k'-k)}\bigr],\label{sm3}\end{aligned}\ ] ] where straightforward application of perturbation theory enforces to taking the principal value ( p.v . ) of the integral in eq.([sm3 ] ) , as intermediate states with energies equal to that of the initial state must be removed from the sums ( integrals in the continuum ) in order to avoid zeros in the denominators , @xmath143 having impossed causality by time - ordering the integrals of eq.([sm2 ] ) and multiplying the integrand by @xmath134 , there is no need to add arbitrarily small imaginary parts @xmath144 to the real poles of the integrand in eq.([sm3 ] ) in order to ensure that the propagators are retarded . also , we have argued in the letter that spontaneous emission enters at higher order , hence it can not provide imaginary shifts @xmath145 to the real poles of eq.([sm3 ] ) either , in contrast to refs.@xcite . lastly , the contours of integration for each of the terms of the frequency integrals in the complex plane is univocally determined by the condition @xmath58 . each term contains complex exponential factors of @xmath93 and @xmath94 of the form @xmath146 , with @xmath147 being generic linear functions of @xmath148 and @xmath13 . that implies that the integration contours must be closed by infinitely large semi - circles either in the upper half plane for @xmath149 , or in the lower half plane for @xmath150 , which is ultimately determined by the condition @xmath58 . it is worth mentioning that the integrand of eq.([sm3 ] ) is invariant under the exchange @xmath151 , which implies that the total integral is independent of the order of integration , as expected . and @xmath94 . ] thus , @xmath54 is unambiguously given by eq.([sm3 ] ) . the final result is given in the eq.(4 ) of the letter . finally , the causal - adiabatic approximation referred to in the conclusions of the letter corresponds to adding up a factor @xmath152 to the integrand of eq.([sm2 ] ) , with @xmath90 , and to extending the lower limits of the time integrals to @xmath111 . after performing the time integrals one obtains the @xmath13-independent terms of eq.([sm3 ] ) ( excluding the heaviside function ) with a small imaginary part @xmath153 added to both real poles , @xmath154 we also note that eq.(6 ) in the letter corresponds to the @xmath13-independent terms of eq.([sm3 ] ) of which only the terms proportional to @xmath155 and @xmath156 have been retained in the @xmath157-functions , and in which small imaginary parts @xmath158 have been added to each real pole respectively . milonni , _ the quantum vacuum _ , academic press , san diego ( 1994 ) . c. cohen - tannoudji , j. dupont - roc and g. grynberg , _ photons and atoms . introduction to quantum electrodynamics _ , wiley - vch verlag gmbh @xmath159 co. kgaa , weinheim ( 2004 ) . t. juffmann _ et al . _ , nat . nanotechnol . * 7 * , 297 ( 2012 ) . m. saffman , t.g . walker and k. mlmer , _ rev . phys . _ * 82 * , 2313 ( 2010 ) . j. israelachvili , _ intermolecular and surface forces _ , academic press ( 1992 ) . d.p . craig and t. thirunamachandran , _ molecular quantum electrodynamics _ , dover ed . , new york ( 1998 ) . f. london , _ z. phys . _ * 63 * , 245 ( 1930 ) . casimir and d. polder , _ phys . _ * 73 * , 360 ( 1948 ) . h. safari , s.y . buhmann , d .- welsch and h. trung - dung , _ _ rev . a__**74 * * , 042101 ( 2006 ) . wylie and j.e . sipe , _ _ phys . rev . a__**30 * * , 1185 ( 1984 ) ; _ _ phys . rev . a__**32 * * , 2030 ( 1985 ) . s. scheel and s.y . buhmann , _ acta phys . slov . _ * 58 * 675 ( 2004 ) . gorza and m. ducloy , _ _ eur . j. d__**40 * * ( 2006 ) 343 . m. donaire , _ _ phys . rev . a__**83 * * , 022502 ( 2011 ) ; _ _ phys . rev . a__**85 * * , 052518 ( 2012 ) . e.a . power and t. thirunamachandran , _ _ phys . rev . a__**51 * * , 3660 ( 1995 ) . mclone and e.a . power , _ _ proc . r. soc . a__**286 * * , 573 ( 1965 ) . l. gomberoff , r.r . mclone and e.a . _ * 44 * , 4148 ( 1966 ) . y. sherkunov , _ _ phys . rev . a__**72 * * , 052703 ( 2005 ) . haakh , j. schiefele and c. henkel , _ int . j. mod : conf . ser . _ * 14 * , 347 ( 2012 ) . h. safari and m.r . karimpour , _ phys . * 114 * , 013201 ( 2015 ) . l. rizzuto , r. passante and f. persico , _ rev . a__**70 * * , 012107 ( 2004 ) . berman , _ _ phys . rev . a__**91 * * , 042127 ( 2015 ) . some of the diagrams of fig.([fig1 ] ) discarded provide also terms with poles in both @xmath93 and @xmath94 . however , after integrated in frequencies , they yield contributions of the order of @xmath160 times smaller than the ones found here , and hence they are negligible . for instance , in diagram @xmath161 this is due to its lack of resonance with the transition of atom @xmath4 , since both photons are simply resonant . sakurai , _ advanced quantum mechanics _ , additon - wesley ( 1994 ) . berman and b. dubetsky , _ _ phys . rev . a__**55 * * , 4060 ( 1997 ) . _ , _ phys . rev . lett . _ * 91 * , 213602 ( 2003 ) . _ , _ phys . lett . _ * 92 * , 223602 ( 2004 ) .

we present a time - dependent quantum calculation of the van der waals interaction between a pair of dissimilar atoms , one of which is initially excited while the other one is in its ground state . for small detuning , the interaction is predominantly mediated at all distances by the exchange of doubly resonant photons between the two atoms . we find that it presents both temporal and spatial oscillations . spatially oscillating terms depend on the resonant frequencies of both atoms , while the frequency of the time oscillations is given by their detuning . we analyse the physical content of our findings and discuss to what extent previous conflicting stationary approaches provide compatible results . a proper account of causality is found essential in order to obtain the correct result . dispersion forces between neutral atoms are often interpreted as a result of the quantum fluctuation of both the electromagnetic ( em ) field and the atomic charges @xcite . a prominent example of those are van der waals ( vdw ) forces acting between neutral atoms and molecules , which are important in atomic and molecular interferometry where they influence the measured interference pattern @xcite . in quantum information , vdw forces between rydberg atoms produce a rydberg blockade which may be exploited to realize quantum gates @xcite . in biophysical and chemical processes vdw forces are known to play a crucial role for the stability and assembling of molecules @xcite . + at zero temperature , two atoms in their ground states undergo a series of virtual transitions to upper levels . it is the coupling of the charges of each atom to the quantum em field that induces the correlation between their transient dipole moments , giving rise to a non - vanishing vdw interaction . the lifetime of the virtual atomic transitions is very short in comparison to ordinary observation times and thus , the use of stationary quantum perturbation theory is well justified for the calculation of this interaction @xcite . for short interatomic distances @xmath0 in comparison to the relevant transition wavelengths ( non - retarded regime ) the interaction scales as @xmath1 , while for large distances ( retarded regime ) it goes like @xmath2 @xcite . + the situation is different for excited atoms . first , excited states are unstable and present finite lifetimes . this implies that , generically , the interaction between excited atoms must depend on time . second , if any of the transitions from the excited to lower atomic levels is relevant to the interaction , the exchange of resonant photons between the atoms must be considered . the energy of the interaction mediated by resonant photons is usually referred to as _ resonant van der waals potential _ in the literature @xcite . in the retarded regime the resonant potential overtakes by far the non - resonant one . it is in this regime that different approaches yield conflicting results concerning the spatial oscillations of the interaction @xcite . this long - standing problem is the main motivation of the present letter . in the following , we address the time - dependent quantum computation of the interaction between two dissimilar atomic dipoles , one of which is excited . the excited atom is taken of type @xmath3 while the atom in its ground state is considered of a different type @xmath4 . without loss of generality we approximate the atoms by two - level systems of resonant frequencies @xmath5 and @xmath6 respectively , with respective linewidths @xmath7 and @xmath8 . further , in order to ensure the perturbative nature of the calculation and to avoid resonant energy transfer we set the detuning @xmath9 such that @xmath10 and @xmath11 , with @xmath12 being the interaction hamiltonian at the time of observation , @xmath13 . since the observation is made for atom @xmath3 excited , we must have @xmath14 . lastly , we assume without much loss of generality @xmath15 , which is easily met by pairs of alkali atoms . we will refer to this condition as _ quasi - resonant_. we will see that it allows for a great reduction in the number of calculations and makes the resonant potential dominant at all distances . we will show that the interaction energy oscillates both in time and in space . it contains time - independent terms which oscillate in space with frequency @xmath16 , and time - dependent terms which oscillate in time with frequency @xmath17 and in space with frequency @xmath18 . we compare our results to previous conflicting approaches and discuss in detail to which extent they provide compatible results . we aim at computing the em energy of atom @xmath3 due to the presence of atom @xmath4 . to this end we apply standard time - dependent quantum perturbative techniques in the electric dipole approximation @xcite . at any given time @xmath13 the state of the two - atom - vacuum system can be written as @xmath19 , where the state of the system at time 0 is @xmath20 . in this expression @xmath21 label the upper / lower internal states of the atoms @xmath3 and @xmath4 respectively and @xmath22 is the em vacuum state . @xmath23 denotes the time evolution operator in the schrdinger representation , @xmath24\bigr\}.\nonumber\ ] ] in this equation @xmath25 is the free hamiltonian of the internal atomic states , @xmath26 , while the hamiltonian of the free em field is @xmath27 , where @xmath28 is the photon frequency , and the operators @xmath29 and @xmath30 are the creation and annihilation operators of photons with momentum @xmath31 and polarization @xmath32 respectively . finally , the interaction hamiltonian reads @xmath33 , with @xmath34 . in this expression @xmath35 are the electric dipole operators of each atom and @xmath36 is the electric field operator evaluated at the position of each atom , which can be written in the usual manner as a sum over normal modes as @xcite @xmath37,\nonumber\end{aligned}\ ] ] where @xmath38 is a generic volume and @xmath39 denote the annihilation / creation electric field operators of photons of momentum @xmath31 , respectively . while the internal atomic and em degrees of freedom are quantum variables , the position vectors @xmath40 are classical variables . we emphasize here that we do not make further simplifications to these potentials . in particular , we do not replace the em response of any of the atoms by its ordinary polarizability , as it is the case in ref.@xcite . next , considering @xmath41 as a perturbation to the free hamiltonians , the unperturbed time - evolution operator for atom and free photon states is @xmath42}$ ] . in order to make contact with a realistic setup , we imagine that atom @xmath3 starts being excited at time @xmath43 by a laser pulse of duration @xmath44 . this fixes our temporal resolution and implies that at time @xmath45 the initial state @xmath46 is well - defined within a time interval of the order of @xmath47 . we are now ready to compute the em energy of atom @xmath3 due to the presence of atom @xmath4 at any time @xmath13 such that @xmath48,@xmath49 the above expression admits an expansion in powers of @xmath41 which can be developed out of the time - ordered exponential equation for @xmath23 , @xmath50 . at leading order , eq.([force ] ) contains a series of terms of fourth order in @xmath41 where an electric field operator creates / annihilates a photon at time @xmath13 at the position of atom @xmath3 . they correspond to the twelve well - known time - ordered diagrams of fig.[fig1 ] @xcite . in the time - dependent approach , each diagram contributes to @xmath51 with two terms in which @xmath52 is flanked by two @xmath53-matrices which make the system evolve , in opposite time directions , from the initial state to two different states at time @xmath13 , which differ from one another in the state of atom @xmath3 and in the number of photons by one unit . at the lowest order in @xmath41 . the time variable runs along the vertical.,width=336,height=128 ] in quasi - resonant conditions , the greatest contribution to @xmath54 comes from diagram @xmath55 , in which two doubly resonant photons are exchanged one after the other . doubly resonant photons are those emitted by one of the atoms in its upper level and absorbed by the other atom in its lower level , while for non - resonant photons the emission / absorpsion processes are inverted . lastly , simply resonant photons are those emitted and absorbed by both atoms in either their upper or lower levels . in addition , the diagrams @xmath56 of fig.[fig1 ] , which contain both doubly resonant and non - resonant photons , provide terms which make it possible to extend the frequency integrals of diagram @xmath55 into the negative domain . their contribution is indeed essential for establishing causality ( cf . ref.@xcite ) . all the other contributions from these and from the rest of diagrams are at the most of the order of @xmath57 times smaller and hence negligible . putting everything together , transforming the sums over photon momenta into continuum integrals and imposing the causality condition @xmath58 with @xmath59 , we find at leading order , @xmath60+[k\leftrightarrow k']^{\dagger}.\nonumber\end{aligned}\ ] ] the time integrals of the time - evolution operators in eq.([laeq ] ) yield a series of terms with poles along the real axis , @xmath61}}{(k - k_{a})(k - k_{b})(k'-k)}+\frac{\cos{[(\omega'-\omega_{a})t]}}{(k'-k_{a})(k'-k_{b})(k'-k)}.\nonumber\end{aligned}\ ] ] further , the development of this expression contains terms in which both photons resonate either with the transition of atom @xmath3 or with the transition of atom @xmath4 only . this is a direct consequence of energy conservation . upon integration in frequencies , the former terms are time - independent while the latter oscillate in time as @xmath62 . important is the fact that only the first term in eq.([poles ] ) arises in the stationary approach @xcite . however , the integration in frequencies of the third and fourth terms provides additional time - independent contributions which are missing in the stationary approach . lastly , replacing the time integrals in eq.([laeq ] ) with the result ( [ poles ] ) and integrating in orientations and frequencies , we obtain see appendix , @xmath63\cos{(2k_{a}r)}+\frac{2\mathcal{u}_{ijpq}}{r^{5}}k_{a}[\beta^{ij}\beta^{pq}\nonumber\\ & -k_{a}^{2}r^{2}\alpha^{ij}\beta^{pq}]\sin{(2k_{a}r)}\label{tdep}\\ & -\frac{\mathcal{u}_{ijpq}}{r^{6}}[\beta^{ij}\beta^{pq}-k_{b}^{2}r^{2}(\beta^{ij}\beta^{pq}+2\alpha^{ij}\beta^{pq})\nonumber\\ & + k_{b}^{4}r^{4}\alpha^{ij}\alpha^{pq}]\cos{(2k_{b}r+\delta_{ab}t ) } -\frac{2\mathcal{u}_{ijpq}}{r^{5}}k_{b}\nonumber\\ & \times[\beta^{ij}\beta^{pq}-k_{b}^{2}r^{2}\alpha^{ij}\beta^{pq}]\sin{(2k_{b}r+\delta_{ab}t)}\nonumber\\ & + \frac{\mathcal{u}_{ijpq}}{r^{6}}[1+ ... +(k_{a , b}r)^{4}]\mathcal{o}(\delta_{ab}/\omega_{a , b})+ ... ,\nonumber\end{aligned}\ ] ] where @xmath64 $ ] , @xmath65 , @xmath66 and @xmath67 , @xmath68 . it is worth stressing that the heaviside function in eq.([laeq ] ) together with the time - order prescription do not only guarantee causality , but also determine univocally the contours of integration over frequencies in the complex plane when taking the principal value ( see appendix ) . the last term in eq.([tdep ] ) indicates the order of the leading corrections to the dominant doubly resonant photon exchange terms of eq.([laeq ] ) @xcite . as anticipated , the time - independent terms of eq.([tdep ] ) oscillate only in space with frequency @xmath69 . on the contrary , the time - dependent terms oscillate in time with frequency @xmath17 and in space with frequency @xmath70 . only for large integration times , @xmath71 , their time average vanishes . in the short time limit , @xmath72 , @xmath54 vanishes identically at our order of approximation . this is a consequence of the fact that , in order to establish the interaction , it is necessary that the excitation be transferred actually to atom @xmath4 . for @xmath73 , the probability of excitation of atom @xmath4 oscillates in time as @xmath74/2]}$ ] , being maximum for the first time at @xmath75 . correspondingly , @xmath54 becomes maximum for the first time at @xmath76 . the lapse @xmath77 between these two times is the time for a photon to travel back from @xmath78 to @xmath79 after the excitation of atom @xmath4 . a long - standing debate exists in the literature concerning the spatial oscillations of the two - atom interaction in the retarded regime when one of the atoms is excited @xcite . the existence of spatial oscillations is indeed supported by experiments @xcite . according to our findings , for @xmath80 and @xmath58 , the interaction oscillates both in time and in space as @xmath81\nonumber\\ & \simeq\frac{-2\mathcal{u}_{ijpq}}{r^{2}}\alpha^{ij}\alpha^{pq}k_{a}^{4}\sin{[\delta_{ab}(r / c - t/2)]}\nonumber\\ & \times\sin{[k_{a}(r+ct/2)+k_{b}(r - ct/2)]}.\nonumber\end{aligned}\ ] ] from the last expression we read that , at fixed time , the interaction is modulated by long - range oscillations of frequency @xmath82 , while short - range oscillations take place at frequency @xmath83 . also as a function of time the interaction is modulated by oscillations of frequency @xmath17 . in fig.[fig3 ] we plot the energy of the interaction between two alkali atoms , one of @xmath84rb which is excited to the state @xmath85 and another one of @xmath86k which is in its ground state , in the retarded regime . in contrast to our result , the stationary approach of power and thirunamachandran in ref.@xcite predicts no oscillations for @xmath87 in the far field . the key point in their calculation is the addition of small imaginary parts to the resonant frequency of atom @xmath3 in such a way that poles get shifted off the real axis . they used the prescription that a positive / negative imaginary part must be added for emitted / absorbed photons in order to account for the finite linewidth of the excited atom . in particular , for @xmath88 the dominant term in their stationary calculation is the first one in eq.([poles ] ) , but with the real poles shifted as @xmath89^{-1}$ ] , @xmath90 . after integrating in orientations an analogous equation to eq.([laeq ] ) @xcite , they must have obtained for the energy in the far field limit , @xmath91 , @xmath92 with @xmath90 . since the pole in @xmath93 lies on the upper half of the complex plane and the pole in @xmath94 lies on the lower half , the only nonvanishing contribution to the above integral comes from the term proportional to @xmath95 . as the real part of the poles is in both cases @xmath96 , taking the limit @xmath90 the exponent vanishes after evaluating the residues and the integral yields the non - oscillating result @xmath97 . rb atom in state @xmath85 @xmath98@xmath99 and a @xmath86k atom in its ground state , for @xmath91 . the black line corresponds to a snapshot of the interaction at time @xmath100s , where the contributions of the d1 and d2 transition lines of the @xmath86k atom ( @xmath101@xmath102 and @xmath103@xmath102 respectively ) add up approximately in - phase . a long - range period @xmath104 , with @xmath105 , is identified . the red line corresponds to the time - independent result of the causal - adiabatic approximation . average over dipole orientations has been taken.,width=291,height=158 ] in the previous stationary calculation of mclone and power @xcite and gomberoff _ et al . _ @xcite the poles in eq.([wad ] ) were not shifted . as a result , when taking the principal value of the integrals in eq.([wad ] ) with @xmath106 , the four exponentials in the numerator contribute as @xmath107 after adding up the residues , yielding the oscillating result @xmath108 . as mentioned after eq.([poles ] ) , some time - independent terms are missing in the stationary calculation , which explains the discrepancy of this result with the time - independent component of ours in eq.([ff ] ) . in fact , the correct time - independent result can be obtained by switching on adibatically the interaction potential , @xmath41 , within the time - dependent causal approach . that is , by replacing @xmath109 in eq.([laeq ] ) with @xmath110 , @xmath90 , and extending the lower limit of the time integrals to @xmath111see appendix . this results in an equation analogous to eq.([wad ] ) but with both poles shifted along the imaginary axis in the same direction an amount @xmath112 , which yields @xmath113 for @xmath91 . recently , safari and karimpour have published a letter @xcite where they claim to obtain for @xmath91 the same oscillating behaviour as gomberoff _ et al . _ @xcite . however , a straightforward comparison of eq.(19 ) of ref.@xcite and eqs.(14,26 ) of ref . @xcite reveals that this is indeed not the case . whereas the result of the latter is the one outlined above , @xmath114 , the authors of the former have found @xmath115 , despite the fact that both approaches are based on fourth order stationary perturbation theory . the origin of the discrepancy is in the algebraic manipulation inherited by the authors of ref.@xcite from ref.@xcite . in the appendix b of ref.@xcite the authors have tried to express the total contribution of the twelve diagrams of fig.[fig1 ] as a single frequency integral whose integrand is a function of the ordinary polarizabilities of the two atoms . in doing so by means of eq.(b2 ) of ref.@xcite , the authors have replaced effectively the denominator of eq.([wad ] ) , which is a symmetric and separable function of @xmath93 and @xmath116 for @xmath106 , by the expression @xmath117^{-1}[1/(k'-k)+1/(k'+k)]$ ] , which is neither symmetric nor separable . as a consequence , that replacement makes the frequency integrals depend arbitrarily on the order of integration . next , integrating in @xmath94 first and in @xmath93 later , one obtains @xmath113 , which agrees with eq.(19 ) of ref.@xcite for @xmath91 , @xmath88 , upon averaging in atomic orientations . interestingly , this result equals the time - independent term of eq.([ff ] ) . however , this coincidence can only be accidental , since the above replacement and the subsequent prescription on the order of integration are neither connected to the time - dependent terms of eq.([poles ] ) which cause the actual discrepancy with respect to the result of refs.@xcite nor to the causal - adiabatic approximation . it is worth noting that while we have invoked the existence of finite lifetimes @xmath118 in order to impose physical constraints on the detuning @xmath17 and on the observation time @xmath13 , no explicit reference to these quantities appear in our expression for @xmath54 . as a matter of fact , only the emission through the exchange of resonant photons between the two atoms has been implicitly accounted for in our calculation of @xmath54 . however , our calculation lacks the inclusion of the spontaneous emission of each atom into free space , whose rates are @xmath119 , respectively . the processes corresponding to the latter phenomenon are generally unimportant in comparison to those depicted in fig.[fig1 ] since their leading contribution to @xmath54 is of order @xmath120 @xmath121 see fig.[fig2 ] . they might only be relevant for the case that the lifetimes are of the order of the temporal frequency of the interaction , @xmath122 , but they can not affect in any case the oscillatory behaviour found here for the terms of order @xmath123 . this argument opposes to the reasons given in ref.@xcite to add imaginary shifts to the real poles at @xmath124 . we finalize by mentioning that berman has shown in a recent publication @xcite how to introuduce spontaneous emission in a consistent manner in an adiabatic approximation . assuming that atom @xmath3 is excited adiabatically with @xmath125 , he has obtained the correct time - independent result . in this letter we have shown that the van der waals interaction between two dissimilar atoms , one of which is initially prepared in an excited state , presents generically oscillations both in time and in space . in quasi - resonant conditions the interaction is dominated at all distances by the exchange of doubly resonant photons between the two atoms . it is modulated in space by long - range oscillations of frequency @xmath82 , while short - range oscillations take place at frequency @xmath83 . the time frequency is @xmath17 , which determines the rate at which the excitation is transferred to atom @xmath4 . in the retarded regime the interaction takes the form of eq.([ff ] ) . only for large integration times , @xmath71 , that expression reduces to a time - independent term which oscillates in space with frequency @xmath69 . the latter is also equivalent to the result of the causal - adiabatic approximations ( see appendix and ref.@xcite ) . it does not agree , however , with the result of stationary perturbation theory @xcite . which incorporate in the calculation of @xmath54 the effect of photon emission into free space . in @xmath126 and @xmath127 the photon @xmath128 is emitted into free space from atom @xmath3 , whereas in @xmath129 it is emitted from atom @xmath4.,width=309,height=83 ] we thank paul berman and marie - pascale gorza for fruitful discussions . financial support from anr-10-idex-0001 - 02-psl and anr-13-bs040003 - 02 is gratefully acknowledged .

the paradigm that ultraluminous infrared galaxies ( ulirgs ) could evolve into qsos was proposed by pioneering studies by sanders et al . ( 1988 ) and norman & scovill ( 1988 ) . by recent observations , the x - ray emission ( brandt et a. 1997 ) or pa@xmath0 lines ( veilleux , sanders , & kim 1999 ) intrinsic for active galactic nuclei ( agns ) have been detected in more than one third of ulirgs . on the other hand , recent high - resolution observations of galactic centers have revealed that the estimated mass of a central `` massive dark object''(mdo ) , which is the nomenclature for a supermassive bh candidate , does correlate with the mass of a galactic bulge ; the mass ratio of the bh to the bulge is 0.002 as a median value ( e.g. , marconi & hunt 2003 ) . in addition , it has been found that qso host galaxies are mostly luminous and well - evolved early - type galaxies ( e.g. , mclure , dunlope , & kukula 2000 ) . comprehensively judging from all these findings , it is likely that ulirgs , qsos , bulges , and smbhs are physically related to each other . a radiation drag model for the formation of smbhs is recently proposed by umemura ( 2001 ) . here , we suppose a simple two - component system that consists of a spheroidal stellar bulge and inhomogeneous optically - thick interstellar medium ( ism ) within it . in this model , radiation drag extracts the angular momentum from inhomogeneous optically - thick ism and allow it to accrete onto the center . then , the mass of an mdo , @xmath1 , which is the total mass of dusty ism assembled to the central massive object , is given by @xmath2 where @xmath3 is the bulge luminosity , @xmath4 is a galactic wind timescale , and @xmath5 is a time before which the optical depth is less than unity . here , @xmath6 is found to be maximally 0.34 in the optically thick limit based on the numerical simulation by kawakatu & umemura ( 2002 ) . in this paper , we should distinguish bh mass from the mass of an mdo although the mass of an mdo is often regarded as bh mass from an observational point of view . supposing the mass accretion driven by the viscosity on to the bh horizon is limited by an order of eddington rate , the bh mass grows according to @xmath7 where @xmath8 is the ratio of bh accretion rate to the eddington rate , and @xmath9 is the eddington timescale , @xmath10 . here @xmath11 is the mass of a seed bh , which could be a massive bh with @xmath12 formed by the collapse of a rotating supermassive star ( shibata & shapiro 2002 ) . . @xmath13 is the time when @xmath14 . here , we assume that @xmath15 is the eddington luminosity . the phase at @xmath16 is a bright and optically thick phase , which may correspond to a ultraluminous infrared galaxy ( ulirg ) phase . after the agn luminosity ( @xmath15 ) exhibits a peak at @xmath17 , it fades out abruptly . the later fading nucleus could be a low luminosity agn ( llagn ) . the optically - thin , bright agn phase ( _ gray area _ ) can be divided into two phases ; one is the host - dominant phase ( proto - qso ) , which is the dark gray area ( @xmath18 ) and the other is the agn - dominant phase ( qso ) , which is the light gray area ( @xmath19 ) . the lifetime of both phases are comparable , @xmath20yr . , height=264 ] here , we construct a scenario of the coevolution of smbh and bulge based on the radiation drag model for smbh formation . in order to treat the realistic chemical evolution of host galaxy , we use an evolutionary spectral synthesis code pegase(fioc & rocca - volmerange 1997 ) . also , we employ a galactic wind model with the wind epoch of @xmath21yr because it can reproduce a present - day color - magnitude relation . in this model , the system is assumed to change from optically - thick to optically - thin phase at @xmath22 . also , we assume the star formation rate is in proportion to gas fraction and initial gas mass is @xmath23 . thereby , we can estimate the evolution of the physical properties of qso host , such as mass , luminosity , color and metallicity . based on the present coevolution model , the mass accretion proportional to the bulge luminosity leads to the growth of an mdo , which is likely to form a massive dusty disk in the nucleus . however , the matter in the mdo does not promptly fall into the bh , because the bh accretion is limited by equation ( [ eq2 ] ) . the bh mass reaches @xmath1 at a time @xmath24 because almost all of the mdo matter has fallen onto the central bh . the resultant bh fraction becomes @xmath25 , which is just comparable to the observed ratio . the evolution of bulge luminosity ( @xmath3 ) and agn luminosity ( @xmath15 ) are shown in figure [ fig:1 ] , assuming the constant eddington ratio ( @xmath26 ) . even after the galactic wind ( @xmath27 ) , @xmath28 continues to grow until @xmath17 and therefore the agn brightens with time . after @xmath15 exhibits a peak at @xmath17 , it fades out abruptly to exhaust the fuel . the fading nucleus could be a low luminosity agn ( llagn ) . ) and the lower panel shows the bh - to - bulge mass ratio ( @xmath29 ) against the bulge fraction ( @xmath30 ) . the hatched area is the prediction of the present analysis . the observational data are plotted by symbols . the data points are categorized into four types . _ crosses _ disk galaxies which do not possess agns , _ open circles _ seyfert 1 galaxies ( sy1s ) , _ filled triangles _ narrow line seyfert 1 galaxies ( nlsy1s ) , and _ filled circles _ seyfert 2 galaxies ( sy2s ) . seyfert galaxies accompanied by starburst activities are specified like sy1/starburst or sy2/starburst . , height=302 ] it is found that the area of @xmath31 can be divided into two phases with a transition time @xmath13 when @xmath14 ; the earlier phase is the host luminosity - dominant phase , and the later phase is the agn luminosity - dominant phase . also , lifetimes of both phases are comparable to each other , which is about @xmath32yr . the agn - dominant phase is likely to correspond to ordinary qsos , but host - dominant phase is obviously different from observed qsos so far . we define this phase as `` a proto - qso '' ( kawakatu , umemura , & mori 2003 ) . we have predicted the observable properties of proto - qsos as follows : ( 1 ) the broad emission lines are narrower , which is less than @xmath33km / s . thus , proto - qso can be regarded as a `` narrow line type i qso ( nlqso ) '' ( 2 ) a massive dusty disk ( @xmath34 ) surrounds a massive bh , and it may obscure the nucleus in the edge - on view to form a type 2 nucleus . ( 3 ) the bh - to - bulge mass ratio , @xmath35 , rapidly increases from @xmath36 to @xmath37 in @xmath38yr . ( 4 ) the colors of @xmath39 at observed bands are about 0.5 magnitude bluer than those of qsos . the predicted properties of proto - qsos are similar to those of high redshift radio galaxies . the proto - qso phase is preceded by an optically thick phase before the galactic wind , which may correspond to ulirgs . the present model predicts that the bh fraction is anticipated to be much less than 0.002 and grows with metallicity in the ulirg phase . we have hitherto applied the radiation drag model to elliptical galaxies , but it could been also applied to disk galaxies . thus , we recently elucidate the efficiency of the radiation drag in disk galaxies ( kawakatu & umemura 2004 ) . as seen in figure [ fig:2 ] , it is found that the smbh should be smaller in a disk galaxy , but correlate with the bulge component in a similar way to an elliptical galaxy . in addition , the observational trends in disk galaxies are broadly consistent with the theoretical prediction . hence , by analogy to proto - qsos , a growing bh phase in a disk galaxy ( e.g. , nls1 ) possibly have a massive dusty disk within a younger bulge . based on the radiation drag model for the bh growth , incorporating the chemical evolution of the early - type host galaxy , we have built up the coevolution model for a qso bh and the host galaxy . as a consequence , we have shown the possibility of the proto - qso phase , which is optically thin and host luminosity - dominant , and has the lifetime comparable to the qso phase timescale of a few @xmath32 yr . also , by considering theoretical predictions for the observable properties in proto - qso phase , we conclude that radio galaxies at high redshifts are a possible candidate for proto - qsos . the proto - qso phase is preceded by an optically - thick ultraluminous infrared galaxy ( ulirg ) phase . furthermore , the present model could be applied to disk galaxies . we found that the mass of a smbh correlates with that of a bulge even in disk galaxies . thus , by analogy to proto - qsos , a growing bh phase in a disk galaxy ( e.g. , nls1 ) may have a massive dusty disk within a younger bulge . in summary , the present model could be a physical picture of evolution of ulirgs ( lirgs ) to qsos ( sy1s ) .

the formation and growth of supermassive black holes ( smbhs ) physically linked with bulges are considered . we focus on the radiation hydrodynamic process for the growth of smbh in the optically thick starburst phase , where radiation from bulge stars drives the mass accretion on to a galactic center through radiation drag effect . in the present scenario , the agn luminosity - dominant phase ( qso phase ) is preceded by the host luminosity - dominat phase , which is called `` proto - qso phase '' . in this phase , there exists the massive dusty disks within younger bulges . also , the proto - qso phase is anticipated by an optically - thick ultraluminous infrared galaxy ( ulirg ) phase . furthermore , such radiation hydrodynamic model has been also applied to disk galaxies . it turns out that the mass of a smbh primarily correlates with a bulge component even in a disk galaxy . thus , by analogy to proto - qsos , the bh growing phase in disk galaxies may have massive dusty disks within younger bulges .

the @xmath0 meson discovered by the cdf collaboration @xcite in @xmath4 collisions at @xmath5 tev completes the family of mixed flavor mesons . the @xmath0 meson has a @xmath6 anti - quark and a @xmath7 quark . current and future experiments at the tevatron and lhc are expected to provide large samples of the excited states of the @xmath0 mesons @xcite . this will make possible the study of the spectroscopy and the decays of the @xmath0 mesons . the @xmath0 meson family lies intermediate in mass and size between the @xmath8 @xmath9 and the @xmath10 ( @xmath11 ) families where the heavy quark interactions are believed to be understood rather well . comparison between experimental measurement and theoretical results will improve our understanding of these interactions and guide us in the search for multiquark and molecular exotics such as the recently claimed ( discovered ) @xmath12 @xcite and @xmath13 @xcite . different models @xcite including various versions of potential models and qcd sum rules have been used to evaluate the @xmath0 spectrum yielding results consistent with the experimentally measured ground state mass and lifetime . the @xmath0 mesons have non - vanishing flavor quantum numbers which are conserved in strong and electromagnetic interactions . therefore , the @xmath0 states , below the open flavor @xmath1 threshold , can only decay weakly or radiatively . these states are expected to be relatively long - lived and easier to be observed experimentally . from the theoretical side , weak and radiative decays are free from uncertainties encountered in strong decays which makes the decays of these states theoretically more tractable . in a previous paper @xcite , we have evaluated a limited set of the @xmath0 spectrum using a model based on reductions of the bethe - salpeter equation ( bse ) . we have used a set of parameters fixed from previous investigations of other meson spectra . our results agreed very well with the experimentally measured ground state mass and lifetime . we also evaluated the @xmath0 decay constant , the @xmath6 antiquark and the @xmath7 quark inclusive decay widths and the weak annihilation width . we also evaluated the exclusive semileptonic ( @xmath14 ) and two - body nonleptonic ( @xmath15 ) decay widths @xcite , where p ( v ) denotes a pseudoscalar ( vector ) meson . we used the bse amplitudes to evaluate the semileptonic form factors and used factorization to obtain the nonleptonic decay widths in terms of the semileptonic form factors and the weak decay constants . in the present paper , we evaluate the complete @xmath0 spectrum below the open flavor @xmath1 threshold and consider the radiative @xmath16 and @xmath17 electromagnetic transitions . this complements our picture @xcite of the @xmath0 mesons . radiative decays are the dominant decay modes of the @xmath0 excited states having widths of about a fraction of mev , much greater than the weak widths at the order of mev . therefore , accurate determination of the masses and the radiative decay widths will be extremely important for understanding the @xmath0 spectrum and distinguishing exotic states . the paper is organized as follows . in the next section we briefly outline our model and compare our spectrum with those of other models . we then evaluate the @xmath16 and @xmath17 radiative decays . finally we discuss our results . we applied a relativistic model based on reductions of the bse to evaluate the @xmath0 spectrum . the bse is a suitable starting point for treating hadrons as relativistic bound states of quarks and antiquarks , just as the dirac equation provides a relativistic description of a fermion in an external field . the bse for a bound state may be written in momentum space in the form @xcite @xmath18 where @xmath19 is the four - momentum of the bound state , @xmath20 is the relative four - momentum of the constituents . the bse has three elements , the two particle propagator ( @xmath21 ) and the interaction kernel ( @xmath22 ) which we provide as input , and the amplitude ( @xmath23 ) obtained by solving the equation . we also solve for the energy , which is contained in the propagator . we used a reduction of the bse where the two particle propagator is modified in a way that keeps covariance and reduces the four - dimensional bse into a three - dimensional equation @xcite . we considered an interactional kernel that consists of two terms , one for the short range one gluon exchange @xmath24 and the other for the long range phenomenological confinement interaction @xmath25 @xcite . @xmath26 here , @xmath27 is the strong coupling , which is weighted by the meson color factor of @xmath28 , and the string tension @xmath29 is the strength of the confining part of the interaction . while the one gluon exchange @xmath24 has the vector nature , we adopt a scalar lorentz structure for @xmath25 as discussed in @xcite . we solve for the energies and the amplitudes in momentum space and transform these amplitudes into coordinate space . we have included seven parameters in our model , four masses ( @xmath30 ) , two parameters to fix the strong coupling @xmath27 and control its running with the meson mass , and the last parameter is the string tension @xmath29 of the confining interaction . we fixed the parameters of our model by fitting the spectra of other mesons as described in @xcite . we obtained a good fit for a wide range of meson masses with root mean square deviation from experimental masses of about 50 mev . table [ parameters ] compares the parameters relevant to the @xmath0 mesons of our model with those of different models in the literature . in table [ parameters ] , @xmath31 and @xmath32 are the masses of the @xmath7 and @xmath33 quark respectively , while @xmath27 is the strong coupling of the one gluon exchange and @xmath29 is the string tension of the confining interaction . in many models , including ours , @xmath27 runs with the meson mass , thus table [ parameters ] gives @xmath27 at the scale of the ground state mass of the @xmath0 mesons . the model used in @xcite employs the martin potential @xcite which is not linear but varies with powers of the quark antiquark distance . we notice that our @xmath31 and @xmath32 values are smaller that those of other models , while our string tension @xmath29 is larger . the values of the strong coupling @xmath27 are consistent around 0.36 except in @xcite where @xmath27 is 0.265 and in @xcite where @xmath27 is 0.21 . .[parameters]the parameters of different models relevant to the @xmath0 mesons . [ cols="^,^,^,^,^,^",options="header " , ] + table [ m1 ] shows differences between the transition energies ( spin - spin splittings ) , while the transition matrix elements are comparable . it also shows that hindered transitions have widths at the same level as the allowed ones . we have evaluated the @xmath0 spectrum below the @xmath1 threshold using a reduction of the bse . we have made predictions for the transition rates of the @xmath16 and @xmath17 radiative decays . we compared our results with the results of other models in the literature . experimental results will help clarify the spin - spin and spin - orbit splittings of different models and consequently improve our knowledge of physical quantities such as the quark masses and the strong coupling @xmath27 at the scale of @xmath34 . measurements of radiative transitions and comparison with such results may indicate the existence of exotic multiquark or molecular exotics . gershtein , v.v . kiselev , a.k . likhoded , a.v . tkabladze , phys . usp . * 38 * , 1 ( 1995 ) ; v.v . kiselev , a.k . likhoded , a.v . tkabladze , phys . rev . * d51 * , 3613 ( 1995 ) ; s.s . gershtein , v.v . kiselev , a.k . likhoded , a.v . tkabladze , a.v . berezhnoi , a.i . onishchenko , hep - ph/9803433 . a. abd el - hady , j. h. muoz , and j.p . vary , phys . rev . * d62 * , 014019 ( 2000 ) . c. itzykson , and j.b . zuber , quantum field theory . mcgraw - hill , new york ( 1980 ) ( chapter 10 gives a review of bethe - salpeter equation ) .

we evaluate the complete spectrum of the @xmath0 mesons , below the open flavor @xmath1 threshold , in a bethe - salpeter model . we make predictions for the radiative decay widths of the @xmath0 excited states . we compare our results with those of other models . epsf -0.5 in 6.5 in 8.5 in -.375 in * radiative decays of @xmath0 mesons in a bethe - salpeter model + * @xmath2 _ physics department , king khalid university , abha 9004 , saudi arabia _ + @xmath3 _ department of physics and astronomy , iowa state university , ames , iowa 50011 , usa _ + .5 in

numerical simulations of lattice field theories are usually performed in the lagrangian formulation . nonetheless , we think there are very good reasons to develop numerical simulation techniques for the hamiltonian approach @xcite : powerful many - body techniques are available @xcite , which allow the direct computation of the vacuum wave function properties ; fermions are implemented directly and need not be integrated out ; properties like the mass spectrum are more immediate . finally , universality checks between the lagrangian and the hamiltonian formalism are very welcome . we study the hamiltonian lattice version of the two - dimensional wess - zumino model described in refs . @xcite ; we only wish to highlight here the main features of the formulation . in the hamiltonian formalism , since @xmath0 is conserved , it is possible to preserve exactly a 1-dimensional subalgebra of the original supersymmetry algebra , i.e. , we can write @xmath1 , where @xmath2 is a fermionic charge . this subalgebra is enough to guarantee some of the most important property of supersymmetry , including a non - negative spectrum , and pairing of fermionic and bosonic states of nonzero energy ; spontaneous breaking of supersymmetry is equivalent to a strictly positive ground - state energy @xmath3 ; the full supersymmetry algebra is recovered in the continuum limit together with lorentz invariance . in order to obtain a hamiltonian free of fermion sign problems , and therefore amenable to quantum monte carlo methods , we adopt free boundary conditions , with lattice size @xmath4 . the model is parametrized by a _ @xmath5 , an arbitrary polynomial in the bosonic field . the two - dimensional wess - zumino model is superrenormalizable ; fields do not renormalize , and only @xmath5 needs to be normal ordered . in strong coupling at leading order , the model reduces to independent copies of supersymmetric quantum mechanics , one for each site ; supersymmetry is broken if and only if the degree of the prepotential @xmath6 is even @xcite . in weak coupling , on the other hand , supersymmetry is broken at tree level if and only if @xmath6 has no zeroes . the predictions of strong coupling and weak coupling are quite different , and it is interesting to study the crossover from strong to weak coupling . we perform our simulations using the green function monte carlo ( gfmc ) algorithm @xcite . a discussion of gfmc in the context of the present problem can be found in ref . @xcite ; we only wish to remark the main features of the algorithm : the aim is to generate a stochastic representation of the ground - state wavefunction , which is then used to compute expectation values of observables . statistical fluctuations are reduced with the help of a guiding wavefunction , whose free parameters are determined dynamically during the simulation . in order to keep the variance of observables finite as the simulation proceeds , it is necessary to simulate a population of @xmath7 _ walkers _ ( field configurations at fixed time ) , and extrapolate the results to @xmath8 . we focus on the case @xmath9 ; strong coupling always predicts supersymmetry breaking ; weak coupling predicts unbroken supersymmetry for @xmath10 ; according to ref . @xcite , unbroken supersymmetry should be accompanied by a nonzero @xmath11 ( parity breaking ) . perturbative computations show that @xmath12 where @xmath13 is the adimensional lattice bare coupling , @xmath14 is the renormalized ( continuum ) coupling , with dimension of @xmath15 , defined at the mass scale @xmath16 , and @xmath17 is the lattice spacing . we study , as @xmath18 , the trajectory @xmath19 corresponding to a perturbative rg trajectory ( [ eq : evol2_l ] ) ; the effect of @xmath20 is small in the range we considered , therefore we expect eq . ( [ eq : trajectory ] ) to be a reasonable approximation to a true rg trajectory . we estimate the correlation length from the exponential decay of the connected correlation function @xmath21 averaged over all @xmath22 pairs with @xmath23 , excluding pairs for which @xmath24 or @xmath25 is closer to the border than ( typically ) 8 . in our formulation , fermions are staggered and even / odd @xmath26 correspond to different channels . we begin with the discussion of the case @xmath27 , for which we have obtained the statistics of @xmath28 gfmc iterations . the even-@xmath26 channel is plotted in fig . [ fig : xieven , l2=0.35 ] ; it is very difficult to extract a correlation length , presumably because @xmath29 has a very small overlap with the lightest state of the channel , and the value of @xmath30 quoted in fig . [ fig : xieven , l2=0.35 ] should be considered tentative . the odd-@xmath26 channel , plotted in fig . [ fig : xiodd , l2=0.35 ] , is much cleaner , and it is possible to estimate @xmath30 with a good precision . for the other values of @xmath31 , the situation is similar but with larger errors ; we have a statistics of at least @xmath32 iterations , which we are increasing to @xmath28 . the values of @xmath33 follow nicely the expected behavior @xmath34 as shown in fig . [ fig : xioddlog ] : the entire range @xmath35 seem to be in the scaling region , with @xmath36 a borderline case . the values of @xmath37 have very large errors , and it is hard to draw any conclusion from them . we measure the ground state energy @xmath3 along the trajectory ( [ eq : trajectory ] ) ; the measurements have a very small statistical error , ranging from 1% for @xmath38 ( where @xmath39 ) to 0.1% for @xmath36 . we extrapolate to @xmath40 and @xmath8 fitting @xmath41 to the form @xmath42 @xmath41 is plotted in fig . [ fig : e0log ] : it seems to behave @xmath43 , while nave scaling would predict @xmath44 . the value of @xmath41 ( disregarding this puzzling exponent ) and the lack of any signal for a breakdown of parity ( like a double - peaked distribution of @xmath29 ) strongly hint that the trajectory ( [ eq : trajectory ] ) belongs to the phase with broken supersymmetry and zero @xmath11 . we are repeating the computation for trajectories with smaller @xmath20 . j. kogut , l. i. susskind , phys . d11 ( 1975 ) 395 ; j. kogut , rev . phys . 51 ( 1979 ) 659 . w. von der linden , phys . rept . 220 ( 1992 ) 53 . m. beccaria , m. campostrini , a. feo , nucl . phys . b ( proc . suppl . ) 106 - 107 ( 2002 ) 944 . m. beccaria , m. campostrini , a. feo , hep - lat/0109005 . e. witten , nucl . b188 ( 1981 ) 513 . e. witten , nucl . b202 ( 1982 ) 253 .

we investigate a hamiltonian lattice version of the two - dimensional wess - zumino model by quantum monte carlo simulations . in order to study the pattern of supersymmetry breaking , we measure the ground state energy and the correlation length along a trajectory approaching the continuum limit . the algorithm is very effective in measuring the ground state energy , and adequate for the correlation length .

generalized parton distributions ( gpds ) @xcite ( see also @xcite for a recent review ) provide a means of parametrizing hadronic contributions to both exclusive and inclusive processes . they reduce in certain limits to form factors and to ( forward ) parton distributions . for a review on the nucleon axial structure see @xcite and for spin - dependent parton distributions consult @xcite . gpds depend on three independent kinematic variables and are therefore far more difficult to extract from experiments than forward parton distributions . lattice simulations provide a general , model - independent way to compute their moments directly . first results for spin - independent gpds have been presented in @xcite . these papers , however , concentrate on rather large quark masses . it is imperative to extend these studies down into the chiral regime . in this talk , we will present a first study of spin - dependent gpds , both with wilson fermions at large quark masses and with staggered sea and domain - wall valence fermions at intermediate quark masses . spin - dependent gpds are specified by @xmath1 and @xmath2 , defined via @xmath3 the upper index f denotes the quark flavor , @xmath4 is the average longitudinal momentum fraction of the struck quark , and @xmath5 the longitudinal momentum transfer . the total invariant momentum transfer squared is given by @xmath6 , with the four - momentum transfer @xmath7 . the average hadron momentum is denoted by @xmath8 . we also use the short - hand notation @xmath9 . by taking moments with respect to @xmath4 , we end up with a tower of local matrix elements of the form @xmath10 * 3c|c + + num & & @xmath11 + @xmath12 & & @xmath13 + @xmath14 & & @xmath15 + @xmath16 & & @xmath17 + + + num & @xmath18 & @xmath19 & @xmath11 + @xmath20 & @xmath21 & @xmath21 & @xmath22 + + @xmath20 & @xmath21 & @xmath23 & @xmath24 + these matrix elements can then be computed by a lattice simulation . the parametrization of these matrix elements follows from their lorentz - structure in the continuum and is expressed in terms of the generalized form factors ( gffs ) @xmath25 and @xmath26 . for example , for @xmath27 : @xmath28 the moments of @xmath29 and @xmath2 are polynomials in @xmath30 with @xmath31 and @xmath32 as coefficients , @xmath33 the reconstruction of the gpds is therefore possible by an inverse mellin transform . we use five samples of unquenched gauge field data in our simulations . the parameters of the lattices are presented in tab . [ tab : latt - pars ] . as valence quarks we use wilson fermions on the sesam lattices and domain wall fermions with a height of @xmath34 and @xmath35 on the milc lattices . in the latter case we also use hyp - smearing @xcite with @xmath36 and @xmath37 . with @xmath38 for @xmath39 , @xmath40 . the form factors have been normalized to one at @xmath41 and fitted by a dipole form . ] the domain - wall masses have been adjusted to keep the pseudoscalar lattice mass in the region of the lowest corresponding staggered one . for the wilson fermion renormalization constants we use the perturbative one - loop results quoted in @xcite . the renormalization constants for the domain - wall case are not yet calculated , so we use the tree - level value . hence , our results are preliminary . . ] . ] we concentrate on the quark flavor combination u - d since the resulting matrix elements are free from disconnected contributions . the gff @xmath42 corresponds to the axial form factor , while @xmath43 is the first gff which is not directly accessible experimentally . both gffs are plotted with normalization @xmath44 for the heaviest quark mass in fig . [ fig : atilde - n ] . the curves provide dipole fits to the data points with the error bands representing one standard error . it is apparent that the dependencies on the parameters @xmath4 and @xmath45 of @xmath46 do not factorize , a result that is very similar to the spin - independent case @xcite . however , the difference between the two moments appears to be smaller in the spin - dependent case . the axial coupling as a function of the quark mass is plotted in fig . [ fig : axialcoup ] . one should note , however , that this quantity is highly sensitive to finite - volume effects @xcite . at least at the lightest mass , a couple of simulations at larger lattice volumes need to be performed to achieve a conclusive result for the chiral behavior . the first moment of the forward parton distribution @xmath47 is displayed in fig . [ fig : atilde - forw ] . although the measured values decrease in the chiral regime toward the experimental value , this result needs to be corroborated with better statistics . in this talk we have presented first results on spin - dependent generalized parton distributions . in the forward case we have presented preliminary results for light quark masses which eventually should allow us to bridge the gap to the chiral regime . 99 d. mller , d. robaschik , b. geyer , f.m . dittes and j. horejsi , fortsch . * 42 * ( 1994 ) 101 . ji , phys . * 78 * ( 1997 ) 610 . radyushkin , phys . d * 56 * ( 1997 ) 5524 . m. diehl , arxiv : hep - ph/0307382 . v. bernard , l. elouadrhiri and u.g . meissner , j. phys . g * 28 * ( 2002 ) r1 . y. goto _ et al . _ [ asymmetry analysis collaboration ] , phys . d * 62 * ( 2000 ) 034017 . m. glck , e. reya , m. stratmann and w. vogelsang , phys . d * 63 * ( 2001 ) 094005 . j. blmlein and h. bttcher , nucl . b * 636 * ( 2002 ) 225 . m. gckeler _ et al . _ [ qcdsf collaboration ] , arxiv : hep - ph/0304249 . p. hgler , j.w . negele , d.b . renner , w. schroers , t. lippert and k. schilling [ lhpc collaboration ] , phys . rev . d * 68 * ( 2003 ) 034505 . a. hasenfratz and f. knechtli , phys . d * 64 * ( 2001 ) 034504 . d. dolgov _ et al . _ , phys . d * 66 * ( 2002 ) 034506 . negele _ et al . _ , these proceedings , arxiv : hep - lat/0309060 . hemmert and a. schfer , private communication .

we present a lattice measurement of the first two moments of the spin - dependent gpd @xmath0 . from these we obtain the axial coupling constant and the second moment of the spin - dependent forward parton distribution . the measurements are done in full qcd using wilson fermions . in addition , we also present results from a first exploratory study of full qcd using asqtad sea and domain - wall valence fermions .

following the main text , the evolution operator associated with the embedding hamiltonian @xmath90 can be implemented via 4 control-@xmath91 gates ( @xmath92 ) , and a single qubit rotation @xmath93 . these gates act as @xmath94 with @xmath95 , and @xmath96 . the indices @xmath97 and @xmath98 indicate on which particle the operators act . the circuit for the embedding quantum simulator consists of a sequence of gates applied in the following order : @xmath99 simple algebra shows that this expression can be recast as @xmath100 explicitly exhibiting the equivalence between the gate sequence and the evolution under the hamiltonian of interest . the evolution of the reduced circuit is given by a @xmath93 rotation of qubit @xmath16 , followed by two consecutive control - z gates on qubits @xmath51 and @xmath12 , both controlled on qubit @xmath16 , see fig . [ fig : sm1 ] ( a ) . these logic operations are experimentally implemented by devices that change the polarization of the photons , where the qubits are encoded , with transformations as depicted in fig . [ fig : sm1 ] ( b ) . for single qubit rotations , we make use of half - wave plates ( hwp s ) , which shift the linear polarization of photons . for the two - qubit gates , we make use of two kinds of partially - polarizing beam splitters ( ppbs s ) . ppbs s of type @xmath51 have transmittances @xmath101 and @xmath102 for horizontal and vertical polarizations , respectively . ppbs s of type @xmath12 , on the other hand , have transmittances @xmath103 and @xmath104 . their effect can be expressed in terms of polarization dependant input - output relations with the transmitted mode corresponding to the output mode of the bosonic creation operators as @xmath105 where @xmath106 ( @xmath107 ) stands for the @xmath97-th input ( output ) port of a ppbs with transmittance @xmath108 for @xmath109-polarized photons . our circuit is implemented as follows : the first @xmath93 rotation is implemented via a hwp oriented at an angle @xmath110 with respect to its optical axis . the rest of the target circuit , corresponding to the sequence of two control - z gates , can be expressed in terms of the transformation of the input to output creation operators as @xmath111 where @xmath112 , @xmath113 , and @xmath114 denote the creation operators acting on qubits @xmath16 , @xmath51 , and @xmath12 , respectively . these polarization transformations can be implemented with a probability of @xmath115 via a @xmath22-fold coincidence detection in the circuit depicted in fig . [ fig : sm1 ] ( b ) . in this dual - rail representation of the circuit , interactions of modes @xmath116 and @xmath117 with vacuum modes are left implicit . the @xmath118 and @xmath119 single qubit gates in fig . [ fig : sm1 ] ( b ) are implemented by hwp s with angles @xmath120 and @xmath16 , respectively . in terms of bosonic operators , these gates imply the following transformations , @xmath121 according to all the input - output relations involved , it can be calculated that the optical elements in fig . [ fig : sm1 ] ( b ) implement the following transformations @xmath122 if events with @xmath16 photons in some of the three output lines of the circuit are discarded . thus , this linear optics implementation corresponds to the evolution of interest with success probability @xmath123 . given the probabilistic nature and low efficiency of down - conversion processes , multi - photon experiments are importantly limited by low count - rates . in our case , typical two - photon rates from source are around @xmath124 khz at @xmath74 pump ( two - photon rates are approx . linear with pump power ) , which after setup transmission ( @xmath125 ) and @xmath126 success probability of one controlled - sign gate , are reduced to about @xmath127 khz ( @xmath51 khz ) at @xmath74 ( @xmath72 ) pump . these count - rates make it possible to run the two - photon protocol , described in the main text , at low powers in a reasonable amount of time . however , this situation is drastically different in the three - photon protocol , where we start with @xmath128 hz of @xmath39-fold events from the source , in which case after setup transmission , @xmath115 success probability of two gates , and @xmath129 transmission in each of two @xmath12 nm filters used for this case , we are left with as few as @xmath130 mhz ( @xmath131 mhz ) at @xmath74 ( @xmath72 ) pump ( @xmath39-fold events reduce quadratically with pump ) . consequently , long integration times are needed to accumulate meaningful statistics , imposing a limit in the number of measured experimental settings . to estimate the effect of power - dependent higher - order terms in the performance of our protocols , we inspect the pump power dependence of extracted concurrence from both methods . [ fig : sm2 ] shows that the performances of both protocols decrease at roughly the same rate with increasing pump power , indicating that in both methods the extracted concurrence at @xmath72 pump is close to performance saturation . the principal difference between the two methods is that in the three - qubit protocol one of the photons originates from an independent down - conversion event and as such will present a slightly different spectral shape due to a difficulty in optimizing the phase - matching condition for both forward and backward directions simultaneously . to reduce this spectral mismatch , we used two @xmath12 nm filters at the output of the two spatial modes where interference from independent events occurs , see fig . [ fig : sm3 ] . note that not identical spectra are observed . this limitation would be avoided with a source that presented simultaneous high indistinguishability between all interfering photons .

measuring entanglement is a demanding task that usually requires full tomography of a quantum system , involving a number of observables that grows exponentially with the number of parties . recently , it was suggested that adding a single ancillary qubit would allow for the efficient measurement of concurrence , and indeed any entanglement monotone associated to antilinear operations . here , we report on the experimental implementation of such a device an embedding quantum simulator in photonics , encoding the entangling dynamics of a bipartite system into a tripartite one . we show that bipartite concurrence can be efficiently extracted from the measurement of merely two observables , instead of fifteen , without full tomographic information . entanglement is arguably the most striking feature of quantum mechanics @xcite , defining a threshold between the classical and quantum behavior of nature . yet its experimental quantification in a given system remains challenging . several measures of entanglement involve unphysical operations , such as antilinear operations , on the quantum state @xcite , and thus its direct measurement can not be implemented in the laboratory . as a consequence , in general , experimental measurements of entanglement have been carried out mostly via the full reconstruction of the quantum state @xcite . while this technique called quantum state tomography ( qst)has been widely used when dealing with relatively low - dimensional systems @xcite , it is known to become rapidly intractable as the system size grows , being outside of experimental reach in systems with @xmath0 qubits @xcite . this difficulty lies in having to measure an exponentially - growing number of observables , @xmath1 , to reconstruct @xmath2-qubits . such constraint can be relaxed somewhat by using , for example , multiple copies of the same quantum state @xcite , prior state knowledge in noisy dynamics @xcite , compressed sensing methods @xcite , or measuring phases monotonically dependent on entanglement @xcite . however , measuring entanglement in scalable systems remains a challenging task . an efficient alternative is to embed the system dynamics into an enlarged hilbert - space simulator , called embedding quantum simulator ( eqs ) @xcite , where unphysical operations are mapped onto physical transformations on the simulator . the price to pay , comparatively small in larger systems , is the addition of only one ancillary qubit and , usually , dealing with more involved dynamics . however , measuring the entanglement of the simulated system becomes efficient , involving the measurement of a low number of observables in the eqs , in contrast to the @xmath1 needed with full tomography . in this letter , we experimentally demonstrate an embedding quantum simulator , using it to efficiently measure two - qubit entanglement . our eqs uses three polarization - encoded qubits in a circuit with two concatenated controlled - sign gates . the measurement of only 2 observables on the resulting tripartite state gives rise to the efficient measurement of bipartite concurrence , which would otherwise need 15 observables . + _ protocol . _ we consider the simulation of two - qubit entangling dynamics governed by the hamiltonian @xmath3 , where @xmath4 is the z - pauli matrix written in the computational basis , @xmath5 , and @xmath6 is a constant with units of frequency . for simplicity , we let @xmath7 . under this hamiltonian , the concurrence @xcite of an evolving pure state @xmath8 is calculated as @xmath9 , where @xmath10 is the complex conjugate operator defined as @xmath11 . and @xmath12 evolve via an entangling hamiltonian @xmath13 during a time interval @xmath14 , at which point quantum state tomography ( qst ) is performed via the measurement of @xmath15 observables to extract the amount of evolving concurrence . ( b ) an efficient alternative corresponds to adding one extra ancilla , qubit @xmath16 , and having the enlarged system the embedding quantum simulator ( eqs)evolve via @xmath17 . only two observables are now required to reproduce measurements of concurrence of the system under simulation.,width=283 ] notice here the explicit dependance of @xmath18 upon the unphysical transformation @xmath10 . we now consider the dynamics of the initial state @xmath19 . under these conditions one can calculate the resulting concurrence at any time @xmath14 as @xmath20 the target evolution , @xmath21 , can be embedded in a @xmath22-qubit simulator . given the state of interest @xmath23 , the transformation @xmath24 gives rise to a real - valued @xmath22-qubit state @xmath25 in the corresponding embedding quantum simulator . the decoding map is , accordingly , @xmath26 . the physical unitary gate @xmath27 transforms the simulator state into @xmath28 , which after the decoding becomes @xmath29 . therefore , the action of the complex conjugate operator @xmath10 corresponds to the single qubit rotation @xmath27 @xcite . now , following the same encoding rules : @xmath30 , with @xmath31 an observable in the simulation . in the case of @xmath32 , we obtain @xmath33 which relates the simulated concurrence to the expectation values of two nonlocal operators in the embedding quantum simulator . regarding the dynamics , it can be shown that the hamiltonian @xmath17 that governs the evolution in the simulator is @xmath34 @xcite . accordingly , in our case , it will be given by @xmath35 . our initial state under simulation is @xmath19 , which requires , see eq . ( [ eq : tosim ] ) , the initialization of the simulator in @xmath36 . under these conditions , the relevant simulator observables , see eq . ( [ eq : c ] ) , read @xmath37 and @xmath38 , from which the concurrence of eq . ( [ eq : csim ] ) will be extracted . therefore , our recipe , depicted in fig . [ fig:1 ] , allows the encoding and efficient measurement of two - qubit concurrence dynamics . to construct the described three - qubit simulator dynamics , it can be shown ( see supplemental material ) that a quantum circuit consisting of @xmath39 controlled - sign gates and one local rotation @xmath40 , as depicted in fig . [ fig:2](a ) , implements the evolution operator @xmath41 $ ] , reproducing the desired dynamics , with @xmath42 . this quantum circuit can be further reduced if we consider only inputs with the ancillary qubit in state @xmath43 , in which case , only two controlled - sign gates reproduce the same evolution , see fig . [ fig:2 ] ( b ) . this reduced subspace of initial states corresponds to simulated input states of only real components . controlled - sign gates and one local rotation @xmath44 implement the evolution operator @xmath45 , with @xmath42 . ( b ) a reduced circuit employing only two controlled - sign gates reproduces the desired three - qubit dynamics for inputs with the ancillary qubit in @xmath46.,width=245 ] _ experimental implementation . _ we encode a three - qubit state in the polarization of 3 single - photons . the logical basis is encoded according to @xmath47 , where @xmath48 and @xmath49 denote horizontal and vertical polarization , respectively . the simulator is initialized in the state @xmath50 of qubits @xmath16 , @xmath51 and @xmath12 , and evolves via the optical circuit in fig . [ fig:2 ] ( b ) . figure [ fig:3 ] is the physical implementation of fig . [ fig:2 ] ( b ) , where the dimensionless parameter @xmath52 is controlled by the angle @xmath53 of one half - wave plate . the two concatenated controlled - sign gates are implemented by probabilistic gates based on two - photon quantum interference @xcite , see supplemental material . in order to reconstruct the two three - qubit observables in eq . ( [ eq : c ] ) , one needs to collect @xmath54 possible tripartite correlations of the observable eigenstates . for instance , the observable @xmath55 is obtained from measuring the @xmath54 projection combinations of the @xmath56 states , where @xmath57 , @xmath58 , and @xmath59 and @xmath60 are their orthogonal states , respectively . to implement these polarization projections , we employed glan - taylor prisms due to their high extinction ratio . however , only their transmission mode is available , which required each of the @xmath54 different projection settings separately , extending our data - measuring time . the latter can be avoided by simultaneously registering both outputs of a projective measurement , such as at the two output ports of a polarizing beam splitter , allowing the simultaneous recording of all @xmath54 possible projection settings . thus , an immediate reconstruction of each observable is possible . our source of single - photons consists of four - photon events collected from the forward and backward pair emission in spontaneous parametric down - conversion in a _ beta_-barium borate ( bbo ) crystal pumped by a @xmath61 mhz frequency - doubled mode - locked femtosecond ti : sapphire laser . one of the four photons is sent directly to an avalanche photodiode detector ( apd ) to act as a trigger , while the other @xmath22 photons are used in the protocol . this kind of sources are known to suffer from undesired higher - order photon events that are ultimately responsible of a non - trivial gate performance degradation @xcite , although they can be reduced by decreasing the laser pump power . however , given the probabilistic nature and low efficiency of down - conversion processes , multi - photon experiments are importantly limited by low count - rates , see supplemental material . therefore , increasing the simulation performance quality by lowering the pump requires much longer integration times to accumulate meaningful statistics , which ultimately limits the number of measured experimental settings . as a result of these higher - order noise terms , a simple model can be considered to account for non - perfect input states . the experimental input @xmath62-qubit state @xmath63 can be regarded as consisting of the ideal state @xmath64 with certain probability @xmath65 , and a white - noise contribution with probability @xmath66 , i.e. @xmath67 . since the simulated concurrence is expressed in terms of tensorial products of pauli matrices , the experimentally simulated concurrence becomes @xmath68 . in fig . [ fig:4 ] , we show our main experimental results from our photonic embedding quantum simulator for one cycle of concurrence evolution taken at different pump powers : @xmath69 mw , @xmath70 mw , and @xmath71 mw referred as to @xmath72 , @xmath73 , and @xmath74 pump , respectively . figure [ fig:4 ] ( a ) shows theoretical predictions ( for ideal pure - state inputs ) and measured fractions of the different projections involved in reconstructing @xmath55 and @xmath75 for @xmath72 pump at @xmath76 . from measuring these two observables , see eq . ( [ eq : c ] ) , we construct the simulated concurrence produced by our eqs , shown in fig . [ fig:4 ] ( b ) . we observe a good behavior of the simulated concurrence , which preserves the theoretically predicted sinusoidal form . the overall attenuation of the curve is in agreement with the proposed model of imperfect initial states . together with the unwanted higher - order terms , we attribute the observed degradation to remaining spectral mismatch between photons created by independent down - conversion events and injected to inputs @xmath16 and @xmath12 of fig . [ fig:3]at which outputs @xmath12 nm band - pass filters with similar but not identical spectra were used . we compare our measurement of concurrence via our simulator with an explicit measurement from state tomography . in the latter we inject one down - converted pair into modes @xmath16 and @xmath51 of fig . [ fig:3 ] . for any value of @xmath14 , set by the wave - plate angle @xmath77 , this evolving state has the same amount of concurrence as the one from our simulation , they are equivalent in the sense that one is related to the other at most by local unitaries , which could be seen as incorporated in either the state preparation or within the tomography settings . figure [ fig:5 ] shows our experimental results for the described two - photon protocol . we extracted the concurrence of the evolving two - qubit state from overcomplete measurements in quantum state tomography @xcite . ( blue ) , @xmath73 ( green ) , and @xmath74 ( red ) pump powers . the corresponding curves indicate @xmath78 , with @xmath79 the maximum extracted concurrence for a given pump power ( pp ) : @xmath80 , @xmath81 , and @xmath82 . errors are estimated from monte - carlo simulations of poissonian counting fluctuations . ] a maximum concurrence value of @xmath83 is predicted in the ideal case of perfect pure - state inputs . experimentally , we measured maximum values of concurrence of @xmath80 , @xmath81 and @xmath82 , for the three different pump powers , respectively . for the purpose of comparing this two - photon protocol with our embedding quantum simulator , only results for the above mentioned powers are shown . however , we performed an additional two - photon protocol run at an even lower pump power of @xmath84 mw ( @xmath85 pump ) , and extracted a maximum concurrence of @xmath86 . a clear and pronounced decline on the extracted concurrence at higher powers is also observed in this protocol . however , a condition closer to the ideal one is reached . this observed pump power behavior and the high amount of measured concurrence suggest a high - quality gate performance , and that higher - order terms larger for higher pump powers are indeed the main cause of performance degradation . while only mixed states are always involved in experiments , different degrees of mixtures are present in the @xmath22- and @xmath12-qubit protocols , resulting in different extracted concurrence from both methods . an inspection of the pump - dependence , see supplemental material , reveals that both methods decrease similarly with pump power and are close to performance saturation at the @xmath72 pump level . this indicates that in the limit of low higher - order emission our @xmath22-qubit simulator is bounded to the observed performance . temporal overlap between the @xmath22 photons was carefully matched . therefore , we attribute the remaining discrepancy to spectral mismatch between photons originated from independent down - conversion events . this disagreement can in principle be reduced via error correction @xcite and entanglement purification @xcite schemes with linear optics . _ discussion . _ we have shown experimentally that entanglement measurements in a quantum system can be efficiently done in a higher - dimensional embedding quantum simulator . the manipulation of larger hilbert spaces for simplifying the processing of quantum information has been previously considered @xcite . however , in the present scenario , this advantage in computing concurrence originates from higher - order quantum correlations , as it is the case of the appearance of tripartite entanglement @xcite . the efficient behavior of embedding quantum simulators resides in reducing an exponentially - growing number of observables to only a handful of them for the extraction of entanglement monotones . we note that in this non - scalable photonic platform the addition of one ancillary qubit and one entangling gate results in count rates orders of magnitude lower as compared to direct state tomography on the @xmath12-qubit dynamics . this means that in practice absolute integration times favor the direct @xmath12-qubit implementation . however , this introduced limitation escapes from the purposes of the embedding protocol and instead belongs to the specific technology employed in its current state - of - the - art performance . this work represents the first proof - of - principle experiment showing the efficient behavior of embedding quantum simulators for the processing of quantum information and extraction of entanglement monotones . this validates an architecture - independent paradigm that , when implemented in a scalable platform , e.g. ions @xcite , would overcome a major obstacle in the characterization of large quantum systems . the relevance of these techniques will thus become patent as quantum simulators grow in size and currently standard approaches like full tomography become utterly unfeasible . we believe that these results pave the way to the efficient measurement of entanglement in any quantum platform via embedding quantum simulators . we thank m. a. broome for helpful discussions . this work was supported by the centre for engineered quantum systems ( grant no . ce110001013 ) and the centre for quantum computation and communication technology ( grant no . ce110001027 ) . m. p. a. acknowledges support from the australian research council discovery early career awards ( no . de120101899 ) . a. g. w. was supported by the university of queensland vice - chancellor s senior research fellowship . j. c. acknowledge support from the alexander von humboldt foundation , while r. d. c. , j. s. p. , and e. s. from basque government it472 - 10 ; 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since the suggestion of @xmath0 suppression as a signal of quark - gluon plasma ( qgp ) formation by matsui and satz @xcite in 1986 the problem of quarkonium dissociation in hot and dense strongly interacting matter has played a key role for qgp diagnostics in relativistic heavy - ion collision experiments . the original idea was that in a qgp the string tension of the confining potential vanishes and the residual one - gluon exchange interaction undergoes a debye screening by the color charges of the plasma . when the temperature dependent debye radius @xmath1 ( the inverse of the debye mass @xmath2 ) becomes shorter than the bohr radius of the charmonium ground state ( @xmath0 ) then the mott effect @xcite ( bound state dissociation ) occurs and the corresponding temperature is @xmath3 . this simple idea grew up to a multifacetted research direction when not only in the first light ion - nucleus collisions at the cern na38 experiment , but also in proton - nucleus collisions at fermilab @xmath0 suppression has been found so that there is not only a qgp but also a cold nuclear matter effect on charmonium production , see @xcite for a recent review . if one wants to explore the question of screening in a plasma more in detail then a variety of approaches is available in the literature , from the original debye - hckel approach @xcite applicable to any vacuum potential ( for example the cornell potential ) , over the thermodynamic green functions approach to the ab - initio studies of heavy - quark potentials in lattice qcd . with the obtained medium - dependent potentials one can then study the bound state problem by solving the thermodynamic @xmath4 - matrix for quarkonia @xcite , or the equivalent schrdinger - type wave equation where medium effects are absorbed in a plasma hamiltonian @xcite . on the other hand one may calculate proper correlators directly from lattice qcd and extract from them spectral functions @xcite . there is an intriguing disagreement between the mott temperatures deduced from these spectral functions and those of the potential models : from the lattice data for quarkonium correlators one has extracted @xmath5 while in potential model calculations @xmath6 . this problem has lead to the discussion of the proper thermodynamical function to be used as a potential in the schrdinger equation , see @xcite and references therein . in this contribution we follow the recently suggested @xcite modification of the standard one - loop calculation of the debye mass in thermal quantum field theory @xcite in the framework of the poyakov - nambu - jona - lasinio model , now widely used for a microscopic qcd - motivated description of mesons in quark matter @xcite . we then solve the schrdinger equation for charmonium and bottomonium states with the plasma hamiltonian @xcite corresponding to the screened cornell potential @xcite and obtain the mott dissociation temperatures of these states . given the static interaction potential @xmath7 , @xmath8 , the statically screened potential is given by a resummation of one - particle irreducible diagrams ( `` bubble '' resummation = rpa ) @xmath9~ , \label{vsc}\ ] ] where the longitudinal polarization function @xmath10 in the finite @xmath11 case can be calculated within thermal field theory as @xmath12~.\ ] ] here @xmath13 are the bosonic and @xmath14 are the fermionic matsubara frequencies of the imaginary - time formalism . the symbol @xmath15 stands for traces in color , flavor and dirac spaces . @xmath16 is the propagator of a massless fermion coupled to the homogeneous static gluon background field @xmath17 . its inverse is given by @xcite @xmath18 where @xmath17 is related to the polyakov loop variable defined by @xcite @xmath19 the physics of @xmath20 is governed by the temperature - dependent polyakov loop potential @xmath21 , which is fitted to describe the lattice data for the pressure of the pure glue system @xcite . after performing the color- , flavor- and dirac traces and making the fermionic matsubara summation , we obtain in the static , long wavelength limit @xmath22 where @xmath23 is the debye mass , the number of degrees of freedom is @xmath24 , @xmath25 and @xmath26 is the quark distribution function @xcite . for the discussion of imaginary parts of the polarization function and their relation to kinetics see , e.g. , @xcite . in comparison to the free fermion case @xcite the coupling to the polyakov loop variable @xmath20 gives rise to a modification of the debye mass , given by the integral @xmath27 the temperature dependence of @xmath20 is taken from ref . @xcite . in the limit of deconfinement ( @xmath28 ) , the case of a massless quark gas is obtained ( @xmath29 ) , while for confinement ( @xmath30 ) one finds that @xmath31 . taking as the unscreened vacuum potential the one - gluon exchange form @xmath32 , the fourier transform of the debye potential results as statically screened potential , @xmath33~.$ ] in order to calculate the temperature dependence of the two - particle energies @xmath34 for charmonium and bottomonium states in a pnjl quark plasma , we solve the schrdinger equation @xmath35 for the hamiltonian @xcite @xmath36 with the screened cornell potential @xcite @xmath37~ , \label{potential}\ ] ] where parameters are fitted to the vacuum spectroscopy of heavy quarkonia by @xmath38 , @xmath39 and the heavy - quark masses @xmath40 gev , @xmath41 gev . here we use the debye mass of the previous section with the temperature dependence of @xmath20 taken from a nonlocal pnjl model @xcite . note that the hamiltonian ( [ h - pl ] ) contains a temperature - dependent shift of the continuum edge due to the hartree selfenergies of the heavy quarks in the potential ( [ potential ] ) , which results in a definition of the dissociation energies as @xmath42 and of the mott temperatures as @xmath43 . [ h ] , compared to the available thermal energy of medium particles @xmath44 . for discussion , see text . , scaledwidth=90.0% ] , compared to the available thermal energy of medium particles @xmath44 . for discussion , see text . , scaledwidth=90.0% ] in the upper panels of fig . [ fig : debye ] we show the temperature dependence of the two - particle energies ( masses ) of the lowest heavy quarkonia states at rest in the medium together with the corresponding two - particle continuum edge for charmonia ( left ) and bottomonia ( right ) . the coupling to the polyakov loop potential leads to a suppression of the quark - antiquark excitations responsible for the screening of the heavy - quark potential in the present model . this entails a stabilization of the bound states ( solid lines ) relative to the case without that coupling ( dashed lines ) . in the lower panels we show the corresponding binding energies @xmath45 comparison with the available thermal energy of medium particles ( @xmath44 ) shows that mott dissociation by thermal activation @xcite is possible well below the mott temperatures estimated from the solution of the schrdinger equation . for more detailed discussions of the dissociation kinetics of heavy quarkonia , see the recent review @xcite and references therein . we have applied the methods of thermal field theory to estimate the effects of debye screening on heavy quarkonia bound state formation . in order to account for residual effects of confining color correlations in the deconfined phase , we have used the pnjl model in the evaluation of the one - loop polarization function . as expected , a stabilization of bound states in the vicinity of the critical temperature for @xmath46 is obtained . we have solved numerically the schrdinger equation to derive the mott criterion for bound states of the statically screened cornell potential and obtained mott temperatures in good agreement with previous results from nonrelativistic potential models exploiting lattice qcd singlet free energies as potentials in the schrdinger equation for heavy quarkonia . this agreement with previous results ( see , e.g. , ref . @xcite ) includes also higher quarkonia resonances . for these states the stabilization effect is most pronounced since their mott temperatures lie in the region of temperatures where the suppression of quark - antiquark excitations due to the polyakov - loop potential is the largest . due to the lowering of the dissociation energies for heavy quarkonia states , their dissociation become possible by thermal activation already well before the mott temperatures are reached . according to the present work , even the tightly bound bottomonium ground state @xmath47 may get `` boiled away '' at temperatures @xmath48 mev , well accessible already at rhic . the detailed discussion of the heavy quarkonia dissociation kinetics and its relationship to imaginary parts of the heavy - quark potentials @xcite is beyond the scope of the present contribution . d. cabrera and r. rapp , phys . d * 76 * 114506 ( 2007 ) ; + c. y. wong , phys . rev . c * 72 * 034906 ( 2005 ) . w. ebeling , w .- d . kraeft , d. kremp , g. rpke , _ quantum statistics of charged many - particle systems _ , plenum , new york ( 1986 ) . m. asakawa _ et al . . part . phys . * 46 * 459 ( 2001 ) ; + a. jakovac _ et al . _ , d * 75 * 014506 ( 2007 ) . h. satz , j. phys . g * 32 * r25 ( 2006 ) . j. jankowski and d. blaschke , arxiv:0903.1263 [ hep - ph ] . h. hansen _ et al . _ , phys . rev . d * 75 * 065004 ( 2007 ) . f. karsch , m. t. mehr and h. satz , z. phys . c * 37 * , 617 ( 1988 ) . d. blaschke _ et al . _ , yad . fiz . * 71 * , 2012 ( 2008 ) . g. rpke _ et al . _ , phys . b * 202 * ( 1988 ) 479 ; phys . d * 38 * , 3589 ( 1988 ) .

we investigate the mott effect for heavy quarkonia due to debye screening of the heavy quark potential in a plasma of massless quarks and antiquarks . the influence of residual color correlation is investigated by coupling the light quark sector to a temporal gauge field driven by the polyakov loop potential . this leads to an increase of the mott dissociation temperatures for quarkonia states which stabilizes in particular the excited states , but has marginal effect on the ground states . the temperature dependence of binding energies suggests that the dissciation of the charmonium ( bottomonium ) ground state by thermal activation sets in at temperatures of 200 mev ( 250 mev ) .

the positron source for the international linear collider ( ilc ) is based on a helical undulator @xcite . before collisions , the accelerated electron beam passes the superconducting helical undulator and creates an intense circularly polarized multi - mev photon beam . the photons hit a positron target and create in an electromagnetic shower longitudinally polarized positrons ( and electrons ) . this method was suggested by balakin and mikhailichenko @xcite and has been successfully tested with the e-166 experiment @xcite . the baseline parameters of the ilc positron source afford a positron polarization of 30% . the distribution of polarization within the photon beam depends on the radial position of the photons , so it is possible to increase the average polarization of positrons by collimation from 30% up to 50 - 60% . however , the collimation of the photon beam causes huge thermal load in the collimator material . in this paper , a photon collimator design is discussed which is based on studies of the dynamic load in the collimator material . in section [ sec : e+source ] the ilc positron source is described , the photon collimator system is presented in section [ sec : colli ] . the thermal load as well as the cooling are discussed in section [ sec : heatload+cool ] ; potential problems due to cyclic maximum load and degradation are considered in section [ sec : problems ] . finally , in section [ sec : alternative ] ideas for alternatives of the photon collimator design are presented which could overcame the drawback of the design presented here . the ilc technical design report ( tdr ) @xcite describes the machine parameters to get electron - positron collisions at centre - of - mass energies of 500gev , 350gev and 250gev and also 1tev . trains of 1312 bunches ( high luminosity option : 2625 bunches ) with 2@xmath210@xmath3 electrons / positrons per bunch are repeated with a frequency of 5hz . the scheme of positron production is shown in figure [ fig : source - sketch ] . the superconducting helical undulator has a period of @xmath4 mm and is located at a distance of 400 m upstream the positron target . depending on the electron beam energy and the desired polarization , the undulator k value varies from @xmath5 up to @xmath6 . the length of the undulator is determined by the requirement to generate 1.5 positrons per drive beam electron and amounts up to 231 m maximum . [ ilc_target_wheel ] the degree of photon polarization depends on the angular distribution of the photons . the intensity of the undulator radiation has the maximum around the beam axis . by cutting the outer part of the radial symmetric photon beam with a collimator , the positron polarization is increased by contemporaneous decreasing the positron yield . the yield of 1.5e@xmath7/e@xmath8 can be recovered by increasing the active length of the undulator and choosing @xmath9 . table [ tab : e+pol ] illustrates the relation between undulator - k values , collimator aperture , active length of the undulator and expected degree of positron beam polarization using a flux concentrator as optical matching device with parameters described in the tdr @xcite . depending on the electron beam energy and the k value , the positron polarization approaches 29% for @xmath10 mm up to 50 - 60% if the photon beam radii are collimated to @xmath11 mm ( see also @xcite and table [ tab : collpar ] ) . .expected positron polarization , @xmath12 , for different undulator k values and photon collimator iris radii at @xmath13gev , high luminosity . the active undulator length , @xmath14 , is adjusted to achieve the positron yield of 1.5e@xmath7/e@xmath8 for the nominal luminosity corresponding to 1312 bunches per train . the undulator period is @xmath15 mm . [ cols="<,^,^,^,^,^",options="header " , ] a high degree of positron polarization is desired for physics studies and can be achieved by collimating the undulator photon beam . due to the close correlation between energy of the electron beam which passes the helical undulator , photon beam intensity , collimator iris and degree of polarization , the photon collimator system must be flexible . further , it has to withstand huge heat loads without breakdown during a long operation time . the multistage collimator design presented in this paper represents a solution to collimate the photon beam at the ilc positron source . for centre - of - mass energies up to 500gev , the material loads stay within acceptable limits taking into account an additionally safety margin against failure due to fatigue stress . depending on the centre - of - mass energy , one , two or all three stages are used to collimate the photon beam . the system is water - cooled , the principal parameters of the cooling system are given . the presented solution can be adopted to electron beam energies up to 500gev . however , further simulation studies are recommended to optimize the design taking into account the special material properties as swelling of pyrolytic graphite or potential change of properties of the material due to long - term irradiation . this will further improve the reliability of the final design . 99 c. adolphsen _ et al . _ , _ the international linear collider technical design report - volume 3.i : accelerator & in the technical design phase _ , http://xxx.lanl.gov/abs/1306.6353[arxiv:1306.6353 ] [ physics.acc-ph ] ; c. adolphsen _ et al . _ , _ the international linear collider technical design report - volume 3.ii : accelerator baseline design _ , http://xxx.lanl.gov/abs/1306.6328[arxiv:1306.6328 ] [ physics.acc-ph ] . v. e. balakin and a. a. mikhailichenko , _ conversion system for obtaining highly polarized electrons and positrons _ , http://www-project.slac.stanford.edu/lc/local/polarizedpositrons/doc/classicalpapers/preprint_balakin-mikhailichenko_inp79-85.htm[inp-79-85 ] . g. alexander _ et al . _ , http://dx.doi.org/10.1016/j.nima.2009.07.091[nucl . instrum . a * 610 * ( 2009 ) 451 ] , [ http://arxiv.org/abs/arxiv:0905.3066[arxiv:0905.3066 ] [ physics.ins-det ] ] ; + g. alexander _ et al . _ , http://dx.doi.org/10.1103/physrevlett.100.210801[phys . * 100 * ( 2008 ) 210801 ] . a. ushakov _ et al . _ , _ production of highly polarized positron beams _ , proc . ipac , san sebastian , spain ( 2011 ) , http://accelconf.web.cern.ch/accelconf/ipac2011/papers/tupc006.pdf[997 ] . j. pappis and s.l . blum , _ properties of pyrolytic graphite _ , http://onlinelibrary.wiley.com/doi/10.1111/j.1151-2916.1961.tb11664.x/abstract[j . . soc . * 44*(1961)592 ] . d. yao and b. kim , http://www.sciencedirect.com/science/article/pii/s1359431102001916[applied thermal engineering * 23 * , ( 2003 ) 341 - 352 ] . m. maslov , m. schmitz , v. sychev , _ layout considerations on the 25gev / 300kw beam dump of the xfel project _ , http://flash.desy.de/sites2009/site_vuvfel/content/e403/e1642/e1132/e1129/infoboxcontent1791/fel2006-05.pdf[tesla-fel 2006 - 05 ] , desy , august 2006 . n. simos , h. g. kirk and k. t. mcdonald , _ experimental study of radiation damage in carbon composites and graphite considered as targets in the neutrino super beam _ , http://accelconf.web.cern.ch/accelconf/e08/papers/mopc093.pdf[conf . c 0806233 ( 2008 ) mopc093 ] . b. j. marsden ( editor ) , _ irradiation damage in graphite due to fast neutrons in fission and fusion systems _ , http://www-pub.iaea.org/mtcd/publications/pdf/te_1154_prn.pdf[iaea-tecdoc-1154 ] , september 2000 . s. riemann , p. sievers , a. ushakov , _ status of target and photon collimator work for polarized positrons _ , http://agenda.linearcollider.org/event/6389/session/9/contribution/248/material/slides/[talk ] given at the international workshop on future linear colliders ( lcws14 ) , belgrade , serbia , october 2014 .

high energy @xmath0linear colliders are the next large scale project in particle physics . they need intense sources to achieve the required luminosity . in particular , the positron source must provide about 10@xmath1 positrons per second . the positron source for the international linear collider ( ilc ) is based on a helical undulator passed by the electron beam to create an intense circularly polarized photon beam . with these photons a longitudinally polarized positron beam is generated ; the degree of polarization can be enhanced by collimating the photon beam . however , the high photon beam intensity causes huge thermal load in the collimator material . in this paper the thermal load in the photon collimator is discussed and a flexible design solution is presented .

_ iscsi _ is a protocol designed to transport scsi commands over a tcp / ip network . + _ iscsi _ can be used as a building block for network storage using existing ip infrastructure in a lan / wan environment . it can connect different types of block - oriented storage devices to servers . + _ iscsi _ was initially standardized by ansi t10 and further developed by the ip storage working group of the ietf @xcite , which will publish soon an rfc . many vendors in the storage industry as well as research projects are currently working on the implementation of the iscsi protocol . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ " the small computer systems interface ( scsi ) is a popular family of protocols for communicating with i / o devices , especially storage devices . scsi is a client - server architecture . clients of a scsi interface are called " initiators " . initiators issue scsi " commands " to request services from components , logical units , of a server known as a " target " . a " scsi transport " maps the client - server scsi protocol to a specific interconnect . initiators are one endpoint of a scsi transport and targets are the other endpoint . the iscsi protocol describes a means of transporting of the scsi packets over tcp / ip , providing for an interoperable solution which can take advantage of existing internet infrastructure , internet management facilities and address distance limitations . " draft - ietf - ips - iscsi-20 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ hyperscsi _ is a protocol that sends scsi commands using raw ethernet packets instead of the tcp / ip packets used for _ iscsi_. thus , it bypasses the tcp / ip stack of the os and does not suffer from the shortcomings of tcp / ip . _ hyperscsi _ focuses on turning ethernet into a usable storage infrastructure by adding missing components such as flow control , segmentation , reassembly , encryption , access control lists and security . it can be used to connect different type of storage , such as scsi , ide and usb devices . _ hyperscsi _ is developed by the _ modular connected storage architecture _ group in the network storage technology division of the data storage institute from the agency for science , technology and research of singapore @xcite . enbd is a linux kernel module coupled with a user space daemon that sends block requests from a linux client to a linux server using a tcp / ip connection . it uses multichannel communications and implements internal failover and automatic balancing between the channels . it supports encryption and authentication . + this block access technology is only useful with a linux kernel because of the linux specific block request format . + it is developed by the linux community @xcite under a gpl license . the following hardware was used to perform the tests : * _ test2 _ : + dual pentium 3 - 1 ghz + 3com gigabit ethernet card based on broadcom bcm 5700 chipset + 1 western digital wd1800jb 180 gbytes + 3ware raid controller 7000-series * _ test11 _ : + dual pentium 4 - 2.4 ghz ( hyperthreading enabled ) + 6 western digital wd1800jb 180 gbytes + 3ware raid controllers 7000-series or promise ultra133 ide controllers + 3com gigabit ethernet card based on broadcom bcm 5700 chipset * _ test13 _ : + dual amd mp 2200 + + 6 western digital wd1800jb 180 gbytes + 3ware raid controllers 7000-series or promise ultra133 ide controllers + 3com gigabit ethernet card based on broadcom bcm 5700 chipset * iscsi server : eurologic elantra ics2100 ip - san storage appliance - v1.0 @xcite + 3 scsi drives all the machines have a redhat 7.3 based distribution , with kernel 2.4.19 or 2.4.20 . + the following optimizations were made to improve the performance : sysctl -w vm.min-readahead=127 sysctl -w vm.max-readahead=256 sysctl -w vm.bdflush = 2 500 0 0 500 1000 60 20 0 elvtune -r 512 -w 1024 /dev / hd\{a , c , e , g , i , k } two benchmarks were used to measure the io bandwidth and the cpu load on the machines : * _ bonnie++ _ : v 1.03 @xcite + this benchmark measures the performance of harddrives and filesystems . it aims at simulating a database like access pattern . + we are interested in two results : _sequential output block_ and _sequential input block_. + bonnie++ uses a filesize of 9gbytes with a chunksize of 8kbytes . bonnie++ reports the cpu load for each test . however , we found that the reported cpu load war incorrect . so we used a standard monitoring tool ( vmstat ) to measure the cpu load during bonnie++ runs instead . * _ seqent_random_io64 : _ + in this benchmark , we were interested in three results : * * _ write _ performance : bandwidth measured for writing a file of 5 gbytes , with a blocksize of 1.5 mbytes . * * _ sequential reading _ performance : bandwidth measured for sequential reading of a file of 5 gbytes with a blocksize of 1.5 mbytes . * * _ random reading _ performance : bandwidth measured for random reads within a file of 5 gbytes with a blocksize of 1.5 mbytes . + this benchmark is a custom program used at cern to evaluate the performance of disk servers . it simulates an access pattern used by cern applications . _ vmstat _ has been used to monitor the cpu load on each machine . the server was the eurologic ics2100 ip - san storage appliance @xcite . the client was _ test13 _ , with kernel 2.4.19smp . two software initiators were used to connect to the iscsi server : ibmiscsi @xcite and linux - iscsi @xcite . we used two versions of linux - iscsi : 2.1.2.9 , implementing version 0.8 of the iscsi draft , and 3.1.0.6 , implementing version 0.16 of the iscsi draft . the results are given in the table below : [ cols="^,^,^,^,^,^ " , ] _ comments : _ softwareraid delivers more bandwidth than hardwareraid , but at a higher cpu cost . i would like to thank all the people from the it / adc group at cern for helping me in this study and particularly markus schulz , arie van praag , remi tordeux , oscar ponce cruz , jan iven , peter kelemen and emanuele leonardi for their support , comments and ideas . 1 ietf ip storage working group + http://www.ietf.org/html.charters/ips-charter.html mcsa hyperscsi + http://nst.dsi.a-star.edu.sg/mcsa/hyperscsi/index.html enhanced network block device + http://www.it.uc3m.es/~ptb/nbd/ eurologic elantra ics2100 + http://www.eurologic.com/products_elantra.htm bonnie++ + http://www.coker.com.au/bonnie++/ ibmiscsi + http://www-124.ibm.com/developerworks/projects/naslib/ linux - iscsi + http://linux-iscsi.sourceforge.net/

we report on our investigations on some technologies that can be used to build disk servers and networks of disk servers using commodity hardware and software solutions . it focuses on the performance that can be achieved by these systems and gives measured figures for different configurations . it is divided into two parts : iscsi and other technologies and hardware and software raid solutions . the first part studies different technologies that can be used by clients to access disk servers using a gigabit ethernet network . it covers block access technologies ( iscsi , hyperscsi , enbd ) . experimental figures are given for different numbers of clients and servers . the second part compares a system based on 3ware hardware raid controllers , a system using linux software raid and ide cards and a system mixing both hardware raid and software raid . performance measurements for reading and writing are given for different raid levels .

the family of iron oxyarsenide @xmath5feaso@xmath6f@xmath7 ( @xmath5 = lanthanide element ) exhibits superconductivity with a maximum @xmath8 up to 56 k @xcite . additionally , the iron - arsenide compounds @xmath9fe@xmath0as@xmath0 ( @xmath9 = alkaline earth element ) , crystallizing in the thcr@xmath0si@xmath0-type structure , are known to become superconducting with @xmath8 s up to 38 k upon alkali metal substitution for the @xmath9 element @xcite , or partial transition metal substitution for fe @xcite . in contrast to undoped bafe@xmath0as@xmath0 with a magnetic ground state , superconductivity with relatively low @xmath8 s was reported in the undoped alkali metal iron - arsenides kfe@xmath0as@xmath0 ( @xmath10 k ) and csfe@xmath0as@xmath0 ( @xmath1 k ) @xcite . interestingly , rbfe@xmath0as@xmath0 is known to exist as well @xcite , although its physical properties have not been reported so far . here we report on the superconductivity in undoped alkali metal iron arsenide rbfe@xmath0as@xmath0 . as@xmath0 polycrystalline sample , measured in a magnetic field of 1 mt . superconductivity sets in at @xmath11 k. ] , here for 1 mt and 200 mt , measured in the zfc mode . a relative shift of the onset of superconductivity of 0.15 k is observed . an additional magnetic moment in the normal state in the 200 mt measurement , originates from a major normal state magnetic contribution . ] polycrystalline samples of rbfe@xmath0as@xmath0 were synthesized in two steps . first , rbas and fe@xmath0as were prepared from pure elements in evacuated and sealed silica tubes . then , appropriate amounts of rbas and fe@xmath0as were mixed , pressed into pellets and annealed at 650 @xmath12c for several days in evacuated and sealed silica ampoules . powder x - ray diffraction analysis revealed , that the synthesized rbfe@xmath0as@xmath0 is single phase material with lattice parameters @xmath13 and @xmath14 . magnetization data have been recorded using a quantum design mpms xl squid magnetometer , equipped with a reciprocating sample option . a polycrystalline sample of rbfe@xmath0as@xmath0 was studied for its low temperature magnetic properties . in fig . 1 the magnetic moment in the field - cooled state ( fc ) and in the zero - field cooled state ( zfc ) in a magnetic field of 1 mt are shown . the data are indicative of bulk superconductivity . the distinct onset of diamagnetism due to superconductivity is observed at @xmath11 k. due to the limited temperature range of the equipment , the full development of the meissner state could not be recorded . nevertheless , the observed zfc diamagnetic response mirrors bulk superconductivity and is consistent with the sample dimensions . the pronounced difference between the zfc and fc curves stemms from remarkable flux - pinning in the sample , suggesting rather high critical current density . + the upper critical field @xmath15 was estimated from magnetization measurements performed at various magnetic fields in the mixed state . in fig . 2 , two representative measurements of the magnetic moment versus temperature are displayed for @xmath16 mt and for @xmath17 mt . we defined the upper critical field @xmath15 as the magnetic field @xmath18 , where @xmath19 is located . an obvious shift of the onset of superconductivity of 0.15 k is observed between the respective fields . in addition to the diamagnetic signal due to superconductivity , a distinct paramagnetic response develops due to the normal state magnetic contribution , rendering an accurate determination of @xmath2 rather difficult . nevertheless , since a clear downward curvature is observed due to the onset of superconducting diamagnetism , the trend of @xmath2 can be followed down to 2 k. figure 3 shows a summary of the results up to a field of 0.8 t , anticipating a linear slope close to @xmath8 of @xmath3 t / k . assuming a simple whh temperature dependence @xcite , which is known not to be applicable for the fe pnictide superconductors with much higher transition temperatures , one would extrapolate @xmath4 t , in comparision to the lower critical field @xmath20 mt , as we estimated from field dependent initial magnetization curves , and the thermodynamic critical field @xmath21 mt . superconductivity is , obviously , of type ii . + the solid solution ( rb , ba)fe@xmath0as@xmath0 offers a particularly simple example where the interrelation between magnetic and superconducting ground states in the fe pnictides can be studied through the controlled shift of the fermi level . bafe@xmath0as@xmath0 shows antiferromagnetic ordering competing with superconducting state . appearently , doping of rbfe@xmath0as@xmath0 with ba leads to a natural picture of enhancing @xmath8 in the superconducting state , as the charge carrier concentration is varied . the appearence of superconductivity in rbfe@xmath0as@xmath0 opens up the window for a new interpretation of the occurence of superconducting state in ( rb , ba)fe@xmath0as@xmath0 @xcite . for rbfe@xmath0as@xmath0 . the estimate of @xmath4 t is made using the whh - approach . ] superconductivity is observed in undoped rbfe@xmath0as@xmath0 with a @xmath11 k. in this sense , it is useful to consider rbfe@xmath0as@xmath0 as a superconductor , located at the opposite end to the nonsuperconducting compound bafe@xmath0as@xmath0 in the ( rb , ba)fe@xmath0as@xmath0 system . therefore , superconductivity is enhanced by doping of an initially superconducting nonmagnetic parent compound . the upper critical field at zero temperature of rbfe@xmath0as@xmath0 is estimated to be @xmath4 t. this work was supported by the swiss national science foundation , by the nccr program manep , and partially by the polish ministry of science and higher education within the research project for the years 2007 - 2009 ( grant no . n n202 4132 33 ) . j. karpinski , n. d. zhigadlo , s. katrych , z. bukowski , p. moll , s. weyeneth , h. keller , r. puzniak , m. tortello , d. daghero , r. gonnelli , i. maggio - aprile , y. fasano , . fischer , k. rogacki , and b. batlogg , physica c 469 ( 2009 ) 370 .

the iron arsenide rbfe@xmath0as@xmath0 with the thcr@xmath0si@xmath0-type structure is found to be a bulk superconductor with @xmath1 k. the onset of diamagnetism was used to estimate the upper critical field @xmath2 , resulting in @xmath3 t / k and an extrapolated @xmath4 t. as a new representative of iron pnictide superconductors , superconducting rbfe@xmath0as@xmath0 contrasts with bafe@xmath0as@xmath0 , where the fermi level is higher and a magnetic instability is observed . thus , the solid solution series ( rb , ba)fe@xmath0as@xmath0 is a promising system to study the cross - over from superconductivity to magnetism . rbfe@xmath0as@xmath0 , iron pnictides , upper critical field , transition temperature , superconductivity 74.70.dd , 74.25.op

in last three years the observation of a narrow baryon state named @xmath4 predicted by diakonov , petrov and polyakov@xcite has been reported by a large number of experiments in the @xmath5 or @xmath6 decay channels . several experiments , mostly at high energies , did not confirm the existence of @xmath4 . the present situation and complete list of references to positive and null results can be found in the reviews@xcite . here we present a new study of the reaction @xmath7 , @xmath8 , @xmath9 , with two independent samples of @xmath2 used@xcite . a detailed description of svd-2 detector and its trigger system can be found elsewhere@xcite . the components of the detector used in current analyses are : the high - precision microstrip vertex detector with active(si ) and passive(c , pb ) nuclear targets ; large aperture magnetic spectrometer ; multicell threshold cherenkov counter . for the analyses we use data obtained in the 70 gev proton beam of ihep accelerator at intensity @xmath10 protons / cycle . the total statistics of @xmath11 inelastic events was collected . the sensivity of this experiment for inelastic @xmath12-interactions taking in account the triggering efficiency was @xmath13 . svd-2 has performed the searches of @xmath4-baryon in two independent samples of the data selected by the @xmath2 decay point . in the first one @xmath2 decayed within the vertex detector were used . the first step in the analysis was to find out events with a well defined secondary vertex at the distance of 0 to 35 mm by the beam direction from the beginning of the active target ( corresponding to the sensitive area of the vertex detector ) . tracks from secondary vertex were explored to the magnetic spectrometer and their momenta were reconstructed . the @xmath6 invariant mass spectrum ( fig.[fig1 ] ) shows a clear peak at the @xmath14 with the significance of about 6.2@xmath15 ( 205 signal over 1050 background events ) . to estimate the natural width of the observed peak additional quality cuts were used : 1 ) the distance of the closest approach between @xmath16 tracks @xmath17 3 standard deviations and 2 ) the number of hits on the track in the magnetic spectrometer @xmath18 12 ( of 18 present ) . taking into account the experimental resolution of the svd-2 detector ( calculated using well - known resonances ) it was estimated that intrinsic width of the @xmath19-resonance is @xmath20 at 95% c.l . for analysis ii , the `` distant '' @xmath2 ( decay region is @xmath21 , outside the vertex detector ) were used . @xmath2-mesons were identified by their charged decay mode @xmath22 . to eliminate contamination from @xmath23 decays , candidates with ( @xmath24 ) mass hypothesis giving less than @xmath25 were rejected . about @xmath26 @xmath2-mesons from the mass window @xmath27 were found in the selected events . proton candidates were selected as positively charged tracks with a number of spectrometer hits more than 12 with a momentum @xmath28 . pions of such energies should leave a hit in the cherenkov counter , therefore absence of hits in tcc was also required . effective mass of the @xmath29 system is plotted in fig.[fig2 ] . an enhancement is seen at the mass @xmath30 with a @xmath31 with statistical significance of 5.6@xmath15 . it was verified that observed @xmath6-resonance can not be a reflection from other ( for example @xmath32 ) resonances . the mechanism for producing spurious peak around @xmath33 involving @xmath2 and @xmath23 decays overlap was also checked . the events were scanned using svd-2 event display and no `` ghost '' tracks were found . it is impossible to determine the strangeness of this state in such inclusive reaction , however we did not observe any narrow structure in @xmath34 invariant mass spectrum in @xmath35 mass area ( fig.[fig4]a ) . when applying a different cut on @xmath23 momentum , @xmath36 , we observe a structure near @xmath37 ( fig.[fig4]b ) . this peak may correspond to the @xmath38 , marked as one - star resonance in the pdg review@xcite . our search for @xmath4-particle is an inclusive experiment with a significant background contribution . we have made an attempt to apply a subtraction method to investigate @xmath39 creation region in terms of @xmath40 . an effective mass distribution in a peak region was fitted with a sum of background ( b ) and gaussian functions . background was taken as a product of a threshold function and a second degree polinomial , . all the fit parameters were given reasonable seeds but no boundaries , to prove a fit stability . we have chosen a peak region as a gaussian mean @xmath41 2 gaussian @xmath15 . a number of effective background events under the peak , @xmath42 , was evaluated by integrating background function over the peak region . @xmath40 distributions were plotted separately for a peak and an out - of - peak regions(``wings '' ) ; the latter ranged from the threshold to the 1.7 gev with a peak region cut out , and a result was scaled to a @xmath42 . assuming that the background characteristics are uniform , we subtract `` wings '' distribution from the peak one . choosing more narrow `` wings '' does not change the general shape of distribution ( a rise at @xmath43 ) but shows larger fluctuations . these operations were performed over the data from both analyses . acceptance corrections were taken from the simulations and were specific for each type of analysis . the results are shown at figs.[fig3 ] and [ fig4 ] . we plot also normalized curves of the predictions made in a baranov regge - based model@xcite . in this model , overall distribution comes from the sum of quark fragmentation(bell - shaped at @xmath43 ) and diquark one(seagull - shaped ) , taken with somewhat arbitrary weights . in @xcite the weights are taken as 1:10 , as coming from the analysis of non - exotic baryons creation . our data may indicate some favoring to the quark fragmentation part of the model . note that the analysis ii has a specific narrow acceptance in x due to the proton momentum restrictions . we `` projected '' the @xmath40-result of analysis i to a second one to check the consistence of our observations . for that , the _ inverse _ acceptance correction for analysis ii was applied to the result of analysis i. we found a plausible agreement of the distribution shapes ( fig.[fig6 ] ) and some difference in a total number of events . the latter makes a contribution to the cross section error calculations . as positive as negative results on the theta particle search are very often presented as the ratio of theta to @xmath44 cross sections . in our case , we estimate it as 0.04 . however we should note that these two particles may have quite different creation mechanisms . for example , extracting @xmath40 for @xmath44 the same way as described above resulted in much more forward - oriented distribution ( not shown here ) , than for theta particle . it weakens the reasons of making this comparison . one may suppose that a best way to present such a ratio would be to accompany it with corresponding acceptances . the re - evaluation of the theta creation cross section gives @xmath45 @xmath46 for @xmath47 . it differs significantly from our previous estimates@xcite . the main reason is an unusual form of @xmath40 distribution , assumed flat in our first publications . taking into account our situation of using inclusive data , and undiscovered yet mechanism of theta particle creation ( that means difficulties in acceptance evaluation ) , we believe that the cross section value is subject to future investigations . in conclusion , svd-2 observes in two independent samples a signal in @xmath48 mass distribution with @xmath49,@xmath50 , significance of @xmath51 , @xmath45 @xmath46 for @xmath47 . @xmath40 peaks at zero with , that agrees qualitatively to a regge - based model suggested by baranov@xcite . while in agreement with evidences of @xmath4 observation , there is no direct contradiction to null results in hadron - hadron fixed target collisions , mainly due to different acceptances at @xmath52 . we thank ichep06 organizing committee for creating an excellent scientific atmosphere during the conference . s.p.baranov kindly supplied us with the data used in his work@xcite , the discussions with him were also very useful .

the inclusive reaction @xmath0 was studied at ihep accelerator with @xmath1 proton beam using svd-2 detector . two different samples of @xmath2 , statistically independent and belonging to different phase space regions were used in the analyses and a narrow baryon resonance with the mass @xmath3 was observed in both samples of the data .

since haider and liu postulated a possible existence of @xmath1-mesic nuclei @xcite , many experimental groups performed measurements dedicated to search for the new kind of nuclear matter in which the @xmath1 meson is bound within a nucleus via the strong interaction . however , till now , none of the experiments have brought the clear evidence for the bound state existence . the status of the search was recently described in the following reviews @xcite . some of the experiments set the upper limits for the bound state production in several processes . group estimated the upper limit of total cross section for @xmath5 process to the value of 270 nb and for @xmath5 @xmath6-@xmath7 @xmath8 to the value 70 nb . cosy - gem measurement of @xmath9 @xmath10 brought the upper limit of the total cross section for @xmath11-@xmath12 production equal to 0.46 @xmath13 0.16(stat ) @xmath13 0.06(syst ) nb @xcite . the wasa measurement in 2008 results in the upper limit of of the total cross section for the @xmath14-@xmath12 creation in @xmath2 @xmath15 reaction , which varies from 20 nb to 27 nb for the range of the bound state width from 5 mev to 35 mev @xcite . the measurement carried out two years later permitted to lower the upper bound for the cross section of @xmath16-@xmath17 @xmath4 process down to the value of few nanobarns . additionally , the upper limit of the preliminary total cross section was determined for the first time for the @xmath14-@xmath12 production in @xmath2 @xmath18 reaction @xcite . this paper presents the preliminary results obtained for the aforementioned processes . in november 2010 , wasa - at - cosy collaboration carried out the experiment dedicated for the search for @xmath0-@xmath1 bound states in @xmath2 @xmath3 and @xmath2 @xmath4 reactions . the ramped beam technique was used to vary the momentum continuously from 2.127 gev / c to 2.422 gev / c , which corresponds to a range of excess energies @xmath19 from -70 to 30 mev @xcite . the detailed description of the wasa experimental setup is presented in @xcite . analysis for the @xmath2 @xmath3 and @xmath2 @xmath4 reactions were carried out independently . next , the set of the cross - check tests was performed to assure the consistency at the pid level . the @xmath20 ions and nucleon - pion pairs were identified in the forward and central detector , respectively . the deposited energy patterns in thick scintillator layers of the forward hodoscope was used to identify the @xmath20 ions ( the ) . the neutral pion @xmath21 was reconstructed based on the invariant mass of two gamma quanta while the neutron was identified via the missing mass technique @xcite . the proton and @xmath22 identification was based on the measurement of the energy loss in the thin plastic scintillator barrel combined with the energy deposited in the electromagnetic calorimeter @xcite . the events which may correspond to the bound states production were selected using criteria based on monte carlo simulations for the @xmath1-mesic nuclei production and decay . we apply the cuts in the momentum of @xmath20 in the cm frame , nucleon cm kinetic energy , pion cm kinetic energy and the opening angle between nucleon - pion pair in the cm . the region rich in signal corresponds to the momenta of the @xmath20 in the range . for this region the excitation function was obtained by normalizing the events selected in individual excess energy intervals by the corresponding integrated luminosities ( the detailed description of the luminosity determination one can find in ref . @xcite ) and corrected for acceptance and efficiency . the excitation function does not reveal the resonance - like structure , which could be the signature of the @xmath1-mesic nuclei existence @xcite , however the interpretation of the results is still in progress . so far , the upper limit of the total cross section for the @xmath16-@xmath17 @xmath3 and @xmath16-@xmath17 @xmath4 processes was determined on the 90% confidence level . preliminary , the upper limits were obtained by the fit of the sum of the polynomial and breit - wigner functions to the experimentally determined excitation functions . it varies from 21 to 36 nb for the first channel and from 5 to 9 nb for the second channel for the bound state width ranging from 5 to 50 mev ( see fig . [ result_sigma_upp ] ) . -@xmath17 @xmath3 ( left panel ) and @xmath16-@xmath17 @xmath4 ( right panel ) reaction as a function of the width of the bound state . the binding energy was set to 30 mev . the green areas denote the systematic uncertainties @xcite . [ result_sigma_upp],title="fig:",width=226,height=151 ] -@xmath17 @xmath3 ( left panel ) and @xmath16-@xmath17 @xmath4 ( right panel ) reaction as a function of the width of the bound state . the binding energy was set to 30 mev . the green areas denote the systematic uncertainties @xcite . [ result_sigma_upp],title="fig:",width=226,height=151 ] a possible broad state in the case of @xmath16-@xmath17 @xmath3 reaction can not be excluded by the current data set @xcite . the kinematic region , where we expect the evidence of the signal from the bound state corresponding to @xmath20 momenta in the cm system in range , can not be fully described only by the combination of the considered background processes ( see left panel of fig . [ fit_plots ] ) . in contrast , as shown in the right panel of fig . [ fit_plots ] the experimental excitation function is very well fitted by the background contributions for the region where the signal is not expected . @xmath3 ( green squares ) and @xmath23 @xmath24 @xmath3 ( magenta squares ) . a sum of both background contributions is shown as blue triangles . left and right panels show results for the regions rich in signal and poor in signal , respectively . the figure is adopted from @xcite . [ fit_plots],title="fig:",width=226,height=151 ] @xmath3 ( green squares ) and @xmath23 @xmath24 @xmath3 ( magenta squares ) . a sum of both background contributions is shown as blue triangles . left and right panels show results for the regions rich in signal and poor in signal , respectively . the figure is adopted from @xcite . [ fit_plots],title="fig:",width=226,height=151 ] the excitation functions were determined for @xmath16-@xmath17 @xmath4 and @xmath16-@xmath17 @xmath3 processes , however none of them reveal any direct narrow structure which could be signature of the bound state with width less than 50 mev . the interpretation of the resuts is still in progress . so far preliminary upper limit of the total cross section for the @xmath1-mesic @xmath0 formation and decay was estimated . in case of @xmath16-@xmath17 @xmath4 reaction we obtained the preliminary upper limit of the total cross section in order of few nb which is about four times lower in comparison with the result obtained from 2008 data @xcite . comparing to theoretically estimated value @xcite , the obtained upper limit value does not exclude the existence of the bound state . the excitation function for the reaction @xmath16-@xmath17 @xmath3 was obtained for the first time in the experiment . the obtained upper limit is here by factor of five larger than predicted value therefore , we can conclude , that the current measurement does not exclude the existence of bound state also in this process @xcite . moreover , the excitation function obtained for this reaction is a subject of interpretation of few theoretical groups with respect to very wide or bound state @xcite . in may 2014 , we extended the search for to @xmath20-@xmath1 sector @xcite . we chose processes corresponding to the three mechanisms : ( i ) absorption of the @xmath1 meson by one of the nucleons , which subsequently decays into @xmath25-@xmath26 pair e.g. : @xmath27 ( @xmath20-@xmath7 @xmath28 , ( ii ) decay of the @xmath1 -meson while it is still `` orbiting '' around a nucleus e.g. : @xmath27 ( @xmath20-@xmath7 @xmath29 or @xmath27 ( @xmath20-@xmath7 @xmath30 reactions and ( iii ) @xmath1 meson absorption by few nucleons e.g. : @xmath27 ( @xmath20-@xmath7 @xmath31 or @xmath27 ( @xmath20-@xmath7 @xmath32 . almost two weeks of measurement with an average luminosity of about 6@xmath33 @xmath34 s@xmath35 allowed to collect a world largest data sample for @xmath20-@xmath1 . the data analysis is in progress . the search for @xmath1 and @xmath36 - mesic bound states is carried out also by other international collaborations , e.g. at j - parc @xcite and at gsi @xcite . in parallel , several theoretical studies are ongoing @xcite . we acknowledge support by the foundation for polish science - mpd program , co - financed by the european union within the european regional development fund , by the polish national science center through grants no . dec-2013/11/n / st2/04152 , 2011/01/b / st2/00431 , 2011/03/b / st2/ 01847 and by the ffe grants of the forschungszentrum jlich . k. yoshiki _ et . arxiv:1503.03566 , proceedings of the 20th international conference on particles and nuclei ( panic 14 ) , doi:10.3204/desy - proc-2014 - 04/106 _ , 24 - 29 august 2014 , hamburg , germany , page 286 , 2015 .

we performed a search for @xmath0-@xmath1 bound state in @xmath2 @xmath3 and @xmath2 @xmath4 reactions with the wasa - at - cosy facility using a ramped beam technique . the measurement was carried out with high statistics and high acceptance . the signature of @xmath1-mesic nuclei was searched for by the measurement of the excitation functions in the vicinity of the @xmath1 production threshold for each of the considered channels . we did not observe the narrow structure which could be interpreted as a bound state . the preliminary upper limits of the total cross sections for the bound state production and decay varies from 21 nb to 36 nb for the @xmath2 @xmath3 channel , and from 5 nb to 9 nb for the @xmath2 @xmath4 channel for the bound state width ranging from 5 to 50 mev .

the swift increase of the number of absorptions ( and the average opacity ) with increasing redshift is the most impressive property of the ly-@xmath4 forest . fig . [ dndz ] shows the number density evolution of the ly-@xmath4 lines @xcite in the column density interval has been chosen to allow a comparison with the hst key - programme sample at @xmath5 @xcite for which a threshold in equivalent width of 0.24 was adopted . ] the long - dashed line is the maximum - likelihood fit to the data at @xmath7 with the customary parameterization : @xmath8 . the uves @xcite observations imply that the turn - off in the evolution does occur at @xmath9 , not at @xmath10 as previously suggested . -0.2 cm the evolution of the @xmath11 is governed by two main factors : the hubble expansion and the metagalactic uv background ( uvb ) . at high @xmath12 both the expansion , which decreases the density and tends to increase the ionization , and the uvb , which is increasing or non - decreasing with decreasing redshift , work in the same direction and cause a steep evolution of the number of lines . at low @xmath12 , the uvb starts to decrease with decreasing redshift , due to the reduced number and intensity of the ionizing sources , counteracting the hubble expansion . as a result the evolution of the number of lines slows down . up to date numerical simulations @xcite have been remarkably successful in qualitatively reproducing the observed evolution , however they predict the break in the @xmath13 power - law at a redshift @xmath14 that appears too high in the light of the new uves results . this suggests that the uvb implemented in the simulations may not be the correct one : it was thought that at low redshift qsos are the main source of ionizing photons , and , since their space density drops below @xmath15 , so does the uvb . however , galaxies can produce a conspicuous ionizing flux too , perhaps more significant than it was thought@xcite . the galaxy contribution can keep the uvb relatively high until at @xmath9 the global star formation rate in the universe quickly decreases , determining the qualitative change in the number density of lines . under relatively general assumptions , it is possible to relate the observed number of lines above a given threshold in column density or equivalent width to the expansion , the uvb , the distribution in column density of the absorbers and the cosmology : @xmath16^{\beta-1 } h^{-1}(z ) , \label{eq : dndz}\ ] ] where @xmath17 is the photoionization rate and the @xmath18 distribution is assumed to follow a power - law of index @xmath19 , as discussed in the next section . -0.7 fig . [ nhi ] shows the differential density distribution function measured by uves @xcite , that is the number of lines per unit redshift path and per unit @xmath18 as a function of @xmath18 . the distribution basically follows a power - law @xmath20 extending over 10 orders of magnitude with little , but significant deviations , which become more evident and easy to interpret if the plot is transformed in the mass distribution of the photoionized gas as a function of the density contrast , @xmath21 , @xcite : 1 ) a flattening at @xmath22 is partly due to line crowding and partly to the turnover of the density distribution below the mean density ; 2 ) a steepening at @xmath23 , with a deficiency of lines that becomes more and more evident at lower z , reflects the fall - off in the density distribution due to the onset of rapid , non - linear collapse : the slope @xmath19 goes from about @xmath24 at @xmath25 to @xmath26 at @xmath27 and recent hst stis data @xcite confirm that this trend continues at lower redshift measuring at @xmath28 a slope of @xmath29 ; 3 ) a flattening at @xmath30 can be attributed to the flattening of the density distribution at @xmath31 due to the virialization of collapsed matter . hydrodynamical simulations successfully reproduce this behaviour , indicating that the derived matter distribution is indeed consistent with what would be expected from gravitational instability . the last ingredient to be determined in eq . [ eq : dndz ] is the ionization rate . in a recent computation @xcite we have investigated the contribution of galaxies to the uvb , exploring three values for the fraction of ionizing photons that can escape the galaxy ism , @xmath32 and @xmath33 ( the latter value corresponds to the lyman - continuum flux detected by @xcite in the composite spectrum of 29 lyman - break galaxies ) . estimates of the uvb based on the proximity effect at high-@xmath12 and on the @xmath34 emission in high - latitude galactic clouds at low-@xmath12 provide an upper limit on @xmath35 , consistent with recent results on individual galaxies both at low-@xmath12 @xcite and at @xmath36 @xcite . introducing a contribution of galaxies to the uvb , the break in the ly-@xmath4 @xmath13 can be better reproduced than with a pure qso contribution @xcite . the agreement improves considerably also at @xmath37 . besides , models with @xmath38 describe the flat evolution of the absorbers much better than @xmath39 . a consistency check is provided by the evolution of the lower column density lines . for @xmath40 the @xmath18 distribution is flatter , and according to eq . [ eq : dndz ] this translates directly into a slower evolutionary rate , which is consistent with the uves observations@xcite : @xmath41 . another diagnostic can be derived from the spectral shape of the uvb and its influence on the intensity ratios of metal lines @xcite . given the cosmological scenario , the amount of baryons required to produce the opacity of the lyman forest can be computed @xcite and a lower - bound to the cosmic baryon density derived from the distribution of the ly-@xmath4 optical depths . applying this approach to the effective optical depths measured in the uves spectra , the estimated lower bound @xmath42 is consistent with the bbn value for a low d / h primordial abundance . most of the baryons reside in the lyman forest at @xmath43 with little change in the contribution to @xmath44 as a function of @xmath12 . conversely , given the observed opacity , a higher uvb requires a higher @xmath45 . as pointed out by @xcite , the large escape fraction measured by @xcite would result in an @xmath46 in strong conflict either with the d / h or in general with the bbn or with the ly-@xmath4 opacity measurements . 99 bianchi s. , cristiani s. , kim . , 2001 , 376 , 1 dodorico s. , cristiani s. , dekker h. et al . , 2000 , spie 4005 , 121 dav r. , tripp t.m . , 2001 , apj 553 , 528 deharveng j .- m . , buat v. , le brun v. , et al . , 2001 , 375 , 805 giallongo e. , cristiani s. , fontana a. , dodorico s. , 2001 , in preparation haehnelt m.g . , madau p. , kudritzki r. , haardt f. , 2001 , 549 , l151 heckman t.m . , sembach k.r . , meurer g.r . et al . , 2001 , 558 , 81 kim t .- s . , cristiani s. , dodorico s. , 2001 , 373 , 757 kim t .- carswell r.f . , cristiani s. , dodorico s. , giallongo e. , 2001 , mnras submitted savaglio s. , cristiani s. , dodorico s. et al . , 1997 , 318 , 347 schaye j. , astro - ph/0104272 steidel c.c . , pettini m. , adelberger k.l . , 2001 , 546 , 665 theuns t. , leonard a. , efstathiou g. , 1998 , mnras 297 , l49 weinberg d.h . , miralda - escud j. , hernquist l. , katz n. , 1997 , 490 , 564 weymann r.j . , jannuzi b.t . , lu l. et al . , 1998 , 506 , 1

a sample of 8 qsos with @xmath0 has been observed with vlt / uves at a typical resolution @xmath1 and s / n @xmath2 . thanks to the two - arm design of the spectrograph , a remarkable efficiency has been achieved below 400 nm and above 800 nm , which translates immediately in the possibility of obtaining new results , especially at @xmath3 . we report here new insight gained about the evolution of the number density of ly-@xmath4 lines , their column density distribution , the ionizing uv background and the cosmic baryon density .

one of the most mysterious of our milky - way galaxy is the `` missing satellite problem '' that cold dark matter scenario predicts its number of satellite galaxies to be around hundred , but only dozens are observed ( e.g. moore et al . 1999 ) . a few solutions have been proposed for this contradictory . one instant question is if we are comparing the right things , i.e , how to relate the observed stellar velocity dispersion to the measured circular velocity from n - body simulation ( hayashi et al . another possible solution is that photoionization suppress the gas accretion in small halos , and only halos formed before reionization can form stars . ( e.g. gnedin 2000 ) . also there is worry about the incompleteness of observation as very faint satellites have too low surface brightness to be observed . in recent years , more faint satellites are observed along with their kinematics and mass measurements , and the satellite luminosity function is also well determined from the sdss ( koposov et al . one the other hand , theoretical modelling of dark matter halo formation history ( cole et al . 2008 ) and galaxy merging time - scales ( jiang et al . 2008 , boylan - kolchin et al . 2008 ) are also improved . given these progress , it is deserved to revisit the `` missing satellite problem '' and there have been a few papers to address this ( e.g. simon & geha 2007 ) . here we use the semi - analytical model of galaxy formation ( kang et al . 2005 ) to predict the luminosity function , mass - to - light ratios for satellite galaxies and compare them with the data . one of the main ingredients to model the satellite galaxy population is to produce their formation and assembly history . here we use the monte - carlo merger tree code from parkinson et al . ( 2008 ) to obtain the formation history of a milk - way type galaxy with mass around @xmath4 . this new monte - carlo algorithm is still based on the eps formula , but revised to match the millennium simulation ( springel et al . 2005 ) results at different mass scales . cole et al . ( 2008 ) have shown that for halo with mass around @xmath4 , the merger tree from the previous monte - carlo algorithm ( cole et al . 2000 ) produces too strong evolution and too many major mergers at lower redshift . we produce 1000 realizations of the merger trees using the new monte - carlo algorithm , and in fig.1 we show their formation history with comparisons to the n - body simulation results ( stewart et al . 2008 , giocoli et al . it can be seen that both the evolution of the main progenitors and the mass function of accreted subhalos agree well with the simulation results . at z=0 . left panel : the mass evolution of the main progenitors . right panel : the mass function of accreted subhalos by the main progenitors . good match are found with n - body simulations ( stewart et al . 2008 , giocoli et al . 2008).,scaledwidth=100.0% ] we then use the semi - analytical model of kang et al . ( 2005 ) to model the formation of satellite galaxies along the merger trees . the semi - analytical model includes a few important physical processes governing galaxy formation : hot gas cooling in halos , star formation from cold gas , supernova feedback to reheat the inter - stellar medium , stellar evolution , galaxy merger . we update the model of kang et al . ( 2005 ) by using an improved fitting formula for the galaxy merging time - scales from jiang et al . ( 2008 ) , who have shown that for massive mergers , the survival time of satellite galaxies in sph simulation is longer than the prediction from lacey & cole ( 1993 ) . here we also include a simple model for photoionization from kravtsov et al . ( 2004 ) . in case of heating from ionized photons , the gas content in halos formed after reionization are suppressed and can be simply described by a filter mass which increases with redshift . the filter mass increase from @xmath5 at z=8 to @xmath6 at z=0 ( okamoto et al . ( 2008 ) recently argue that the filter mass should be smaller ) . the gas fraction in a filter mass halo is about half of the universal fraction . with photoionization the amount of gas available for star formation is decreased significantly in less massive halos formed after reionization . in this paper , we take the reionization redshift as z=7 . in fig.2 we show the model luminosity function ( lf ) of satellites with comparison to the recent results of koposov et al . ( 2008 ) from sdss dr5 . koposov et al measured the lf up to @xmath7 , and found that lf can be described by a power law with slope of 0.1 . at the very faint end ( @xmath8 ) the solid circle points in fig.2 are extrapolated assuming the satellite galaxies following a nfw density distribution , and empty circles are assumed with an isothermal distribution ( see koposov et al . it can be seen that if there is only supernova feedback ( dashed line ) , the predicted total number of satellites are more than observed by a factor of 3 . with the suppression of gas accretion by photoionization , the lf ( solid line ) can be brought into abroad agreement with the data . this is expected that the decrease of gas content produce less stellar mass . compared to the model prediction of benson et al . ( 2002 ) , our model produces more luminous satellites with @xmath9 . this success is credited to the combination of improved models for halo merger tree and galaxy merging time - scales . the merger tree used by benson et al . ( 2002 ) is based on cole et al . ( 2000 ) , which produces too many recent major mergers . as the galaxy merging time is shorter for major merger , so less is the number of survived massive satellites . also we use the new fitting formula from jiang et al . ( 2008 ) for galaxy merging time - scales , which is longer than the often used dynamical friction time scale from lacey & cole ( 1993 ) . as we can see that without photoionization , there are only a few satellites fainter than @xmath10 . this is because hot gas can not cool via hydrogen line emission in halos with virial temperature below @xmath2 ( @xmath11 ) and @xmath12 cooling is very inefficient . the solid line shows that those faint satellites formed in halos with virial temperature just over @xmath2 , but have their gas content strongly suppressed by photoionization ( similar conclusion was also obtained by kravtsov et al . 2004 ) . in our model , it is difficult to produce satellite ( @xmath13 ) with number around 30 , and this favors the satellites to have an isothermal density distribution . with the advent of accurate measurements of satellites kinematics , it is possible to obtain the total mass of satellite galaxies inside their luminous radii . it is found that most satellites are dominated by dark matter inside their luminous radii . here we show the mass - to - light ratio of satellites in fig.3 , where the data points are from compilation by simon & geha ( 2007 ) . we model the dark matter mass evolution of satellite galaxies using the model of giocoli et al . ( 2008 ) , and we further assume that about 5% of the total dark matter mass are inside their luminous radii . the model prediction ( solid line ) along with 20th and 80th percentiles of the distribution ( dashed lines ) are shown in fig.3 . we can find good agreement with the data from @xmath14 up to @xmath15 . ) . dashed line is their mass distribution before accretion , and solid line is the distribution of their present mass after evolution . the distribution has a sharp peak at @xmath16 before accretion , where hydrogen line emission cooling is efficient . the present mass has a broad distribution around @xmath17 , and the wide spread is from the dispersion of accretion times . , scaledwidth=50.0% ] the above results of lf and mass - to - light ratio are encouraging as they indicates that we can model the luminosity and mass of satellites simultaneously . now we make prediction for the dark matter mass of satellites faint than @xmath18 . in fig.4 , we show their host halo mass before accretion ( dashed line ) and the present dark matter mass after evolution ( solid line ) . as we can see that the faint satellites ( @xmath19 ) formed in halos with mass peak at @xmath16 , and they have a broad distribution for their present mass with peak at about @xmath17 . the broad distribution is from the spread of their accretion times . we revisit the `` missing satellite problem '' using a semi - analytical model of galaxy formation combined with a high - resolution merger tree from monte - carlo algorithm ( parkinson et al . we model the luminosity function and mass - to - light ratio for the satellites . the model luminosity function agrees well with the recent results of koposov et al . ( 2008 ) from the sdss dr5 only if the photoionization effect is included to suppress the gas fraction in less massive halos . our ability to produce more luminous satellite galaxies than previous semi - analytical models ( e.g. , benson et al . 2002 ) is from the improvement on modelling of halo merger tree and galaxy merging time - scales . very faint satellites ( @xmath20 ) form in halos with virial temperature above @xmath2 , but their gas content are strongly suppressed by photoionization . in addition their number density favors an isothermal density distribution in the milky - way . we model the mass evolution of subhalos using the model of giocoli et al . ( 2008 ) , and find that the measured total kinematic mass inside the luminous radii of satellite galaxies are about 5% of their present dark matter mass . i thank nicolas martin , jeta t. de jong and simon white for helpful discussions .

we revisit the milky way satellite problem using a semi - analytical model of galaxy formation and compare the predicted luminosity function to recent result from the sdss . with cosmic photoionization , the luminosity function can be brought into broad agreement with the data between @xmath0 . this improvement over previous semi - analytical model results ( e.g. , benson et al . 2002 ) is from our adoption of improved models for galaxy merger history and galaxy merging time - scales . the very faint satellites ( @xmath1 ) formed in halos with virial temperature over @xmath2 ( mass around @xmath3 before accretion ) , but their baryon content are strongly suppressed by photoionization . we model the mass evolution of the subhalos , and compare the predicted mass - to - light ratio with the data . we find that the measured total mass inside the luminous radii of satellites are about 5% of their present total dark matter mass .

in the accordance with the conventional regge - gribov approach , the one - pomeron contribution to the differential cross section of shdid can be expressed at @xmath25 in the form : @xmath26 where @xmath27 and @xmath28 are cms total interaction energy , total cross section , transverse momentum transferred , and invariant masses of final diffractively excited states respectively , @xmath29 is three - pomeron vertex and @xmath30 is the pomeron trajectory ; the parameter @xmath31 is to be chosen to single out diffraction processes from other ones [ 7 ] . since the mean slope of the pomeron trajectory is the only dimensional parameter which can be responsible for the decrease of the function @xmath29 as @xmath32 is increased , the domain where @xmath29 is expected to be nearly constant is estimated as @xmath33 where @xmath34 is an effective mean value of the derivative @xmath35 there which is reasonably evaluated to be @xmath36 . it is why this domain is expected to be remarkably large , from @xmath37 to @xmath38 or even larger ( it has been observed long ago by comparison of the elastic and single inelastic diffraction differential cross sections that @xmath39 at @xmath40 [ 7 ] , wherefrom , in particular , a rather slow @xmath41-dependence of double inelastic diffraction differential cross section at @xmath42 follows ) . the double inelastic diffraction is the only type of hadron interaction which is expected to exhibit such slow transverse momentum dependence . at still larger values of squared 4-momentum transferred pomeron is expected to be dissolved to its constituents [ 6 ] that begin to interact independently , so that the `` normal '' qcd regime @xmath43 is to be approached gradually . in what follows the logarithmic dependence on @xmath41 and rather ambiguous but definitely slow decrease of @xmath44 in the right - hand side of eq.(1 ) are accounted on the average as @xmath45 . the rough estimate of screening corrections to the one - pomeron shdid scattering amplitude @xmath46 associated with diagrams depicted in fig.3 shows that @xmath47 , @xmath48 being the corrected amplitude . it is reasonable to adopt @xmath49 and enhance the above correction ( i.e.,to multiply the denominator in eq.(2 ) ) by the phenomenologically approved ( for forward elastic scattering amplitude ) factor about 1.5 , accounting the shadowing by the inelastic intermediate states . then the corrected shdid amplitude is expected to be @xmath50 and the corresponding differential cross section is @xmath51 after integration of eq.(1 ) over the region @xmath52 one obtains the total cross section of shdid @xmath53 if one chooses a reasonable values @xmath54 , @xmath55 and the experimental value of @xmath56 , @xmath57 , then the fraction of shdid is expected to be @xmath58 and 0.10 at @xmath59 and @xmath60 respectively . it can be several times less or larger , since the above estimate is rather rough , but its smooth logarithmic threshold - like energy increase is independent of the choice of parameters . it seems reasonable to expect that hadronization of diffractively excited final states produced by shdid is dominated by mechanism of string rupture as shown in fig.4 , string been formed between scattered colored hadron constituent ( quark , diquark or gluon ) and remnant of the same hadron . any alternative string configuration would be unfavorable since it implies formation of some strings of a very high energy ( it is worthy to mention that diffractively produced state associated with target particle was always out of the game in cosmic ray experiments under discussion because it is never seen within the area of observation ; it is why the projectile inelastic diffraction only is thought of throughout the paper ) . at the same time , transferred momentum @xmath61 is insufficiently large for the fragmentation mechanism of hadronization to prevail . let us consider the above string in its own cms and adopt that secondary particle rapidity and transverse momentum distributions in pomeron - proton interaction is similar to that in real hadron one at cms energy @xmath62 ( as to the rapidity distribution , it is supported by the well known result of ua4 collaboration [ 8 ] ) . since what is observed is nothing else , than transverse plane projection of the picture which is resulted from its rupture , it becomes obvious that the typical ratio of a secondary transverse momentum projection normal to reaction plane ( i.e. , to the plane of draft ) to `` transverse momentum string length '' ( i.e. to ls relative transverse momentum of leading particles oppositely directed in string cms ) is about @xmath63 where @xmath64 is mean transverse momentum of secondaries in hadron interactions , and mean leading particle energy is experimentally proved to be about half of incident particle one . at @xmath65 this ratio is about 0.13 . the only point what remains to be discussed to compare the above consideration to the experimental data is an obvious estimate of the role of atmospheric cascade . since the atmosphere thickness above the altitude where the calorimeter is mounted corresponds to about 3.5 nuclear mean free paths , the probability of at least one shdid collision is about @xmath66 at @xmath67 . if it does happen , then the subsequent soft collisions can not , most probably , blur essentially the target plane picture it initiates , especially for energy distinguished cores . it is why the additional assumption suggested by experimenters [ 2 ] seems to be not necessary , that alignment is caused by some peculiarities of the lowest nuclear collision above the chamber only . at the same time , the threshold - like dependence of alignment on core energies is associated , may be , with the violating role of nuclear cascade . thus , the main puzzling experimental features of alignment phenomenon , namely , the fraction of alignment events about ( 20 - 40)% and the ratio of mean value of normal to reaction plane projection of core transverse momentum to maximal value of core relative transverse momenta ( @xmath68 ) ( string `` half - thickness '' to its `` length '' in transverse momentum space ) are compatible qualitatively with the above theoretical consideration ( 30% and 0.13 respectively ) , if one adopts that each core is originated ( due to electromagnetic cascade ) from a hadron created along with string rupture . the threshold - like dependence of shdid cross section on interaction energy can elucidate why the phenomenon has not been noticed at lower energies ( especially , accounting a poor statistics and other ambiguities of cosmic ray experiments ) . however , this point as well as some other features of the phenomenon , such as its threshold - like dependence on core energies , core energy distribution , their energy sequence along the alignment line , etc . , needs both the enrichment of statistics and mc simulation of cascade and shdid collisions themselves ( especially , accounting that hadrons of different masses can be produced at the end of string and along its length ) which are in progress . unfortunately , it is rather questionable , whether an attempt to observe the alignment phenomenon will be undertaken in accelerator experiments soon . 99 pamir collaboration , `` analysis of structure of halo in families with energy @xmath69 '' , proceedings 5th international symposium on very high energy cosmic ray interactions , lodz , 1988 , v. contributed papers , p. 9 . amineva , g.f . fedorova et al . , `` alignment of increased background region in gamma - hadron superfamilies '' , proceedings 6th international symposium on very high energy cosmic ray interactions , tarbe , 1990 v. contributed papers , p. 264 ; i.p . ivanenko , v.k . kopenkin , a.k . managadze and i.v . rakobolskaya , pisma jetf , 1992 , v. 56 , p. 192 . f. halzen and d.a . morris , phys . , 1990 , v. d42 , p. 1435 . ua1 collaboration , g. arnison et al . lett . , 1985 , v.158b , p. 494 a. managadze , private communication . a. mironov and i. royzen , sov . fiz . , 1988 , v. 47 , p. 1125 ; v. 48 , p. 194 . a. alberi and g. goggi , phys . rep . 1984 , v. 74 , no . ua4 collaboration , d. bernard et al . lett . , 1986 , v. 166b , p.459 fig.1 . the example of target plane picture with energy distinguished cores for event with alignment , @xmath70 ; figures stand for energy in tev ( already multiplied by factor 3 for hadrons);andor stand for electromagnetic halo and hadrons of high energy respectively . other particles of the family are marked as(@xmath1 -quanta ) and ( hadrons ) . one - pomeron exchange approximation to shdid . wavy lines refer to pomeron exchange , @xmath71 and @xmath28 are invariant masses of diffractively excited states , q is 4-momentum transferred , @xmath72 is triple - pomeron vertex function .

an explanation of the puzzling alignment effect observed in cosmic ray experiments is suggested * theoretical approach to alignment phenomenon * + * i. royzen * + p.n . lebedev physical institute of russian academy of sciences 53 leninsky prospect , 117924 moscow , russia + few years ago the observation has been made [ 1 ] in cosmic ray experiments that the alignment of the main energy fluxes along a straight line in target ( transverse ) plane exceeds significantly the background level . more precisely , at superhigh energies of initial particle ( @xmath0 ) the secondary particle superfamilies detected by deep lead x - ray emulsion chamber appeared to be situated almost along straight line in target plane ( fig.1 ) . the coplanar scattering of such a type was so surprising that an attempt has been made to revise the result but instead they were confirmed with much better confidence level [ 2 ] . the analysis of the alignment effect for 74 high energy @xmath1-families induced by hadrons above and within the chamber has been carried out . their energies energies are selected to be @xmath2 ( hadron energies being restored , accounting that the energy of induced @xmath1-family is about @xmath3 of the hadron energy it is originated from ) . this analysis suggested that superfamily production happened predominantly rather low above the chamber ( at the altitude @xmath4 , since it seemed that nuclear - electromagnetic cascade development would blur alignment , if several interactions contributed ) . it confirmed a coplanar scattering and scaling - like fragmentation spectrum of energy distinguished cores . the alignment parameter @xmath5 , @xmath6 is used as the alignment criterion where @xmath7 stands for a number of centers of highest energy and @xmath8 is the angle between the two - dimensional vectors @xmath9 and @xmath10 in target plane , an event being recognized to have alignment , if @xmath11 . actually , events with @xmath12 were chosen only because of too high statistical background for @xmath13 and rather poor statistics for @xmath14 . the threshold - like behavior of the effect has been observed : no alignment at @xmath1-family energies @xmath15 , then its gradual increase within energy range @xmath16 to manifest itself finally in ( 20 - 40)% of total number of events . 14 events with @xmath17 have been observed , exhibiting most striking alignment structure ( @xmath18 ) . core transverse momentum @xmath19 was estimated by rough relation @xmath20 , @xmath21 being the distance of a spot from the interaction axis . the mean ratio of value of maximal relative core transverse momentum to its normal to the alignment line projection ( in target plane ) @xmath22 is @xmath23 . no other peculiarities of alignment events compared to `` usual '' cascade have been noticed . the first attempt of theoretical consideration of the above alignment phenomenon has been made by f. halzen and d.a . morris [ 3 ] , whose approach was based on the assumption that semihard gluon jets is a feature of all events at energies above @xmath24 . it was shown that within this approach the cosmic ray observations were associated probably with the jet alignment in three - jet events observed already in the collider experiment [ 4 ] . i would like to suggest an alternative treatment which makes it possible to understand many features of cosmic ray alignment observations quite naturally , including the threshold - like energy behavior and fraction in extensive atmospheric showers as well as the typical projections of core transverse momenta to the alignment line and normal to it , and allowing for events with more , than four cores aligned , that have been extracted recently from cosmic ray data [ 5 ] . the main point of the approach under consideration is that the alignment events are assumed to be associated with semihard double inelastic diffraction ( shdid ) of hadrons [ 6 ] . let us trace them step - by - step .

here we present a two - loop renormalisation - group analysis of the multifractal properties of a disordered weyl semimetal in @xmath19 dimensions using the minimal subtraction scheme@xcite . a similar scheme has been applied recently @xcite to compute the correlation - length and dynamical exponents for a wsm to the two - loop order , following previous studies of graphene@xcite and of the equivalent gross - neveu model@xcite . also , a similar multifractality analysis has been carried out in ref . @xcite for 2d ( @xmath124 ) dirac fermions on the surface of a 3d topological insulator . although there is no disorder - driven phase transition in such a 2d system , the wavefunctions display multifractal behaviour on sufficiently short length scales . @xmath125 \psi\,d\br , \label{l0minimal } \\ \cl_{\text{int}}=&\frac{1}{2}\varkappa_0\int(\psi^\dagger\psi)^2d\,\br \\ \cl_{v_0}= & v_0\int\left[s_r(\br)s_r^*(\br)\right]^{q-1 } s_a(\br)s_a^*(\br ) d\br . \label{lv0}\end{aligned}\ ] ] here we have introduced a positive matsubara frequency @xmath126 that ensures the convergence of the superintegral ( [ zpartition ] ) with respect to the bosonic components of the supervectors @xmath50 and @xmath49 and , in the below calculation , also regularises infrared divergences of momentum integrals in @xmath19 dimensions for @xmath127 . the lagrangian of the system in the minimal subtraction scheme is separated into the effective lagrangian @xmath128 that describes the long - wave behaviour of the physical observables and the counterterm lagrangian @xmath129 that cancels contributions divergent in the powers of @xmath130 : @xmath131 \psi\,d\br \nonumber \\ & + \frac{1}{2}\varkappa\int(\psi^\dagger\psi)^2d\,\br \label{le } \\ & + v\int\left[s_r(\br)s_r^*(\br)\right]^{q-1 } s_a(\br)s_a^*(\br ) d\br , \label{lv}\end{aligned}\ ] ] where the velocity of the renormalised weyl fermions ( the coefficient before @xmath132 ) is set to unity , without loss of generality , by appropriately choosing the field @xmath133 . the scale @xmath134 sets the characteristic momentum of the long - wave behaviour . the coefficients @xmath67 and @xmath135 before the source terms ( [ lv0 ] ) and ( [ lv ] ) are considered infinitesimal in the calculation below . we note , that in general the renormalisation generates additional terms @xmath136^{m } s_a(\br)s_a^*(\br ) d\br $ ] with @xmath137 , which we neglect here because their contributions to the partition function ( [ zpartition ] ) are less singular @xmath138 at @xmath139 than that of the term ( [ lv ] ) , and , thus , they do not contribute to the iprs ( [ iprminimals ] ) . the minimal subtraction scheme@xcite consists in calculating perturbative corrections to the lagrangian ( [ le ] ) and choosing the counterterms @xmath129 to cancel divergent in powers of @xmath130 contributions . the rg equations can then be derived by relating the `` observable '' parameters @xmath133 , @xmath140 , @xmath33 , and @xmath67 to the `` bare '' ones @xmath50 , @xmath141 , @xmath142 , and @xmath135 . all momentum integrals in such a calculation are convergent in low dimensions @xmath19 with @xmath127 . the results have to be analytically continued to higher dimensions , @xmath17 , at the end of the calculation ( dimensional regularisation ) . the `` dephasing rate '' @xmath36 , sent to zero at the end of the calculation [ cf . ( [ iprminimals ] ) and ( [ l0minimal ] ) ] , may be assumed to be significantly smaller than the scale @xmath140 and neglected when computing the parameters of the renormalised lagrangian . the one - loop perturbative correction to the vertex @xmath67 is described by the diagrams in fig . 2c - e and the topologically equivalent diagrams . since the `` dephasing rate '' @xmath36 may be neglected when considering the respective high - momentum scattering processes , the advanced and retarded green s functions may be taken identical @xmath143 when evaluating these diagrams . the sum of diagrams 2c - e is given by @xmath144 where the prefactors @xmath99 and @xmath42 account for the numbers of topologically equivalent diagrams , @xmath145 , and @xmath94 , and @xmath146 is the tensor product of the two subspaces of the two @xmath147 propagators connected by impurity lines in figs . 2d and 2e ; the structure of the correction is trivial in the other propagators subspaces . the perturbative corrections to the disorder strength @xmath33 and the frequency @xmath140 have been calculated in detail in ref . . the velocity of the weyl fermions [ the coefficient before the @xmath132 term in eq . ( [ le ] ) ] does not receive first - order corrections . the presence of the one - loop counterterms ( [ lcounter1 ] ) requires introducing the respective diagrammatic elements , fig . [ oneloopcounter ] , in addition to the propagators and impurity lines , when calculating diagrammatically perturbative corrections beyond the one - loop order . diagrams in fig . [ diagrams](a)-(m ) are computed similarly to the two - loop diagrams for the renormalisation of the disorder strength , obtained by replacing the zigzag line by an impurity line and considered in detail in ref . . the values of diagrams [ diagrams](a)-(m ) , together with the numbers of equivalent diagrams , are provided in table [ table : samediagr ] . diagrams [ diagrams](n)-(p ) are regular in @xmath14 due to the mutual cancellation of the singularities coming from blocks with vertical and diagonal impurity lines . for instance , the sum of the diagrams in fig . [ diagrams](n ) ( see also fig . [ diagramn ] ) can be evaluated ( in units @xmath152 ) as @xmath153 } { ( \omega^2+p^2)^2(\omega^2+q^2)[\omega^2+(\bp+\bq)^2 ] } \nonumber\\ = 4\omega^2\int\frac{(\hbsigma\bp)(\hbsigma\bq ) } { ( \omega^2+p^2)^2(\omega^2+q^2)[\omega^2+(\bp+\bq)^2 ] } \nonumber\\ + 4\omega^2\int\frac{1 } { ( \omega^2+p^2)(\omega^2+q^2)[\omega^2+(\bp+\bq)^2 ] } \nonumber\\ -8\omega^4\int\frac{1 } { ( \omega^2+p^2)^2(\omega^2+q^2)[\omega^2+(\bp+\bq)^2 ] } \nonumber\\ = \co(1).\end{aligned}\ ] ] ( for detailed calculations of the last integrals see ref . ) . the values of diagrams 3(n)-(q ) are given in table [ diagrnq ] . diagrams [ diagrams](r)-(w ) are the two - loop diagrams for the corrections to the vertex @xmath67 that contain one - loop counterterms and are equivalent to similar diagrams in ref . , up to replacing the zigzag line or its counterterm by the impurity line or its counterterm , with the values provided in table [ table : counter ] . the one - loop and two - loop corrections to the lagrangian ( [ le ] ) are cancelled by the counterterm lagrangian @xmath157\psi\ : d\br \nonumber\\ & + \frac{1}{2}\delta\varkappa\int\left(\psi^\dagger\psi\right)^2d\br \nonumber\\ & + \delta v\int\left[s_r(\br)s_r^*(\br)\right]^{q-1 } s_a(\br)s_a^*(\br ) d\br,\end{aligned}\ ] ] where the values of @xmath158 , @xmath159 , and @xmath160 have been calculated previously@xcite ( see also refs . ): @xmath161 , \label{omegadivergent } \\ & \delta(\hbsigma\hat\bk ) = \frac{1}{4\varepsilon}(\varkappa c_{2-\varepsilon}\omega^{-\varepsilon})^2\hbsigma\hat\bk , \\ & \delta\varkappa = \varkappa\left[-\frac{2}{\varepsilon}\varkappa c_{2-\varepsilon}\omega^{-\varepsilon } + \left(\frac{4}{\varepsilon^2}-\frac{1}{2\varepsilon}\right)\left(\varkappa c_{2-\varepsilon}\omega^{-\varepsilon}\right)^2\right ] . \label{kappadivergent}\end{aligned}\ ] ] introducing the dimensionless disorder strength @xmath163 the full lagrangian ( [ lfull ] ) can be rewritten as @xmath164\psi \,d\br \nonumber\\ + \frac{\gamma\omega^\varepsilon}{4c_{2-\varepsilon } } \left(1-\frac{\gamma}{\varepsilon}-\frac{\gamma^2}{8\varepsilon } + \frac{\gamma^2}{\varepsilon^2}\right)\int(\psi^\dagger\psi)^2d\br \nonumber\\ + v\left[1-\frac{q}{2\varepsilon}\gamma + \frac{1}{\varepsilon^2}\left(\frac{q^2}{8}+\frac{q}{4}\right)\gamma^2 -\frac{1}{\varepsilon}\left(\frac{3}{16}q^2-\frac{3}{16}q\right)\gamma^2\right ] \nonumber\\ \int\left[s_r(\br)s_r^*(\br)\right]^{q-1 } s_a(\br)s_a^*(\br ) \,d\br . \label{lagrangianfinal}\end{aligned}\ ] ] by comparing the lagrangian ( [ lagrangianfinal ] ) , that depends on the renormalised observables @xmath133 , @xmath140 , @xmath33 , and @xmath67 , with the lagrangian ( [ l0minimal])-([lv0 ] ) expressed in terms of the `` bare '' variables @xmath50 , @xmath141 , @xmath142 , and @xmath135 , we can relate the `` bare '' and the renormalised observables : the input parameters @xmath135 and @xmath142 of the lagrangian are independent of the characteristic momentum scale @xmath168 at which the long - wave properties of the system are observed , which gives @xmath169 eqs . ( [ cs ] ) , analogous to the callan - symanzik equation@xcite , immediately lead to the rg equations ( 11c ) and ( 11a ) with @xmath170 . the rg equation ( 11b ) follows from eq . ( [ omegabare ] ) using that @xmath171 .

systems with the power - law quasiparticle dispersion @xmath0 exhibit non - anderson disorder - driven transitions in dimensions @xmath1 , as exemplified by weyl semimetals , 1d and 2d arrays of ultracold ions with long - range interactions , quantum kicked rotors and semiconductor models in high dimensions . we study the wavefunction structure in such systems and demonstrate that at these transitions they exhibit fractal behaviour with an infinite set of multifractal exponents . the multifractality persists even when the wavefunction localisation is forbidden by symmetry or topology and occurs as a result of elastic scattering between all momentum states in the band on length scales shorter than the mean free path . we calculate explicitly the multifractal spectra in semiconductors and weyl semimetals using one - loop and two - loop renormalisation - group approaches slightly above the marginal dimension @xmath2 . = 1 after half a century of studies , disorder - driven transitions in conducting materials still motivate extensive research efforts . anderson localisation ( al ) transition is responsible for turning a metal into an insulator when increasing the disorder strength in dimensions @xmath3 and was believed for several decades to be the only possible disorder - driven transition in non - interacting systems . al continues to fascinate researchers by its peculiar and universal properties , such as , e.g. , _ multifractality_ fractal behaviour of the wavefunctions at the transition with an infinite set of multifractal exponents@xcite . a broad class of systems with the power - law quasiparticle dispersion @xmath0 in dimensions @xmath1 displays , however , another single - particle disorder - driven transition distinct from al@xcite . this transition , unlike al , occurs only near a band edge or at a nodal point ( in a semimetal ) . it reflects in the critical behaviour of the disorder - averaged density of states ( in contrast with al ) , as well as in other physical observables , e.g. , conductivity . such a transition has first been proposed@xcite for the specific case of dirac semimetals ( @xmath4 , @xmath5 ) and has recently sparked vigorous studies@xcite@xcite @xcite of its critical properties in 3d weyl and dirac systems@xcite . other playgrounds for the observation of this non - anderson disorder - driven transition are 1d and 2d arrays of trapped ultracold ions with long - range interactions@xcite , quantum kicked rotors@xcite ( mappable onto high - dimensional semiconductors ) , and numerical simulations of schroedinger equation in @xmath6 dimensions@xcite . despite these comprehensive studies , the wavefunction structure at these non - anderson disorder - driven transitions is rather poorly understood . such transitions are not necessarily accompanied by localisation ; they can occur between two phases of localised states [ like in 1d ( non - chiral ) chains of trapped ions@xcite ] or between two phases of delocalised states [ e.g. , in single - node weyl semimetals ( wsms ) ] or between localised and delocalised states ( in a high - dimensional semiconductor@xcite ) . particle wavefunctions in all of these cases are characterised by a correlation length that diverges from both sides of the transition . _ results . _ in this paper we study microscopically wavefunctions @xmath7 at the non - anderson disorder - driven transitions and demonstrate their _ multifractal _ nature . when delocalised states are allowed by symmetry , dimensions , and topology , the typical wavefunctions at the critical disorder strength have a fractal structure and are characterised by a universal non - linear multifractal spectrum @xmath8 , defined@xcite by the inverse participation ratios ( iprs ) @xmath9 in the limit of an infinite system size @xmath10 . such multifractal behaviour persists even if the wavefunctions are delocalised on both sides of the transition ( like in a single - node wsm ) . unlike the al transition , here the multifractal spectrum @xmath8 is determined by the elastic scattering on length scales shorter than the mean free path . in systems that allow for localised states near the transition , these states scale as @xmath11 when approaching it , where @xmath12 is the localisation length divergent at the transition . in this paper we also calculate the multifractal spectrum @xmath8 explicitly for several systems . we find the multifractal spectrum of a disordered system with the power - law quasipatricle dispersion @xmath13 in dimensions @xmath1 in the orthogonal symmetry class , in the expansion in powers of @xmath14 , to be @xmath15 where @xmath16 ( and @xmath17 ) . for weyl semimetals , @xmath18 , in @xmath19 dimensions @xmath20 we note that on sufficiently short length scales the multifractality in a weyl semimetal is similar ( with @xmath14 replaced by the dimensionless disorder strength ) to that of 2d dirac fermions on the surfaces of a 3d topological insulator , studied in ref . @xcite . although there is no phase transition in such 2d systems , their wavefunctions display non - universal short - length multifractal behaviour@xcite , in contrast with the universal multifractality ( [ weylresult ] ) that persists at all length scales . ) near a non - anderson disorder - driven transition . the transition occurs at the energy @xmath21 near the ( renormalised@xcite ) band edge or near a nodal point ( for semimetals).,scaledwidth=40.0% ] _ the phase diagram _ of a finite - size system near a non - anderson disorder - driven transition is shown in fig . [ phasediagr ] . in what follows we measure all energies from a nodal point or a ( renormalised@xcite ) band edge[45 ] set to @xmath21 . for disorder strengths weaker than a critical value ( `` weak - disorder phase '' in fig . [ phasediagr ] ) , @xmath22 , the disorder is perturbatively irrelevant@xcite with the dimensionless disorder strength @xmath23^{-1}$ ] vanishing at small energies @xmath24 , where @xmath25 is the elastic scattering time . unlike the case of low dimensions , the lowest - energy levels of a sufficiently large high - dimensional system are _ discrete _ for @xmath22 , as the `` level width '' @xmath26 vanishes faster than the spatial - quantisation gaps @xmath27 between the lowest levels at @xmath28 . the interplay of the level discreteness with multifractality will be discussed below . for supercritical disorder strength , @xmath29 , the dimensionless disorder strength grows at low energies , until reaching the value @xmath30 that marks the boundary of the `` strong - disorder phase '' ( that for @xmath31-dimensional semiconductors in the orthogonal symmetry class also matches the mobility threshold ) in fig . [ phasediagr ] . _ inverse participation ratios . _ the wavefunction structure at energy @xmath32 and disorder strength @xmath33 is conveniently characterised by the disorder - averaged iprs@xcite @xmath34^{q-1}g_a(\br,\br , e,\eta)\right>_{\text{dis } } , \label{iprmain}\end{aligned}\ ] ] where @xmath35 are the retarded and advanced green s functions with an artificially introduced `` dephasing rate '' @xmath36 , @xmath37 are the energies of the eigenstates @xmath38 for a given disorder realisation , and @xmath39 is the ( disorder - averaged ) density of states . below we compute the disorder - averaged iprs ( [ iprmain ] ) near the critical point @xmath40 as a function of the system size @xmath41 or the localisation length @xmath12 . the iprs , eq . ( [ iprmain ] ) , are mimicked by the diagram in fig . [ basicdiagr]a . green s functions before disorder averaging , cf . eq . ( [ iprmain ] ) . b ) vertex that connects @xmath42 green s functions . c)-e ) diagrams for the one - loop renormalisation of the vertex . for @xmath43 , diagrams c)-e ) have equal values . in weyl semimetals and other odd - spectrum ( @xmath44 ) systems diagrams d ) and e ) cancel each other . ] unlike the case of low dimensions , @xmath45 , the low - energy properties of high - dimensional materials under consideration are affected by elastic scattering between all momenta in the band@xcite . such ultraviolet processes are qualitatively important on length scales shorter than the mean free path @xmath46 , and , in particular , determine the criticality and multifractality near the transition point due to the diverging @xmath46 . this leads to the critical properties and multifractal spectrum different from those at the usual al transition , that occurs for states away from nodes and band edges and is described by non - linear sigma - models@xcite on length scales longer than the mean free path . _ renormalisation procedure . _ the effects of the ultraviolet scattering can be addressed in a controlled way by means of a perturbative renormalisation - group ( rg ) controlled by the small parameter@xcite@xcite @xcite @xmath16 . the results obtained from this approach are expected to hold qualitatively also in systems with @xmath47 . to perform renormalisations , we rewrite the disorder - averaged iprs using a supersymmetric@xcite field theory : @xmath48^{q-1 } \nonumber\\ & s_a(\br)s_a^*(\br ) \:\exp({-\cl_0-\cl_{\text{int } } } ) , \label{pqsuper } \\ \cl_0=&-i\int \psi^\dagger\lambda^\frac{1}{2 } \left[e\,\lambda(k)+i\eta\lambda\lambda(k)-\epsilon_{\hat\bk}\right ] \lambda^\frac{1}{2}\psi\,d\br , \label{l0 } \\ \cl_{\text{int}}&=\frac{1}{2}\varkappa(k)\int(\psi^\dagger\lambda\psi)^2d\,\br , \label{lint}\end{aligned}\ ] ] where @xmath49 and @xmath50 are @xmath51-component supervectors in the @xmath52 ( fermion - boson @xmath53 retarded - advanced ) space , @xmath54 and @xmath55 are the bosonic components of the supervectors , and @xmath56 . the factors with @xmath57-matrices in eq . ( [ l0 ] ) ensure the convergence of the supersymmetric integral with respect to the bosonic variables@xcite . upon repeatedly integrating out shells of highest momenta , the action ( [ l0])-([lint ] ) reproduces itself with renormalised disorder strength @xmath58 and the parameters @xmath59 and @xmath60 that `` flow '' with the running cutoff @xmath61 and initial values @xmath62 , @xmath63 , and @xmath64 , where @xmath65 is the ultraviolet momentum cutoff set by the bandwidth or the impurity size@xcite . the parameters @xmath66 and @xmath67 grow upon coarse - graining and exhibit singular behaviour with @xmath68 at the critical disorder , @xmath69 . the iprs ( [ iprmain ] ) can be rewritten as @xmath70 , \label{pqrenormgen}\end{aligned}\ ] ] where @xmath71 $ ] is the ipr of an effective renormalised system with the same quasiparticle dispersion @xmath0 , but with renormalised disorder strength @xmath33 and energy @xmath72 and that excludes scattering into momentum states @xmath73 that were removed by the rg procedure . the rg has to be stopped either when the spatial quantisation effects become important or if it runs into the regime of strong disorder , @xmath74 . the renormalised system is then equivalent to a simple ( low - dimensional ) system with discrete energy levels or with a constant density of states and unaffected by scattering into high - momentum modes ; the ipr @xmath75 of such a system can be found using conventional methods developed for low - dimensional systems@xcite . _ fractality of delocalised states . _ in what immediately follows we consider a system with delocalised finite - energy states at @xmath69 [ along path @xmath76 in fig . ( [ phasediagr ] ) ] , as , e.g. , in a @xmath77-dimensional system with potential disorder . the rg procedure at critical disorder is terminated when either the momentum @xmath61 reaches @xmath78 or the spatial quantisation effects become important ( i.e. the energy levels become discrete ) . the renormalised system is then either ballistic ( for small @xmath14 , that ensures weak disorder at the critical point ) or equivalent to a usual weakly disordered metal ( for larger @xmath14 ) , with@xcite @xmath79 . the characteristic energy @xmath80 of terminating the rg is related to the system size @xmath41 as @xmath81 , where @xmath82 is the dynamical critical exponent . using that @xmath83 , we find @xmath84 , which , together with eq . ( [ pqrenormgen ] ) gives the multifractal spectrum @xmath85 _ localised states . _ for trivial - topology systems in the orthogonal symmetry class the states in the `` strong - disorder phase '' ( fig . [ phasediagr ] ) are localised . also , all states on the phase diagram are localised in systems in @xmath86 dimensions ( if allowed by symmetry / topology ) . near the critical point of the non - anderson disorder - driven transition localised states are still multifractal on length scales shorter than the localisation length @xmath12 ( that diverges at the transition ) . for zero - energy states at supercritical disorder , @xmath29 , ( along path 2 in fig . [ phasediagr ] ) the rg is stopped when reaching strong disorder , @xmath87 . such @xmath21-states are then characterised by only one length scale @xmath88 that gives the localisation length @xmath12 . similarly to the case of delocalised states in a size-@xmath41 system , we find that @xmath89 , and the participation ratio @xmath90 with the multifractal spectrum ( [ deltageneral ] ) . the non - trivial scaling of the ipr ( [ iprloc ] ) with the size of the localisation cell reflects the multifractality of the wavefunctions on length scales @xmath91 . _ orthogonal semiconductors . _ for a disordered system with the quasiparticle dispersion @xmath92 the rg flow of the system parameters is given in terms of the dimensionless disorder strength @xmath93 , with @xmath94 , by the rg equations @xmath95 where @xmath96 and @xmath97 are the terms of higher orders in @xmath98 . eqs . ( [ rglambdao ] ) and ( [ rggammao ] ) for the renormalisation of the energy and the disorder strength have been obtained previously in refs . and . eq . ( [ rgvo ] ) describes the flow of the preexponential in eq . ( [ pqsuper ] ) . the renormalisations ( [ rgvo])-([rggammao ] ) can be also easily obtained diagrammatically . for instance , the one - loop renormalisation of the vertex @xmath67 , fig . [ basicdiagr]b , is given by @xmath42 diagrams equivalent to [ basicdiagr]c , @xmath99 diagrams equivalent to [ basicdiagr]d , and @xmath99 diagrams equivalent to [ basicdiagr]e . all these diagrams have the same value for the dispersion under consideration , hence the prefactor @xmath100 in eq . ( [ rgvo ] ) . the renormalisation of the disorder strength @xmath98 and the parameter @xmath66 for the dispersion under consideration has been described in detail in ref . . in the one - loop order we find from eqs . ( [ rgvo])-([rggammao ] ) that @xmath101 and@xcite @xmath102 , which , together with eq . ( [ deltageneral ] ) , gives the multifractal spectrum ( [ semicondresult ] ) . _ chiral systems , _ such as weyl semimetals or chiral chains with long - range hopping@xcite , often have odd quasiparticle spectra , @xmath44 , which leads to the mutual cancellation of diagrams [ basicdiagr]d and [ basicdiagr]e . the rg flow of the vertex @xmath67 is given by eq . ( [ rgvo ] ) with the replacement @xmath103 and with the dimensionless disorder strength @xmath104 . the flow of @xmath66 is given by eq . ( [ rglambdao ] ) with the replacement @xmath105 . from the rg equations we find @xmath106 [ cf . eq . ( [ zeta ] ) ] , which , according to eq . , gives vanishing multifractality @xmath107 in the one - loop order . thus , finding the multifractal behaviour in such chiral systems requires rg analysis in higher orders . in what follows we present the result for a weyl semimetal ( see appendix for a detailed two - loop rg analysis of multifractality using the minimal - subtraction scheme ) . _ weyl semimetals _ are 3d systems with the quasiparticle dispersion @xmath108 , where @xmath109 is a vector of pauli matrices . wsm properties near the non - anderson disorder - driven transition can be studied by performing rg analysis in @xmath19 dimensions with setting @xmath110 at the end of the calculation . although the rg procedure is controlled by small @xmath14 , it is known@xcite to give good agreement with numerical results even for @xmath111 . the flows of the parameters of a disordered wsm in @xmath112 dimensions are given by ( see appendix ) @xmath113 eqs . ( [ lambdargwsm ] ) and ( [ gammargwsm ] ) for the renormalisation of the energy and disorder strength in a disordered wsm have been derived previously in refs . and and in refs . for the equivalent gross - neveu model . an equation equivalent to eq . ( [ vrgwsm ] ) has also been derived in ref . @xcite to describe the wavefunctions of 2d dirac fermions on the surface of a 3d topological insulator@xcite . from eqs . ( [ vrgwsm])-([gammargwsm ] ) we find to the two - loop order @xmath114 , which , together with @xmath115 and eq . ( [ deltageneral ] ) , gives the multifractal spectrum ( [ weylresult ] ) . _ level discreteness and observability of multifractality . _ observation of multifractality at the critical point ( @xmath21 , @xmath69 ) requires that the disorder - averaged energy spectrum of the system at this point is continuous , i.e. smeared by disorder and unaffected by the spatial quantisation . this condition is always met in systems with @xmath116 as the `` level width '' @xmath117 for the lowest levels @xmath118 is of the order of their energies @xmath37 . however , for some systems , e.g. , chains of ultracold ions@xcite , it is possible to realise@xcite @xmath119 , that corresponds to weak disorder @xmath120 at the critical point and the existence of a large number @xmath121 of energy levels that remain discrete [ @xmath122 at the critical disorder , although the energies and the spacings between these levels vanish in the limit @xmath10 . the multifractal behaviour in such systems is observable only on sufficiently short length scales @xmath123 that correspond to the wavelengths of higher levels belonging to the continuous part of the energy spectrum . _ rare - region effects . _ the perturbative rg that we used in this paper neglects non - perturbative instantonic contributions [ , ] to the field theory ( [ pqsuper])-([lint ] ) , that , e.g. , result in the formation of lifhsitz tails near band edges and always lead to a finite density of states@xcite near nodes . the effects of such instantons on physical observables , such as the density of states and conductivity , are rather small near the critical point in high - dimensional systems and were undetectable in all numerical studies@xcite so far except ref . . another potential consequence of rare - region ( instantonic ) effects , albeit currently not demonstrated analytically , may be the `` rounding '' of the criticality , i.e. preventing the divergence of the correlation length near the critical point , and thus converting the phase transition of the type discussed here into a sharp crossover , with the latter scenario advocated in ref . . in our view , the plausibility of this scenario deserves further investigation , in particular , in systems that disallow localisation by symmetry and topology . in the case the criticality does get smeared in a system , the wavefunction multifractality studied here is observable on distances shorter than a large characteristic length set by the rare - region effects . _ acknowledgements . _ we are grateful to a.w.w . ludwig for useful motivating discussions at the initial stages of this work and to p.m. ostrovsky for previous collaboration . also , we thank m.s . foster for valuable discussions . our work was financially supported by the nsf grants dmr-1001240 ( lr and svs ) , dmr-1205303(vg and svs ) , phy-1211914 ( vg and svs ) , phy-1125844 ( svs ) and by the simons investigator award of the simons foundation ( lr ) .

during the expansion of the outcoupled atoms , optical levitation is performed with a blue - detuned @xmath67 nm laser beam to compensate for gravity and a radio frequency dressing @xcite is used to keep the out - coupled fraction confined and clearly detectable after the @xmath9 ms expansion . in particular , the rf field is such to produce a mexican - hat potential which limits the radial expansion to about @xmath68 @xmath25 m , whereas the slower axial expansion is barely perturbed . @xmath25 m . the in - situ value can be obtained considering a scale factor of @xmath69 , given by the ratio between the in - situ and expanded tf radius at @xmath46 ms ; this because the assumption of a constant @xmath70 during the expansion . this gives a mean @xmath71 of @xmath72 with a standard deviation of @xmath73 . there is no statistical difference between the single - vortex distribution and the double - vortex one . ] a precise statistical analysis is not possible here because information on the phase shift can be extracted only in the data subset where the crossing point occurs at about half of the inspected time evolution ( @xmath74 of the cases ) . clear phase shifts are present in about half of this subset .

we study the real - time dynamics of vortices in a large elongated bose - einstein condensate ( bec ) of sodium atoms using a stroboscopic technique . vortices are produced via the kibble - zurek mechanism in a quench across the bec transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate . good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms . in configurations with two or more vortices , we see signatures of vortex - vortex interaction in the shape and visibility of the orbits . in addition , when more than two vortices are present , their decay is faster than the thermal decay observed for one or two vortices . the possible role of vortex reconnection processes is discussed . vortex dynamics is an essential feature of quantum fluids @xcite and plays a key role in superfluid helium @xcite , superconductors @xcite , neutron stars @xcite and magnetohydrodynamics @xcite . the interaction between vortices is crucial for understanding the formation of vortex lattices in rotating superfluids and is the basic mechanism leading to quantum turbulence _ via _ vortex reconnection @xcite . vortices have been extensively investigated in atomic gases @xcite , where a variety of techniques permits the observation of single ones up to a few hundreds , interacting in a clean environment and on a spatial scale ranging from the healing length ( core size ) @xmath0 to a few tens of @xmath0 . the fact that atoms are confined by external fields of tunable geometry makes them suitable to explore the physics of reconnection and dissipation in inhomogeneous systems and in the presence of boundaries . seminal experiments were performed in rotating bose - einstein condensates ( becs ) , where the effect of rotation and long - range interaction favors vortex alignment and the formation of vortex lattices @xcite and hence crossing and reconnection mechanisms are inhibited . interacting vortices have been observed in nonrotating oblate becs , where vortex lines are short and either parallel or antiparallel , thus behaving as pointlike particles dominated by their long - range interaction in a quasi-2d background @xcite . in our experiment we use a cigar - shaped bec which is particularly suitable for studying the dynamics of vortex lines in 3d . because of the boundary conditions imposed by the tight radial confinement each vortex line lies in a plane perpendicular to the long axis @xmath1 of the trap , such to minimize its length and therefore its energy , as in the solitonic vortex configuration predicted in refs . @xcite and recently observed both in a bec @xcite and in a superfluid fermi gas @xcite . the line is randomly oriented in the plane and away from it , at distances of the order of the system transverse size , the superfluid flow quickly vanishes and the long - range part of the vortex - vortex interaction is suppressed . hence , vortices can move almost independently along elliptic orbits except when they approach each other and may collide with a random relative angle . at the scale of the healing length , where reconnection can take place , the system is still equivalent to a uniform superfluid , like liquid he , but with the advantage that vortex filaments collide at measurable relative velocities . the experimental apparatus is described in ref . @xcite . we evaporate sodium atoms in a magnetic harmonic trap with frequencies @xmath2 hz . vortices with random position and velocity spontaneously originate _ via _ the kibble - zurek mechanism @xcite from phase defects in the condensate when crossing the bec transition and their average number scales as a power law with the evaporation rate . at the end of the evaporation we have an almost pure prolate bec with about @xmath3 atoms at @xmath4 nk in the state @xmath5 . in refs . @xcite we counted and characterized defects using destructive absorption imaging . here we apply a stroboscopic technique , similar to that in refs . @xcite , which allows us to observe the real - time dynamics . starting from an initial number of atoms @xmath6 , we remove a small fraction @xmath7 by outcoupling them to the antitrapped state @xmath8 _ via _ a microwave pulse , short enough to provide a resonance condition throughout the whole sample . outcoupled atoms are imaged along a radial direction after a @xmath9 ms expansion @xcite without affecting the trapped ones . the extraction mechanism is repeated @xmath10 times with time steps @xmath11 , keeping @xmath12 fixed . raw images are fitted to a thomas - fermi ( tf ) profile @xcite and the residuals are calculated . because of the peculiar structure of the superfluid flow of solitonic vortices @xcite , after expansion the whole radial plane containing a vortex exhibits a density depletion and vortices are seen as dark stripes independently of their in - plane orientation . during the extraction sequence the remaining condensate evolves in trap , only weakly affected by atom number change , provided @xmath13 is sufficiently small . we can then identify the axial position of the vortex in each image of the outcoupled atoms and analyze its oscillation as a faithful representation of the in - trap dynamics . typical examples are shown in figs . [ figure1](a)-[figure1](i ) . alternatively we image the full bec along the axial direction after a long expansion with a destructive technique as in @xcite and directly see the shape and orientation of the vortex lines as in figs . [ figure1](j)-[figure1](m ) . images of the density distribution of the atoms extracted from three becs ; frames are taken every @xmath14 ms , each after a @xmath9 ms expansion . ( a ) static vortex . ( b)-(c ) vortices precessing with different amplitudes . each vortex is randomly oriented in the @xmath15 plane and , after expansion , it forms a planar density depletion @xcite which is visible as a stripe . ( d)-(i ) sequences with two and three vortices , with @xmath16 ms ; here frames are not to scale and vertically squeezed to enhance visibility . ( j)-(m ) destructive absorption images of the whole bec taken along the axial direction @xmath1 after @xmath17 ms of expansion , showing ( j ) a single vortex filament crossing the condensate from side to side and ( k)-(m ) two vortices with different relative orientation and shape . all images show the residuals after subtracting the fitting tf profile . ] we first choose an evaporation rate of @xmath18 khz / s , yielding one vortex in each bec on average . from the sequence of radial images we extract the axial position of each vortex @xmath19 . frames are recorded every @xmath14 ms . figures [ figure2](a ) and [ figure2](b ) show two examples corresponding to the raw images of figs . [ figure1](b ) and [ figure1](c ) , respectively . the observations are consistent with a vortex precession around the trap center , as the one observed in oblate becs @xcite . in a nonrotating elongated condensate , a straight vortex line , oriented in a radial plane , is expected to follow an elliptic orbit in a plane orthogonal to the vortex line , corresponding to a trajectory at constant density @xcite . the observed motion of each dark stripe in figs . [ figure1](a)-[figure1](c ) is the axial projection of such a precession . given @xmath20 the in - trap amplitude of the orbit normalized to the tf radii @xmath21 and @xmath22 @xcite , the precession period is predicted to be @xmath23 where @xmath24 is the axial trapping period and @xmath0 is related to the chemical potential @xmath25 by @xmath26 . this result , which is valid to logarithmic accuracy , has been derived for a disk - shaped nonaxisymmetric condensate in refs . @xcite within the gross - pitaevskii theory at @xmath27 and in the tf approximation , corresponding to @xmath28 ( in our case , @xmath29 ranges from @xmath30 to @xmath10 ) . it can also be obtained by means of the superfluid hydrodynamic approach introduced in ref . @xcite to describe the motion of vortex rings in elongated condensates , appropriately generalized to the case of solitonic vortices as in ref . @xcite . the quantity @xmath31 is the local chemical potential along the vortex trajectory and we assume @xmath32 to be constant during expansion , as distances are expected to scale in the same way in the slow axial expansion . in comparing the observed period with eq . ( [ eqn : period ] ) we must consider that the number of atoms is decreasing from shot to shot . since extraction is spatially homogeneous , the gradients of the density , and hence the equipotential lines for the vortex precession and the orbit amplitude remain almost unchanged . however , @xmath33 ( hence @xmath34 ) decreases in time and so does the vortex orbital period @xmath35 , as is clearly visible in figs . [ figure2](a ) and [ figure2](b ) . we define an instantaneous period at time @xmath36 as the period obtained from a sinusoidal fit to the measured position in a time interval centered at @xmath36 and containing about one oscillation . such @xmath37 is plotted in fig . [ figure2](c ) and [ figure2](d ) and compared to eq . ( [ eqn : period ] ) , where we include the effect of the observed @xmath36 dependence on @xmath38 , shown in fig . [ figure2](e ) , both in @xmath25 and @xmath0 . the agreement is good , the major limitation being the experimental uncertainty in @xmath38 . we also show the period expected for the oscillation of a dark or grey soliton , which is @xmath39 independently of @xmath38 @xcite . in fig . [ figure2](f ) we plot the period of vortices orbiting with different amplitude @xmath32 . the agreement with theory is again good and can be further appreciated by considering the ratio between each value of @xmath35 measured at a given @xmath32 and the theoretical value in eq . ( [ eqn : period ] ) obtained for the same @xmath32 and @xmath38 . figure [ figure2](g ) shows the histogram of all values obtained by extracting @xmath35 and @xmath32 from a fit to the first oscillation , using @xmath40 in eq . ( [ eqn : period ] ) . the histogram gives @xmath41 . this remarkable agreement with theory is nontrivial since eq . ( [ eqn : period ] ) assumes @xmath42 and a rigid straight vortex line , while off - centered vortices actually bend toward the curved bec surface . for rotating condensates the bending mechanism has been discussed in refs . @xcite and observed in ref . @xcite . examples of straight and bent vortices in our condensate are given in figs . [ figure1](j)-[figure1](m ) . in our elongated bec , with strong radial inhomogeneity , this bending mechanism is expected to be more effective than in oblate becs . our observations seem to indicate that its effect on the period is small , possibly of the same order of the logarithmic corrections to eq . ( [ eqn : period ] ) predicted for a straight vortex in a 2d geometry @xcite . this may be due to the fact that the difference in length between a bent and a straight vortex , at a comparable @xmath32 , is relatively small and the overall structure of the vortical flow is also quite similar , so that the key quantities entering the hydrodynamic description ( i.e , the force acting on a unit of length of the vortex and the momentum of the vortex , in the language of ref . @xcite ) are almost the same in the two cases . , remaining in a condensate at time @xmath36 starting from configurations with @xmath43 ( circles ) , @xmath44 ( triangles ) and @xmath45 ( diamonds ) at @xmath46 . solid lines are exponential fits . ] vortex lifetime in nonrotating becs is limited by scattering of thermal excitations , which causes the dissipation of the vortex energy into the thermal cloud . since a vortex behaves as a particle of negative mass , dissipation causes an antidamping of the orbital motion and vortices decay at the edge of the condensate @xcite . we can measure the lifetime @xmath47 by counting the average number of vortices @xmath48 remaining in the condensate at time @xmath36 , starting with @xmath49 . if @xmath50 we find a clear exponential decay with @xmath51 ms ( fig . [ figure3 ] ) , close to that measured in refs . @xcite and of the same order of the one observed in a fermionic superfluid @xcite . ( d)-[figure1](g ) , respectively . solid and empty symbols are used to distinguish high and low density contrast , respectively . ] using a faster evaporation ramp ( @xmath52 khz / s ) , we produce more vortices and search for signatures of mutual interaction . examples are shown in fig . [ figure1](d)-[figure1](i ) and typical trajectories are also reported in fig . [ figure4 ] . in some cases , vortices perform unperturbed oscillations [ fig . [ figure4](a ) ] ; in others , we clearly see a shift in their trajectories at the crossing point [ fig . [ figure4](b ) ] . the average relative velocity at the crossing in the latter case is systematically smaller ( @xmath53 mm / s ) than in the former ( @xmath54 mm / s ) @xcite . the shift has a consequence also in the determination of the orbital period as it causes a broadening of the probability distribution of the ratio @xmath55 which now gives @xmath56 , with a standard deviation three times larger than for the single vortex [ fig . [ figure2](g ) ] . in addition , crossings are frequently associated with a sudden change of visibility of one or both vortices [ figs . [ figure1](e)-[figure1](h ) ) . finally , by analyzing the lifetime of vortices for the initial condition @xmath57 and @xmath58 we observe a lifetime @xmath59 ms for the two - vortex configuration , consistent with the one - vortex configuration . the situation instead changes in the three - vortex configuration , where a faster decay is observed , @xmath60 ms ( fig . [ figure3 ] ) . the frequent observation of unperturbed orbits for multiple vortices is intriguing . two vortex lines moving back and forth in the condensate with random radial orientations should have large probability to cross each other at some point . if crossings occur , reconnections are expected to take place @xcite with possible drastic ( and almost temperature independent @xcite ) effects on the vortical dynamics . the actual dynamics can strongly depend on the relative angle @xmath61 between vortex lines as well as the relative velocity @xmath62 between the planes where they lie . when @xmath61 is close to @xmath63 ( @xmath64 ) , the vortex lines tend to align ( antialign ) , thus reducing the chance of reconnection for vortices on different orbits . but when vortices approach with @xmath65 reconnection can be hardly avoided . the fact that we observe the same vortex lifetime for @xmath50 and @xmath44 implies that such reconnections are either suppressed or they induce a negligible dissipation . a possible explanation is the occurrence of double reconnection processes @xcite . vortex reconnection corresponds to the switching of a pair of locally coplanar vortex lines , accompanied by a change of topology . in our geometry a finite @xmath62 implies that the newly formed filaments must stretch in the condensate while the two planes separate again after reconnection . the consequent energy cost is instead avoided if vortices perform a consecutive second reconnection when they are still at close distance . this would preserve the vortex number , consistent with our observation of an equal vortex lifetime for @xmath50 and @xmath44 . it is worth mentioning that a similar scenario has also been recently suggested for the collision of cosmic strings @xcite . the occurrence of a shift in the trajectories , that apparently depends on @xmath62 , could be associated with the role of the collision time : faster vortices have less time to interact and their trajectories are marginally affected , and this scenario may be applicable both to fly - by vortices and double reconnections . also kelvin modes can be excited in the collision @xcite but , if present , they seem not to affect the lifetime , while they are likely responsible for the change of visibility of the vortices , as they can produce out - of - plane distortions and hence a change of contrast in the density distribution . finally , the observation of a shorter lifetime in configurations with @xmath66 can be understood by considering the role of a third vortex in the collision of two other vortices , whose tendency to rotate in the radial plane is frustrated by three - body interaction , thus enhancing the probability of collisions and reconnections . a similar role of three - body interactions in the dynamics of vortices was recently investigated in the context of 2d classical turbulence @xcite . our experimental results demand new theoretical models . so far , numerical simulations of vortex reconnection are usually performed with vortex lines initially at rest , at small distance , which then evolve in time @xcite , while in our case the role of the relative velocity seems to be crucial . shedding light on this , and generally on the dynamics of few vortices in such a relatively simple configuration , can help to understand the physics of vorticity in more complex settings , like those of refs . @xcite , in the search of a satisfactory comprehension of quantum turbulence in superfluids with boundaries . we thank l.p . pitaevskii , n.p . proukakis , i - kang liu , n.g . parker and c.f . barenghi for insightful discussions . we acknowledge provincia autonoma di trento for funding . 63ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty in link:\doibase 10.1016/s0079 - 6417(08)60077 - 3 [ _ _ ] , vol . , ( , ) p. @noop _ _ ( , ) p. @noop _ _ ( , ) p. link:\doibase 10.1146/annurev.ns.25.120175.000331 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.115.025001 [ * * , ( ) ] link:\doibase 10.1146/annurev - conmatphys-062910 - 140533 [ * * , ( ) ] link:\doibase 10.1063/1.4772198 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.81,647 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.84.806 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevlett.89.100403 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.90.170405 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.91.100402 [ * * , ( ) ] link:\doibase 10.1038/nature07334 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.104.160401 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physreva.84.011605 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.110.225301 [ * * , ( ) ] link:\doibase 10.1103/physreva.90.063627 [ * * , ( ) ] link:\doibase 10.1103/physreva.65.043612 [ * * , ( ) ] link:\doibase 10.1103/physreva.68.043617 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.113.065302 [ * * , ( ) ] link:\doibase 10.1140/epjst / e2015 - 02389 - 7 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1016/0370 - 1573(80)90091 - 5 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) \doibase http://dx.doi.org/10.1063/1.4747163 [ * * , ( ) ] @noop , * * , ( ) link:\doibase 10.1103/revmodphys.71.463 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.85.2857 [ * * , ( ) ] link:\doibase 10.1103/physreva.70.063620 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop ( ) link:\doibase 10.1103/physrevlett.84.2298 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.93.240403 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physreva.64.043611 [ * * , ( ) ] link:\doibase 10.1103/physreva.63.041603 [ * * , ( ) ] link:\doibase 10.1103/physreva.64.053611 [ * * , ( ) ] link:\doibase 10.1140/epjd / e2003 - 00015-y [ * * , ( ) ] link:\doibase 10.1103/physrevlett.89.200403 [ * * , ( ) ] link:\doibase 10.1103/physreva.61.063612 [ * * , ( ) ] link:\doibase 10.1103/physreva.70.043624 [ * * , ( ) ] link:\doibase 10.1103/physreva.60.r1779 [ * * , ( ) ] @noop * * , ( ) \doibase http://dx.doi.org/10.1016/j.physd.2009.03.006 [ * * , ( ) ] link:\doibase 10.1103/physreva.90.013601 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevd.84.105036 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1073/pnas.1312536110 [ * * , ( ) ] link:\doibase 10.1103/physreve.84.056317 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.71.1375 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physreve.58.2576 [ * * , ( ) ] link:\doibase 10.1007/s10909 - 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sharpe ratio @xcite has become a `` gold standard '' for measuring performance of hedge funds and other institutional investors ( this note uses the generic term `` portfolio '' ) . it is sometimes argued that it is applicable only to i.i.d . gaussian returns , but we will follow a common practice of ignoring such assumptions . for simplicity we assume that the benchmark return ( such as the risk - free rate ) is zero . the ( ex post ) _ sharpe ratio _ of a sequence of returns @xmath0 is defined as @xmath1 , where @xmath2 ( none of our results will be affected if we replace , assuming @xmath3 , @xmath4 by @xmath5 , as in @xcite , ( 6 ) . ) intuitively , the sharpe ratio is the return per unit of risk . another way of measuring the performance of a portfolio whose sequence of returns is @xmath6 is to see how this sequence of returns would have affected an initial investment of 1 assuming no capital inflows and outflows after the initial investment . the final capital resulting from this sequence of returns is @xmath7 . we are interested in conditions under which the following anomaly is possible : the sharpe ratio @xmath8 is large while @xmath9 . ( more generally , if we did not assume zero benchmark returns , we would replace @xmath9 by the condition that in the absence of capital inflows and outflows the returns @xmath6 underperform the benchmark portfolio . ) suppose the return is @xmath10 over @xmath11 periods , and then it is @xmath12 in the @xmath13th period . as @xmath14 , @xmath15 and @xmath16 . therefore , making @xmath13 large enough , we can make the sharpe ratio @xmath17 as large as we want , despite losing all the money over the @xmath13 periods . if we want the sequence of returns to be i.i.d . , let the return in each period @xmath18 be @xmath10 with probability @xmath19 and @xmath12 with probability @xmath20 , for a large enough @xmath13 . with probability one the sharpe ratio @xmath21 will tend to a large number as @xmath22 , despite all money being regularly lost . of course , in this example the returns are far from being gaussian ( strictly speaking , returns can not be gaussian unless they are constant , since they are bounded from below by @xmath23 ) . it is easy to see that our examples lead to the same conclusions when the sharpe ration is replaced by the _ sortino ratio _ @xcite @xmath24 , where @xmath25 the examples of the previous section are somewhat unrealistic in that there is a period in which the portfolio loses almost all its money . in this section we show that only in this way a high sharpe ratio can become compatible with losing money . for each @xmath26 $ ] , define @xmath27 where @xmath28 ranges over the positive integers and @xmath29 over @xmath30 . in other words , @xmath31 is the best achievable sharpe ratio for sequences of returns that lose money , assuming that none of the returns falls below @xmath32 . it is not difficult to show that @xmath33 , and in the previous section we saw that @xmath34 . in this section we are interested in the behaviour of @xmath31 for the intermediate values of @xmath35 , @xmath36 . the function @xmath31 in the ranges @xmath37 $ ] ( left ) and @xmath38 $ ] ( right).,title="fig:",scaledwidth=48.0% ] the function @xmath31 in the ranges @xmath37 $ ] ( left ) and @xmath38 $ ] ( right).,title="fig:",scaledwidth=48.0% ] figure [ fig : f1 ] shows the graph of @xmath39 over @xmath37 $ ] and over @xmath38 $ ] . over the interval @xmath37 $ ] the slope of @xmath39 is roughly 1 . we can see that even for a relatively large value of @xmath40 , the sharpe ratio of a losing portfolio never exceeds 0.5 ; according to table [ tab : f1 ] , @xmath41 ( much less than the conventional threshold of 1 for a good sharpe ratio @xcite ) . .[tab : f1]the approximate values of @xmath31 , @xmath42 , and @xmath43 for selected @xmath35 . [ cols="^,^,^,^,^,^,^,^",options="header " , ] the values of @xmath44 and @xmath45 for selected @xmath35 are shown in table [ tab : g ] , @xmath46 on the left and @xmath47 on the right . the meaning of @xmath43 is the same as in tables [ tab : f1 ] and [ tab : f2 ] . we do not give the values of @xmath42 ; they are huge on the left - hand side of the table and equal to @xmath35 on the right - hand side . the left - hand side suggests that @xmath48 , and this can be verified analytically . figures [ fig : f1][fig : g2 ] can be regarded as a sanity check for the sharpe and sortino ratio . not surprisingly , they survive it , despite the theoretical possibility of having a high sharpe and , _ a fortiori _ , sortino ratio while losing money . in the case of the sharpe ratio , such an abnormal behaviour can happen only when some one - period returns are very close to @xmath23 . in the case of the sortino ratio , such an abnormal behaviour can happen only when some one - period returns are very close to @xmath23 or when some one - period returns are huge .

a simple example shows that losing all money is compatible with a very high sharpe ratio ( as computed after losing all money ) . however , the only way that the sharpe ratio can be high while losing money is that there is a period in which all or almost all money is lost . this note explores the best achievable sharpe and sortino ratios for investors who lose money but whose one - period returns are bounded below ( or both below and above ) by a known constant .

hypercat maintains catalogues of data collected in the literature or at the telescope , concerning the photometry , kinematics and spectrophotometry of galaxies . some catalogues contain `` global '' properties as total magnitude and other spatially resolved data . they give basic data to study the scaling relations of galaxies , as for instance the fundamental plane , and contain all the information needed to make the necessary corrections and normalizations in order to compare measurements of galaxies at different redshifts . the catalogues of global properties are : * _ the catalogue of central velocity dispersions _ ( for galaxies and globular clusters ) has been presented in a preliminary form in prugniel & simien 1996 . the present version gives 5470 measurements published in 352 references for 2335 objects . hypercat allows one to retrieve the published measurements as well as homogenized ( ie . corrected for systematics effects between datasets ) and aperture corrected data . * _ the catalogue of magnitudes and colours _ ( published in prugniel & heraudeau , 1998 ) presents the photometry of 7463 galaxies in the u to i bands . the global parameters , asymptotic magnitude , surface brightness , photometric type ( ie . shape of the growth curve ) , colour and colour gradients were computed from circular aperture photometry . * _ the catalogue of mg2 index _ ( published in golev & prugniel , 1998 ) have 3712 measurements for 1416 galaxies . aperture corrections and homogenization are available . * _ the maximum velocity of rotation _ is available for the stellar rotation of 720 galaxies ( mostly early - type ) . they represents 1491 measurements taken in 224 dataset . a bibliographical catalogue of spatially resolved kinematics ( prugniel et al . 1998 ) indexes 6214 measurements for 2677 galaxies . in addition , other parameters , like the recession velocity , galactic absorption or environment parameters , are automatically extracted from other databases and hypercat provides procedures to compute derived parameters . however , the present understanding of the scaling relations becomes limited by the quality of the parameterization restricted to these `` global '' values . for instance , in prugniel et al . ( 1996 ) we have shown that a more detailed description , including rotation and non - homology of the structure , must be taken into account when studying the fundamental plane of early - type galaxies . for this reason , hypercat has also embarked in the gathering and distribution of spatially resolved data such as _ multi - aperture photometry _ for 20537 galaxies ( 222045 measurements ) , _ kinematic profiles _ `` rotation curve '' , velocity dispersion profiles ... ) for 1761 galaxies ( 73520 measurements ) and _ catalogue of line strength profiles _ ( currently under development ) . an original aspect in the development of hypercat is that the different catalogues are _ separately maintained in different sites_. the database is automatically updated by procedures running over the network at time of low - traffic . at present , observatories participating to the project are : capodimonte ( napoli ) , sternberg ( moscow ) , brera ( milano ) , university of sofia and lyon . the distribution , over several astronomers , of the work to maintain this database makes the individual charge affordable and we can foresee that we will be able to continue this part of the project . in addition , as hypercat becomes known in the community , people begin to send us their data in a form making them easy to implement . the usual approach when new measurements are needed is to make new observations . this is justified when the past observations do not have the required quality , but archived observations offer in many cases a serious alternative _ if _ the data can be accessed easily and have a good enough description . we started in 1998 the construction of a fits archive in hypercat ( hfa ) coupled to data - mining procedures aimed at distributing data at any desired stage of processing or even measurements . at present hfa contains 29366 fits files ( for 14631 galaxies ) mainly from the our medium resolution spectra of galaxies ( golev et al 1998 for details ) and eso - lv survey ( lauberts et al . 1989 ) . in the near future , we will archive other datasets , and in particular we call for contributions from astronomers outside our group which may be interested to distribute their data through this channel . golev , v. , prugniel , ph . , 1998 132 , 255 lauberts , a. , valentijn , e. a. , 1989 , eso ( 1989 ) , 0 maubon , g. , prugniel , ph . , golev , v. , simien , f. , 1998 _ la lettre de lohp _ 18 prugniel , ph . , simien , f. , 1996 309 , 749 prugniel , ph . heraudeau , ph . , 1998 128 , 299

the hypercat database is developed at _ observatoire de lyon _ and is distributed on the web(www - obs.univ - lyon1.fr / hypercat ) through different mirrors in europe . the goal of hypercat is to gather data necessary for studying the evolution of galaxies ( dynamics and stellar contains ) and particularly for providing a @xmath0 reference for these studies .

the lattice formulation of quantum chromodynamics ( qcd ) is presently considered as the only first principle tool to investigate a transition between the confined and deconfined states of strongly interacting matter . such a phase transition ( pt ) is also expected in a pure non abelian su(n ) gauge theory which is known as gluodynamics . the svetitsky - jaffe hypothesis [ ] relates the deconfinement pt in ( d+1)-dimensional su(n ) gluodynamics to the magnetic pt in the d - dimensional z(n ) symmetric spin model . the key element of this correspondence is that the role of spin in the original su(n ) gluodynamics is played by the so called polyakov loop . the latter is interpreted as the time propagator of an infinitely heavy static quark . a high level of understanding of the spin systems along with the svetitsky - jaffe hypothesis led to a significant progress in studies of the su(n ) gluodynamics properties in the pt vicinity . formation of geometrical clusters composed of the polyakov loops is an important feature of the pure gauge theories [ , ] . a similar phenomenon is well known in spin systems and it is responsible for percolation of clusters . moreover , the deconfinement pt in gluodynamics already was studied within the percolation framework in refs . [ , ] , where the main attention was paid to the largest and the next to the largest clusters whereas the smaller clusters were ignored . however , in many respects the pt details are encoded in the properties of smaller clusters which is well - known after formulating the fisher droplet model ( fdm ) [ ] . an important finding of the fdm is that at the critical point the size distribution of physical clusters obeys a power law which is controlled by the fisher topological exponent @xmath0 . hence the value of this exponent is rather important in order to develop a consistent theory of pt in strongly interacting matter and to localize the critical point of qcd phase diagram which is a hot topic of the physics of heavy ion collisions . therefore , in this work we study the geometrical clusterization in su(2 ) gluodynamics and analyze the properties of clusters of all possible sizes . such an approach allows us to explain the deconfinement of color charges as a specific kind of the liquid - gas pt [ ] . [ cols="^ " , ] in this contribution we present a novel approach to study the deconfinement pt in the su(2 ) pure gauge theory in terms of the geometrical clusters composed of the polyakov loops of the same sign . we demonstrate that the separation of ( anti)clusters into liquid " droplet and gas " of smaller fragments is well justified and reflects the physical properties of the lattice system . this concept allows us to explain the deconfinement pt as a special kind of the liquid - gas transition . however , in contrast to the ordinary liquids , the su(2 ) gluodynamics contains two types of liquid whose behavior is drastically different in the region of broken global z(2 ) symmetry . the cluster liquid droplet evaporates above pt whereas the anticluster liquid droplet experiences the condensation of the accompanying gas of anticlusters . a successful application of the ldf to the description of the size distributions of gaseous ( anti)clusters is the main result of this study . surprisingly , even the monomers are qualitatively described by eq . ( [ eqii ] ) . the fit of the ( anti)cluster size distributions by the ldf formula allows us to determine the @xmath2-dependences of the reduced chemical potential and the reduced surface tension coefficient . while in the symmetric phase this quantities are identical for fragments of both kinds , their behavior is drastically different in the deconfined phase . another important finding of this study is a high precision determination of the fisher topological constant @xmath3 which is the same both for clusters and for anticlusters . this result is in line with the exactly solvable model of the nuclear liquid - gas pt [ ] . at the same time it disproves the fdm prediction that @xmath4 [ ] . we showed that the reduced surface tension coefficient and the mean size of the largest ( anti)cluster can be used as the new order parameters of deconfinement pt in su(2 ) gluodynamics . in contrast to the fdm the power law for the size distribution is found only for the gas of clusters and not at the pt point , but at @xmath5 . the authors thank d. b. blaschke , o. a. borisenko , v. chelnokov , ch . gattringer , d. h. rischke , l. m. satarov , h. satz and e. shuryak for the fruitful discussions and valuable comments . the present work was supported in part by the national academy of sciences of ukraine and by the nas of ukraine grant of grid simulations for high energy physics .

the liquid droplet formula is applied to an analysis of the properties of geometrical ( anti)clusters formed in su(2 ) gluodynamics by the polyakov loops of the same sign . using this approach , we explain the phase transition in su(2 ) gluodynamics as a transition between two liquids during which one of the liquid droplets ( the largest cluster of a certain polyakov loop sign ) experiences a condensation , while another droplet ( the next to the largest cluster of the opposite sign of polyakov loop ) evaporates . the clusters of smaller sizes form two accompanying gases , which behave oppositely to their liquids . the liquid droplet formula is used to analyze the size distributions of the gas ( anti)clusters . the fit of these distributions allows us to extract the temperature dependence of surface tension and the value of fisher topological exponent @xmath0 for both kinds of gaseous clusters . it is shown that the surface tension coefficient of gaseous ( anti)clusters can serve as an order parameter of the deconfinement phase transition in su(2 ) gluodynamics . the fisher topological exponent @xmath0 of ( anti)clusters is found to have the same value @xmath1 . this value disagrees with the famous fisher droplet model , but it agrees well with an exactly solvable model of nuclear liquid - gas phase transition . this finding may evidence for the fact that the su(2 ) gluodynamics and this exactly solvable model of nuclear liquid - gas phase transition are in the same universality class . + * kewords : * geometrical clusters , size distributions , liquid droplet model formula , surface tension

the non - baryonic dark matter in the form of weakly interacting massive particles ( wimps ) still eludes detection despite recent achievements in the detection technology @xcite . aside from scaling up the size of existing detectors , the improvement in the detection sensitivity is possible by detecting the direction of the incoming dark matter particles . as the earth moves in the galactic halo , the dark matter particles appear to come from cygnus constellation . the direction tag of the of the incoming particle , often referred to as the effect , increases the sensitivity of a directional detector by one order of magnitude @xcite . in this paper we present improved results for tagging the direction of low - energy nuclear recoils created by neutrons from a @xmath0cf source by using a time - projection chamber with optical readout . the neutrons are used in lieu of the dark matter particles because they create similar distributions of recoil energies and angles . the measurement of directionality tag relies on the fact that the ionization rate of recoiling nuclei depends on their residual energy , and therefore the direction of the recoil can be tagged from the light distribution along the track . the detector is in more details described in @xcite . the chamber utilizes @xmath1 wire frames . the drift region between the cathode mesh and the ground wire plane is 2.6 cm with average electric field of 580 v / cm , while the amplification region between the ground and the anode wire plane ( + 2.2 kv ) is about 3 mm . the pitch of the wires for the ground ( anode ) plane is 2 mm ( 5 mm ) and the wire diameter is 15 @xmath2 m ( 50 @xmath2 m ) . the chamber is filled with 4 at 200 torr . the scintillation light is recorded with a cooled ccd camera equipped with a photographic lens that images approximately 2 @xmath3 of the anode plane . the spread of pixel yields due to adc noise and dark current is 25 counts . images are corrected for adc bias and hot channels are identified and excluded from analysis . neutrons are created in the fission of the nucleus , which occurs in approximately 3% of all decays and produces 3.8 neutrons per fission @xcite . the radioactivity of our source is 3.4 mci and we estimate the total flux of @xmath4 neutrons per second into the solid angle ( @xmath5 sr ) of the detector . the wires of the tracking chamber are aligned with the direction of the neutron beam . the recoil length projected to the wire axis is longer in case of wimp scattering , therefore , of effect in neutron scattering is expected to be harder . we take sequential 1-second exposures with the ccd camera . we reject images that have segments shorter than 0.7 mm , and recoil tracks that fall close to the boundary of the ccd field of view . the energy of the recoil segment is determined from the projection of the light intensity to the axis perpendicular to the wire . the relation between the light intensity and the energy is determined using alpha particles that travel perpendicular to the wire and deposit a known amount of energy . the range of the recoil segment is calibrated using the known pitch of anode wires and the observed distance between wires in the ccd images . , width=283 ] an image of a nuclear recoil in figure [ fg::recoil_images ] shows noticeable asymmetry of the light yield along the wire . in order to quantify this effect , we define the skewness @xmath6 as the dimensionless ratio between the third and second moments of the light yield along the wire coordinate ( @xmath7 ) : @xmath8 the sign indicates the slope of the light intensity along the track : recoils that travel in the direction of the incoming neutrons have a negative skewness . [ cols= " < , < " , ] a plot of the measured skewness as a function of the segment length is shown in the top plot of figure [ fg::recoil_energy_vs_skewness ] . the data in this plot corresponds to 3.6 h of live time using 5 mg of 4 gas . the head - tail asymmetry is easier to observe for longer tracks that are better aligned with the anode wires and create more scintillation light . the bottom plot in figure [ fg::recoil_energy_vs_skewness ] shows the fraction of events with negative skewness as a function of the track length . since the measured light yield is proportional to the energy of the recoil segment and the length is proportional to the track range projected to the wire , these two quantities should be correlated . figure [ fg::recoil_energy_vs_length ] shows clear correlation between the light yield versus length of the recoil segments . , width=283 ] we collect 1 day of live - time of data without sources and find two events that pass our standard selection cuts . we verify good rejection of gammas by collecting 1/3 day of live - time of data with @xmath9cs source ( 8 @xmath2ci ) placed near the sensitive area of our detector and find zero events passing the cuts . we assign a conservative error of 10% to the density of the 4 gas . the statistical uncertainty on the energy measurements is about 10% . the systematic error on the energy comes from non - uniformity in wire gain , stability of the gain over time , the pressure measurement and the calibration method that assumes the energy - independent proportionality of the stopping power with the ionization rate . the error on the recoil range comes from the analysis technique that overestimates the range for low - energy recoils with the range close to the diffusion width . we have presented improved results for tagging the direction of low - momentum nuclear recoils generated in the elastic scattering of low - energy neutrons with 4 gas . we have shown that in our current experimental setup the tag of incoming particle can be determined for recoil energies above 200 kev . this threshold can be further reduced with expected improvements in the detector preformance . this study has profound implications for the development of dark matter detectors , as the directionalty will be essential to produce convincing evidence for dark matter particles in the presence of backgrounds .

we present new results with a prototype detector that is being developed by the dmtpc collaboration for the measurement of the direction tag ( ) of dark matter wind . we use neutrons from a source to create low - momentum nuclear recoils in elastic scattering with the residual gas nuclei . the recoil track is imaged in low - pressure time - projection chamber with optical readout . we measure the ionization rate along the recoil trajectory , which allows us to determine the direction tag of the incoming neutrons .

neutrino oscillations have been experimentally observed in a variety of situations , and are among the first evidence of physics beyond the standard model . typically , these oscillations are explained by attributing mass to neutrinos ; however , not all experiments can be explained using the same masses - notably , lsnd@xcite and miniboone@xcite require a larger mass - squared difference than the other experiments , and can not be explained using a three - flavor theory of mass . furthermore , recent results at minos and miniboone have hinted at an asymmetry between neutrinos and antineutrinos @xcite , which would be evidence for lorentz violation . it has already been shown that models incorporating lorentz violations can reproduce many of the results of the mass model@xcite . examples include the bicycle model@xcite and the tandem model@xcite . here , a new model is introduced to attempt to explain these experiments . we consider three generations of light , left - handed neutrinos , and three generations of light , sterile , right - handed neutrinos , and their antiparticles . we allow for small mass and small general lorentz violations . to first order , the general hamiltonian is a 12 @xmath2 12 matrix , given in block form by @xmath3\ ] ] where @xmath4 \\ h_{12 } & = & \left [ \begin{array}{cc } -ig^{\lambda \mu \nu}_d p_\lambda q_\mu p_\nu + ih_d^{\lambda \mu}p_\lambda q_\mu & -ig_m^{\lambda \mu \nu}p_\lambda q_\mu p_\nu + ih_m^{\lambda \mu}p_\lambda q_\mu\\ -ig_m^{\dagger \lambda \mu \nu}p_\lambda q_\mu p_\nu + ih_m^{\dagger \lambda \mu}p_\lambda q_\mu & -ig_d^{t \lambda \mu \nu}p_\lambda q_\mu p_\nu - ih_d^{t \lambda \mu}p_\lambda q_\mu\\ \end{array } \right ] \\ h_{21 } & = & \left [ \begin{array}{cc } ig_d^{\lambda \mu \nu}p_\lambda q^*_\mu p_\nu - ih_d^{\lambda \mu}p_\lambda q^*_\mu & ig_m^{\lambda \mu \nu}p_\lambda q^*_\mu p_\nu - ih_m^{\lambda \mu}p_\lambda q^*_\mu \\ ig_m^{\dagger \lambda \mu \nu}p_\lambda q^*_\mu p_\nu - ih_m^{\dagger \lambda \mu}p_\lambda q^*_\mu & ig_d^{t\lambda \mu \nu}p_\lambda q^*_\mu p_\nu + ih_d^{t \lambda \mu}p_\lambda q^*_\mu \\ \end{array } \right ] \\ h_{22 } & = & \left [ \begin{array}{cc } -c_r^{\mu \nu}p_\mu p_\nu + a_r^\mu p_\mu & -c_m^{t\mu\nu}p_\mu p_\nu - a_m^{t\mu}p_\mu \\ -c_m^{*\mu \nu}p_\mu p_\nu - a^{*\mu}_m p_\mu & -c_l^{t \mu \nu}p_\mu p_\nu - a_l^{t\mu}p_\mu \\ \end{array } \right]\end{aligned}\ ] ] in the basis @xmath5 . note that mass does not appear because it enters only at second order . such a hamiltonian allows many unusual features , including neutrino - antineutrino mixing , neutrino - sterile neutrino mixing , strange energy dependence and direction dependence . we propose a tricycle model , in which we assume that @xmath6 so that the off - diagonal terms can be ignored . this allows us to restrict our attention to one quadrant of the matrix , the @xmath7 sector ( @xmath8 ) . note that we have only considered the isotropic part of each of the lorentz - violating coefficients . in particular , the model to be investigated has the form @xmath9\ ] ] where @xmath10 is taken to be hermitian and @xmath10 and @xmath11 commute , so that they can be simultaneously diagonalized . we assume that the diagonalizing matrix has the conventional form@xcite @xmath12\ ] ] ( we are assuming that @xmath13 ) . the model is then fixed by 8 parameters : the two mixing angles and the three eigenvalues of each block , which we call @xmath14 and @xmath15 respectively . the eigenvalues of the hamiltonian are @xmath16 the model employs a seesaw mechanism to produce very different behavior at high and low energies . at high energy the @xmath17 matrix dominates , which cuts off left - right oscillations and allows the left - handed neutrinos to oscillate among themselves as normal . at low energies , however , the @xmath10 terms dominate , and oscillations into sterile neutrinos are predicted . observe that @xmath18 so that three of the eigenvalues have the expected @xmath19 energy dependence at high energies . transition probabilities can be calculated exactly . for example , @xmath20\end{aligned}\ ] ] where @xmath21\ ] ] and @xmath22\ ] ] the mixing angles and two of the eigenvalues are determined by the high - energy , mass - like behavior widely detected . there remain four independent parameters in the model , which can be adjusted to control the low energy behavior without disrupting the high - energy limit . as energy decreases , the probabilities diverge smoothly from the standard mass predictions . the model introduced above ( 6 ) will never produce observable cpt violations . this is because @xmath10 is a cpt - odd variable , but @xmath11 is cpt - even , so that under cpt transformations , @xmath23 goes to @xmath24\ ] ] however , the eigenvalues and mixing angles on which the probability depends do not observe the sign of @xmath10 , as can be seen from their definitions ( 8 , 11 , 12 ) . this causes the probabilities to be the same whether @xmath10 or @xmath25 is used . in fact , even if @xmath10 does not commute with @xmath11 , cpt symmetry will still be preserved ; to introduce cpt violation , @xmath10 and @xmath11 terms must be mixed ( for example , an ordinary rotation of ( 6 ) will introduce cpt violations ) . this model is intended to show that behavior typical of mass models can be reproduced by a lorentz - violating model without mass . a variety of low - energy behavior is consistent with the same behavior at high energy . however , it remains difficult to explain all experiments , even with four free parameters . we would like to thank swarthmore college for funding the research reported here . thanks also to matt mewes for his advice and assistance in this project . xx lsnd collaboration , a. aguilar , phys . d * 64 * , 112007 ( 2001 ) . miniboone collaboration , a. a. aguilar - arevalo , phys . lett . * 103 * , 111801 ( 2009 ) . p. vahle ( minos collaboration ) , neutrino 2010 plenary talk , june 14 , 2010 ; to be published in the proceedings . v. alan kosteleck and matthew mewes , phys . rev . d * 69 * , 016005 ( 2004 ) . v. alan kosteleck and matthew mewes , phys . d * 70 * , 031902 ( 2004 ) . teppei katori , v. alan kosteleck and rex tayloe , phys . d * 74 * , 105009 ( 2006 ) . c. amsler , phys . . * b667 * , 1 ( 2008 ) .

a new model for neutrino oscillations is introduced , in which mass - like behavior is seen at high energies , but various behavior can be predicted at low energies . the model employs no neutrino masses , but instead relies on the lorentz - violating parameters @xmath0 and @xmath1 . oscillations into sterile neutrinos and into antineutrinos are also considered .

our task is to compute the maximal quantum violation @xmath80 of a two - party bell inequality defined by the vector of coefficients @xmath81 , given a fixed set of measurements operators @xmath82 for alice . let s write @xmath83 for the assemblage created on alice s side by bob s measurements on the state @xmath0 . with this , we have the conditional probabilities @xmath84 and we have to maximize @xmath85 for fixed @xmath86 and @xmath1 . the following sdp program is a relaxation of the above problem : @xmath87 it is well known that one can always find a quantum state @xmath0 and quantum measurements @xmath88 for bob which attain the maximum @xmath89 . hence , @xmath90 , and the above sdp provides the exact quantum bound of @xmath80 for a fixed set of alice s measurements @xmath1 on the bell inequality defined by coefficients @xmath81 .

we investigate the relation between the incompatibility of quantum measurements and quantum nonlocality . we show that a set of measurements is not jointly measurable ( _ i.e._incompatible ) if and only if it can be used for demonstrating einstein - podolsky - rosen steering , a form of quantum nonlocality . moreover , we discuss the connection between bell nonlocality and joint measurability , and give evidence that both notions are inequivalent . specifically , we exhibit a set of incompatible quantum measurements and show that it does not violate a large class of bell inequalities . this suggest the existence of incompatible quantum measurements which are bell local , similarly to certain entangled states which admit a local hidden variable model . the correlations resulting from local measurements on an entangled quantum state can not be explained by a local theory . this aspect of entanglement , termed quantum nonlocality , is captured by two inequivalent notions , namely bell nonlocality @xcite and epr steering @xcite . the strongest form of this phenomenon is bell nonlocality , witnessed via the violation of bell inequalities . steering represents a strictly weaker form of quantum nonlocality @xcite , witnessed via violation of steering inequalities @xcite . both aspects have been extensively investigated in recent years , as they play a central role in the foundations of quantum theory and in quantum information processing . interestingly quantum nonlocality is based on two central features of quantum theory , namely entanglement and incompatible measurements . specifically , performing ( i ) arbitrary local measurements on a separable state , or ( ii ) compatible measurements on an ( arbitrary ) quantum state can never lead to any form of quantum nonlocality . hence the observation of quantum nonlocality implies the presence of both entanglement and incompatible measurements . it is interesting to explore the converse problem . two types of questions can be asked here ( see fig . [ fig1 ] ) : ( a ) do all entangled states lead to quantum nonlocality ? ( b ) do all sets of incompatible measurements lead to quantum nonlocality ? an intense research effort has been devoted to question ( a ) . first , it was shown that all pure entangled states violate a bell inequality @xcite , hence also demonstrating epr steering . for mixed states , the situation is much more complicated . there exist entangled states which are local , in the sense that no form of quantum nonlocality can be demonstrated with such states when using non - sequential measurements @xcite . these issues become even more subtle when more sophisticated measurement scenarios are considered @xcite . question ( b ) has received much less attention so far . in the case of projective measurements , it was shown that incompatible measurements can always lead to bell nonlocality @xcite . note that in this case , compatibility is uniquely captured by the notion of commutativity @xcite . however , for general measurements , _ i.e._positive - operator - valued - measures ( povms ) , no general result is known . in this case , there are several inequivalent notions of compatibility . here we focus on the notion of joint measurability , see e.g.@xcite , as this represents a natural choice in the context of quantum nonlocality . several works discussed question ( b ) for povms @xcite . the strongest result is due to wolf et al . @xcite , who showed that any set of two incompatible povms with binary outcomes can always lead to violation of the clauser - horne - shimony - holt bell inequality . however , this result may not be extended to the general case ( of an arbitrary number of povms with arbitrarily many outcomes ) , since pairwise joint measurability does not imply full joint measurability in general @xcite . here we explore the relation between compatibility of general quantum measurements and quantum nonlocality . we start by demonstrating a direct link between joint measurability and epr steering . specifically , we show that for any set of povms that is incompatible ( _ i.e._not jointly measurable ) , one can find an entangled state , such that the resulting statistics violates a steering inequality . hence the use of incompatible is a necessary and sufficient ingredient for demonstrating epr steering . this raises the question of how joint measurability relates to bell nonlocality . specifically , the question is whether , for any set of incompatible povms ( for alice ) , one can find an entangled state and a set of local measurements ( for bob ) , such that the resulting statistics violates a bell inequality . here we give evidence that the answer is negative . in particular , we exhibit sets of incompatible measurements which can provably not violate a large class of bell inequalities ( including all full correlation bell inequalities , also known as xor games , see @xcite ) . we therefore conjecture that non joint measurability and bell nonlocality are inequivalent . hence , similarly to local entangled states , there may exist incompatible quantum measurements which are bell local . _ steering vs joint measurability . _ we start by defining the relevant scenario and notations . we consider two separated observers , alice and bob , performing local measurements on a shared quantum state @xmath0 . alice s measurements are represented by operators @xmath1 such that @xmath2 , where @xmath3 denotes the choice of measurement and @xmath4 its outcome . upon performing measurement @xmath3 , and obtaining outcome @xmath4 , the ( unnormalized ) state held by bob is given by @xmath5 the set of unnormalised states @xmath6 , referred to as an _ assemblage _ , completely characterizes the experiment , since @xmath7 is the probability of alice getting the output @xmath4 ( for measurement @xmath3 ) and given that information and bob s state is described by @xmath8 . importantly , one has that @xmath9 for all measurements @xmath10 and @xmath11 , ensuring that alice can not signal to bob . in a steering test @xcite , alice want to convince bob that the state @xmath0 is entangled , and that she can steer his state . bob does not trust alice , and thus wants to verify alice s claim . asking alice to perform a given measurement @xmath3 , and to announce the outcome @xmath4 , bob can determine the assemblage @xmath12 via local quantum tomography . to ensure that steering did indeed occur , bob should verify that the assemblage does not admit a decomposition of the form @xmath13 where @xmath14 . clearly , if a decomposition of the above form exists , then alice could have cheated by sending the ( unentangled ) state @xmath15 to bob and announce outcome @xmath4 to bob according to the distribution @xmath16 . note that here @xmath17 represents a local variable of alice , representing her choice of strategy . assemblages of the form are termed unsteerable and form a convex set @xcite . hence any steerable assemblage can be detected via a set of linear witnesses called steering inequalities @xcite . by observing violation of a steering inequality , bob will therefore be convinced that alice can steer his state . for a demonstration of steering , it is necessary for the state @xmath0 to be entangled . however , not all entangled states can be used to demonstrate steering @xcite ; at least not when non - sequential measurements are performed on a single copy of @xmath0 . moreover , steering also requires that the measurements performed by alice are incompatible . to capture the compatibility of a set of quantum measurements we use here the notion of joint measurability , see e.g. @xcite a set of @xmath18 povms @xmath1 is called jointly measurable if there exists a measurement @xmath19 with outcome @xmath20 $ ] where @xmath21 gives the outcome of measurement @xmath3 , that is @xmath22 where @xmath23 stands for the elements of @xmath24 except for @xmath25 . hence , all povm elements @xmath1 are recovered as marginals of the _ mother observable _ @xmath19 . importantly , the joint measurability of a set of povms does not imply that they commute @xcite . hence joint measurability is a strictly weaker notion of compatibility for povms . moreover , joint measurability is not transitive . for instance , pairwise joint measurability does not imply full joint measurability in general @xcite ( see below ) . our main result is to establish a direct link between joint measurability and steering . specifically , we show that a set of povms can be used to demonstrate steering if and only if it is not jointly measurable . more formally we prove the following result . the assemblage @xmath26 , with @xmath27 , is unsteerable for any state @xmath0 acting in @xmath28 if and only if the set of povms @xmath29 acting on @xmath30 is jointly measurable . the if part is straightforward . our goal is to show that @xmath26 admits a decomposition of the form when @xmath29 is jointly measurable , for any state @xmath0 . consider @xmath19 , the mother observable for @xmath29 , and define alice s local variable to be @xmath31 , distributed according to @xmath32 , where @xmath33 . next alice sends the local state @xmath34 . when asked by bob to perform measurement @xmath3 , alice announces an outcome @xmath4 according to @xmath35 . we now move to the only if part . consider an arbitrary pure state @xmath36 with schmidt number @xmath37 . notice that we can always write @xmath38 , where @xmath39 is an ( unormalized ) maximally entangled state in @xmath40 , and @xmath41 is diagonal matrix that contains only strictly positive numbers . the assemblage resulting from a set of povms @xmath29 on @xmath0 is given by @xmath42 where @xmath43 is the transpose of @xmath44 . our goal is now to show that if @xmath45 is unsteerable then @xmath29 is jointly measurable . as @xmath45 is unsteerable , we have that @xmath46 which allows us to define the positive definite operator @xmath47 form which we can recover the assemblage @xmath48 as marginals , _ i.e._@xmath49 . since the diagonal matrix @xmath41 is invertible , we can define @xmath50 . it is straightforward to check that @xmath19 is a mother observable for @xmath51 : ( i ) it is positive , ( ii ) sums to identity , and ( iii ) has povm elements @xmath44 as marginals . hence @xmath51 is jointly measurable , which concludes the proof . note finally an interesting point that follows from the above . considering a set of incompatible measurements acting on @xmath30 , any pure entangled state of the schmidt number @xmath37 can be used to demonstrate epr steering . _ bell nonlocality vs joint measurability . _ it is natural to ask whether the above connection , between joint measurability and steering , can be extended to bell nonlocality . recall that in a bell test , both observers alice and bob are on the same footing , and test the strength of the shared correlations . specifically , alice chooses a measurement @xmath3 ( bob chooses @xmath52 ) and gets outcome @xmath4 ( bob gets @xmath53 ) . the correlation is thus described by a joint probability distribution @xmath54 . the latter can be reproduced by a pre - determined classical strategy if it admits a decomposition of the form @xmath55 where @xmath17 represents the shared local ( hidden ) variable , and @xmath56 . any distribution that does not admit a decomposition of the above form is said to be bell nonlocal . the set of local distributions , _ i.e._of the form is convex , and can thus be characterized by a set of linear inequalities called bell inequalities @xcite . hence violation of a bell inequality implies bell nonlocality . in quantum theory , bell nonlocal distributions can be obtained by performing suitably chosen local measurements , @xmath1 and @xmath57 , on an entangled state @xmath0 . in this case , the resulting distribution @xmath58 does not admit a decomposition of the form . bell nonlocality is however not a generic feature of entangled quantum states . that is , there exist mixed entangled states which are local , in the sense that the statistics resulting from arbitrary non - sequential local measurements can be reproduced by a local model @xcite . given the above , we investigate now how joint measurability relates to bell nonlocality . first the above theorem implies that , if the set of povms @xmath59 used by alice is jointly measurable , then the statistics @xmath54 can always be reproduced by a local model , for any state @xmath0 and measurements of bob @xmath60 . the converse problem is much more interesting . the question is whether for any set of povms @xmath59 that is not jointly measurable , there exists a state @xmath0 and a set of measurements @xmath60 such that the resulting statistics @xmath54 violates a bell inequality . this was shown to hold true for the case of sets of two povms with binary outcomes @xcite . in this case , joint measurability is equivalent to violation of the chsh bell inequality . here we give evidence that this connection does not hold in general . specifically , we exhibit a set of povms which is not jointly measurable but nevertheless can not violate a large class of bell inequalities . consider the set of three dichotomic povms ( acting on @xmath61 ) given by the following positive operators @xmath62 for @xmath63 , where @xmath64 are the pauli matrices , and @xmath65 . indeed , one has that @xmath66 . this set of povms should be understood as noisy pauli measurements . the set is jointly measurable if and only if @xmath67 , although any pair of povms is jointly measurable for @xmath68 @xcite ( see also @xcite ) . hence in the range @xmath69 , the set @xmath70 forms a _ hollow triangle _ : it is pairwise jointly measurable but not fully jointly measurable . we now investigate whether the above hollow triangle can lead to bell inequality violation . the most general class of bell inequalities to be considered here are of the form : @xmath71 where @xmath72 all ( tight ) bell inequalities of the above form for @xmath73 are known ( see appendix ) . using a numerical method based on semi - definite - programming ( sdp ) @xcite ( see appendix ) we could find the smallest value of the parameter @xmath74 for which a given inequality can be violated using the set of povms . the results are summarized in table i. notably , we could not find a violation in the range @xmath69 where the set @xmath70 is a hollow triangle . in fact , no violation was found for @xmath75 , whereas pairwise joint measurability is achieved for @xmath76 , thus leaving a large gap . note also that pairwise joint measurability implies violation of the chsh inequality here , since we have povms with binary outcomes @xcite . we thus conjecture that there is a threshold value @xmath77 , such that all hollow triangles with @xmath78 do not violate any bell inequality . [ table ] . bell inequality violation with incompatible povms . specifically , we consider the sets given in equations and . for each set , we determine the smallest value of the parameter @xmath74 , such that the set becomes jointly measurable ( jm ) , and achieve bell inequality violation . we consider tight bell inequalities with up to @xmath79 measurements for bob ( see appendix ) . note that pairwise joint measurability is equivalent to violation of the chsh bell inequality . [ cols="^,^,^",options="header " , ]

let us provide the rigorous analysis of the experimental data regarding fermi gas vs wigner solid transition . according to ref.@xcite , the melting diagram of 2d wigner solid obeys the condition @xmath1 , where @xmath2 is the coefficient assumed to be a constant at the phase transition , @xmath3 is the coulomb energy associated to neighboring pair of electrons , @xmath4 is the 2d density . within conventional fermi gas model , @xmath5 is the average kinetic energy of single electron , where @xmath6 is the fermi integral of the order of @xmath7 , @xmath8 the dimensionless temperature . note that the average kinetic energy @xmath9 coincides with the thermal energy @xmath10 for classical boltzmann carriers @xmath11 . in contrast , @xmath12 for degenerate electrons @xmath13 . in general , the solidification of strongly degenerated electrons is believed to occur at certain value of the coulomb to fermi energy ratio @xmath14 . we therefore conclude that @xmath15 . in refs.@xcite , this ratio has been erroneously defined as @xmath16 , thus provides wrong estimate for wigner crystal solidification . for low - disorder 2d system wigner solid was claimed@xcite to exist when @xmath17 . the diagram of fermi gas to wigner solid transition @xcite according to eq.([wigner_solid ] ) at @xmath18@xcite . the color rectangular figures correspond to density and temperature range of apparent metal - to insulator transition in si - mosfet@xcite ; p - gaas@xcite ; n - gaas@xcite and n - sige@xcite 2d systems , modified wit respect to dimensional density @xmath19 and temperature @xmath20 depicted in table [ tab : table1 ] . ] following ref.@xcite , the phase transition can be parameterized as it follows : @xmath21 here , the dimensional temperature @xmath22 and 2d density @xmath23 contain the valley splitting factor @xmath24 . then @xmath25 and @xmath26 is the effective borh radius and rydberg energy respectively , @xmath27 is the effective mass . note , for certain value of @xmath28 the correct values @xmath29 are lower by a factor of @xmath0 with respect to those predicted in refs.@xcite . for actual 2d systems the values @xmath30 are generalized in table [ tab : table1 ] . in fig.[fig1 ] we plot the melting curve@xcite specified by eq.([wigner_solid ] ) and , moreover , the observed range of 2d densities and temperatures attributed to apparent metal - insulator transition@xcite . evidently , wigner solidification regime remains unaffected . hence , we suggest the typical 2d systems can be described within routine fermi gas model . in conclusion , we demonstrate that wigner solidification has been never achieved in experiments dealt with apparent metal to insulator transition . the observed anomalies of 2d transport behavior is explained within conventional fermi gas formalism invoking the important correction to measured resistivity caused by peltier and seebeck effects combined . we represent the experimental evidence confirming the solidity and universality of the above model . 100 s.v . kravchenko et al , phys.rev.b . * 51 * , 7038 , 1995 v.m . pudalov et al , phys.rev.b.,*60 * , r2154 , 1999 y. hanein et al , phys.rev.lett . , * 80 * , 1288 , 1998 jian huang et al , phys.rev.b . , * 74 * , 201302(r ) , 2006 x.p.a . gao et al , phys.rev.lett . , * 93 * , 256402 , 2004 jian huang et al , phys.rev.b . , * 83 * , 081310(r ) , 2011 m. p. lilly et al , phys.rev.lett . , * 90 * , 056806 , 2003 k.lai et al , phys.rev.b . , * 72 * , 081313(r ) , 2005 k.lai et al , phys.rev.b . , * 75 * , 033314 , 2007 p.t . coleridge et al , phys.rev.b . , * 56 * , 12764(r ) , 1997 v. senz et al , ann . phys.(paris ) , * 8 * , 237 , 1999 p. m. platzman and h. fukuyama , phys.rev.b . , * 10 * , 3150 , 1974 b.tanatar and d.m.ceperley , phys.rev.b . , * 39 * , 5005 , 1989 t. ando et al , rev.mod.phys . , * 54 * , 437 , 1982 m.v.cheremisin , physica e , * 27 * , 151 , 2005 c.g.m.kirby , m.j.laubitz , metrologia , * 9 * , 103 , 1973 m. m. radonjic et al , phys.rev.b . , * 85 * 085133 , 2012 x.p.a . gao et al , phys.rev.lett . , * 94 * , 086402 , 2005 x.p.a . gao et al , arxiv : cond - mat/0308003 , 2003 n.f . mott , j. non - cryst . solids , * 1 * , 1 , 1968 b.i . shklovskii and a.l . efros , electronic properties of doped semiconductors , springer - verlag , berlin , 1984 .

the melting condition for two - dimensional wigner solid ( p.m. platzman , h.fukuyama , 1974 ) is shown to contain an error of a factor of @xmath0 . the analysis of experimental data for apparent 2d metal - to - insulator transition shows that the wigner solidification ( b.tanatar , d.m.ceperley , 1989 ) has been never achieved . within routine fermi gas model both the metallic and insulating behavior of different 2d system for actual range of carrier densities and temperatures is explained . recently , much interest has been focused on the anomalous transport behavior of a wide variety of low density two - dimensional ( 2d ) systems . it has been found that below some critical density , cooling causes an increase in resistivity , whereas in the opposite , high - density case , the resistivity decreases . the apparent metal to insulator transition was observed in n - si mosfet @xcite , p - gaas@xcite , n - gaas@xcite , n - sige@xcite and p - sige @xcite 2d systems .

one of the formidable tasks in heavy - ion physics is to identify a precise understanding of the jet - medium dynamics , the jet - medium interactions , and the jet - energy loss formalism . below , we study the influence of the details of the jet - medium coupling and the medium background on the simultaneous description of the nuclear modification factor ( @xmath1 ) and the high-@xmath0 elliptic flow ( @xmath2 ) measured at rhic and lhc @xcite for a radiative pqcd energy - loss ansatz @xcite . we contrast media determined via the viscous hydrodynamic approach vish2 + 1 @xcite with the parton - cascade bamps @xcite as well as a jet - medium coupling depending on the collision energy with a jet - medium coupling influenced by the energy of the jet , the temperature of the medium and non - equilibrium effects around the phase transition . besides this , we compare the jet - energy loss based on radiative pqcd @xcite with the hybrid ads energy - loss ansatz of ref . we contrast the pion nuclear modification factor obtained via the radiative pqcd - energy loss @xcite and the hybrid ads energy - loss ansatz with a parton - jet nuclear modification factor that can be considered as an idealized lo jet @xmath1 at rhic and lhc energies . the pqcd - based energy loss model studied is parametrized as @xcite @xmath3 with the jet - energy dependence @xmath4 , the path - length dependence @xmath5 , and the energy dependence @xmath6 . in the following , the jet - medium coupling @xmath7 will depend either on the collision energy @xmath8 or the energy of the jet and the temperature of the background medium considered @xmath9 . the jet - energy loss fluctuations are distributed via @xmath10 , allowing for an easy interpolation between non - fluctuating ( @xmath11 ) , uniform dirac distributions and distributions increasingly skewed towards small @xmath12 . the jets are spread according to a transverse initial profile specified by the bulk flow fields given by the vish2 + 1 and bamps backgrounds considered @xcite . on the other hand , the jet - energy loss of the hybrid ads energy - loss ansatz @xcite is based on falling strings @xcite where @xmath13 the initial jet energy is given by @xmath14 and the string stopping distance for quark and gluon jets is determined via @xmath15 with the jet - medium coupling @xmath16 for quarks and @xmath17 for gluons , including the respective casimir operators @xmath18 and @xmath19 . this energy loss ansatz has been integrated into our existing model @xcite . please note that ref . @xcite uses natural units , @xmath20 . for a direct comparison , we quote our results below using a dimensionless coupling . the main differences between the two energy - loss descriptions is the square - root dependence that leads to the formation of a bragg peak with the explosive burst of energy close to the end of the jet s evolution . there have been discussions in literature @xcite on the impact of the bragg peak . in line with previous findings @xcite we will show below that there is a difference between the hybrid ads energy - loss ansatz featuring a bragg peak and the pqcd model without a bragg peak , however , this difference is only marginal . fig . [ fig01 ] shows the pion nuclear modification factor ( @xmath1 ) for central ( left panel ) and mid - central ( middle panel ) collisions at rhic ( black ) and lhc ( red ) as well as the high-@xmath0 elliptic flow ( @xmath2 ) for mid - central events ( right ) . the measured data @xcite is compared to the pqcd - based energy loss of eq . ( [ eq1 ] ) with @xmath21 . jet - energy loss fluctuations ( @xmath22 ) and the transverse expansion of the background flow ( @xmath23 ) are included , as well as a running jet - medium coupling that depends on the energy of the collision , @xmath8 . [ fig01 ] demonstrates that there is a surprising similarity between the results that can not be expected a priori given the fact that the two background media are so different : while the hydrodynamic description of vish2 + 1 @xcite assumes an equilibrated system , the parton cascade bamps @xcite also includes non - equilibrium effects in the bulk medium evolution . in addition , the figure exhibits the so - called high-@xmath0 @xmath2-problem @xcite : the high-@xmath0 elliptic flow below @xmath24 gev is about a factor of two below the measured data @xcite . this effect has been discussed in literature @xcite and recently it has been suggested by cujet3.0 @xcite that a temperature and energy - dependent jet - medium coupling @xmath9 , which includes non - perturbative effects around the phase transition of @xmath25 mev , can overcome this problem . this jet - medium coupling was derived from the dglv gluon number distribution @xcite and is given by the analytic formul @xmath26 it includes a running coupling @xmath27 with @xmath28 , the polyakov - loop suppression of the color - electric scattering @xcite via @xmath29 with pre - factors @xmath30 for quarks and gluons , and the polyakov loop @xmath31 as parametrized from lattice qcd , as well as an enhancement of scattering due to the magnetic monopoles near the critical temperature @xmath32 also derived from lattice qcd @xcite . this temperature and energy - dependent jet - medium coupling shows an effective running as it decreases with temperature . we included the above jet - medium coupling @xmath9 in our jet - energy loss approach @xcite . the result is shown in fig . [ fig02 ] , again for the hydrodynamic background vish2 + 1 ( solid lines ) and a medium determined via the parton cascade bamps ( dashed lines ) . for comparison , we depict the results from cujet3.0 @xcite . as in fig . [ fig01 ] , the ion nuclear modification factor is well described both at rhic and lhc . the high-@xmath0 elliptic flow , however , increases drastically below @xmath24 gev as compared to fig . [ fig01 ] , especially for the bamps background which already includes non - equilibrium effects @xcite . finally , we compare results from the linear pqcd approach of eq . ( [ eq1 ] ) with the highly non - linear hybrid ads holographic model of jet - energy loss , see eq . ( [ eq2 ] ) . we compare the pion nuclear modification factor and an idealized lo jet @xmath1 given by @xmath33 naturally , this lo jet @xmath1 represents a reconstructed jet with vanishing cone radius and is only a lower bound for the nlo jet @xmath1 with jet - cone radii @xmath34 . [ fig03 ] shows this comparison at lhc ( left ) and rhic ( right ) energies for two different jet - medium couplings that are treated as constants : a larger one ( red ) fitted to the pion @xmath1 data ( dashed - dotted lines ) at rhic and a lower one ( blue ) fitted the pion @xmath1 data at lhc . to guide the eye , we include the reconstructed jet @xmath1 from cms @xcite with @xmath35 in fig . [ fig03 ] . the solid blue lines for the lo jet @xmath1 in the left panels of fig . [ fig03 ] lie in the same ballpark as the experimental data . fragmenting this result to pions ( dashed - dotted lines ) leads to an @xmath1 that reproduces the measured pion nuclear modification factor at lhc . a straight extrapolation of this results to rhic energies shows that the lo jet @xmath1 for _ the same _ jet medium couplings lie on top of the measured _ pion _ nuclear modification factor . however , fragmenting this result to pions leads to a @xmath36 that is larger than the measured data at rhic . larger jet - medium couplings ( red lines ) , on the other hand , describe the _ pion _ nuclear modification factor at rhic for the pqcd scenario and the lo jet @xmath1 at lhc is again close to the experimental data . the pion nuclear modification factor at lhc , however , only touches the lower bound of present error bars . in case of the hybrid ads energy loss the results always only touch the lower end of the experimental error bars . [ fig03 ] demonstrates that the results for the pqcd and the hybrid ads energy - loss including a bragg peak are remarkably similar . thus , unfortunately , neither the pion nor a lo jet @xmath1 are sensitive to the difference in the path - length between pqcd and ads models . we compared the measured data on the nuclear modification factor for pions and reconstructed jets as well as on the high-@xmath0 elliptic flow at rhic and lhc energies to results obtained by a linear pqcd and a highly non - linear hybrid ads holographic model of jet - energy loss . we found that the simultaneous description of the @xmath1 and @xmath2 requires a jet - medium coupling that depends on the energy of the jet , the temperature of the medium @xcite , and non - equilibrium effects around the phase transition . we also contrasted a hydrodynamic background ( vish2 + 1 ) @xcite with a medium obtained from the parton cascade bamps @xcite and showed that the influence of the underlying bulk medium considered is suprisingly small . unfortunately , neiter the pion nor the lo jet @xmath1 are sensitive to the difference in the path - length between pqcd and ads models . this work was supported in part through the bundesministerium fr bildung und forschung , the helmholtz international centre for fair within the framework of the loewe program ( landesoffensive zur entwicklung wissenschaftlich - konomischer exzellenz ) launched by the state of hesse , the us - doe nuclear science grant no . de - ac02 - 05ch11231 within the framework of the jet topical collaboration , and the us - doe nuclear science grant no.de-fg02-93er40764 . numerical computations have been performed at the center for scientific computing ( csc ) .

the measured data on the nuclear modification factor for pions and reconstructed jets as well as on the high-@xmath0 elliptic flow at rhic and lhc energies are compared to results from a linear pqcd and a highly non - linear hybrid ads holographic model of jet - energy loss . we find that the high-@xmath0 ellitic flow requires to include realistic medium transverse flow fields and a jet - medium coupling including the effects of the energy of the jet , the temperature of the bulk medium , and non - equilibrium effects close to the phase transition . we extend our jet - energy loss model that is coupled to state - of - the - art hydrodynamic prescriptions to backgrounds generated by the parton cascade bamps . we demonstrate that the results for the hydrodynamic and the parton - cascade backgrounds show a remarkable similarity . unfortunately , the results for both the pion and a parton - jet nuclear modification factor are insensitive to the jet - path dependence of the models considered . jet quenching , viscous hydrodynamics , transport model , jet holography

presently planned @xmath0 linear collider ( lc ) projects will operate at an initial center of mass system ( cms ) energy of about 500 gev , with upgrades to higher energies designed in from the start . the tev class colliders tesla @xcite and nlc / jlc @xcite target 800 gev and 1 - 1.5 tev , respectively , as their maximum cms energies . increasing the energy further would require either a change in acceleration technology or an extension in accelerator length beyond the presently foreseen 30 - 40 km @xcite . this would also increase the number of active elements , which will likely decrease the overall efficiency of such a facility . the nature of the new physics which will hopefully be discovered and studied at the lhc and a tev class lc will determine the necessity and importance of exploring the multi - tev range with a precision machine such as an @xmath2 collider . this paper summarizes the work of the e3 subgroup 2 on multi - tev colliders of the snowmass 2001 workshop ` the future of particle physics ' . based on our knowledge today , the case for the multi - tev collider rests on the following physics scenarios : ( 200,1 ) ( 25,-357)_presented at the aps / dpf / dpb summer study on the future of particle physics ( snowmass 2001 ) , _ ( 120,-369)_30 june - 21 july 2001 , snowmass , colorado , usa _ * the study of the higgs + for a light higgs , a multi - tev @xmath2 collider can access with high precision the triple higgs coupling , providing experimenters with the opportunity to measure the higgs potential . the large event statistics will allow physicists to measure rare higgs decays such as @xmath3 . for heavy higgses , predicted by e.g. supersymmetric models , the range for discovery and measurement will be extended for masses up to and beyond 1 tev . * supersymmetry + in many susy scenarios only a subset of the new sparticles will be light enough to be produced directly at a tev class lc . some of the heavier sparticles will be discovered at the lhc , but a multi - tev lc will be needed to complete the spectrum and to precisely measure the heavy sparticles properties ( flavor , mass , width , couplings ) . furthermore , polarized beams will help disentangle mixing parameters and aid cp studies . ultimately we _ will _ need to measure all sparticles as precisely as possible to fully pin down and test the underlying theory . * new resonances + many alternative theories and models for new physics predict new heavy resonances with masses larger than 1 tev . if these new resonances ( e.g. new gauge bosons , kaluza - klein resonances , or @xmath4 resonances ) have masses in the 1 tev - 5 tev range , a multi - tev collider becomes a particle factory , similar to lep for the @xmath5 . the new particles can be produced directly and their properties can be accurately determined . * no new particles + if _ no _ new particles are observed directly , apart from perhaps one light higgs particle , then a multi - tev collider will probe new physics indirectly ( extra dimensions , @xmath6 , contact interactions ) at scales in the range of 30 - 400 tev via precision measurements . * unexpected phenomena + this is probably the most exciting of all : perhaps nature has chosen a road as yet not explored ( extensively ) by our imagination . recent examples of new ideas are string quantum gravity effects , non - commutative effects , black hole formation , nylons , and split fermions . .event rates for several processes in the multi - tev range , for 1 ab@xmath7 integrated luminosity . [ cols="^,^,^ " , ] [ tab : sum ] linear @xmath0 colliders operating in the multi - tev energy range are likely to be based on the clic two - beam acceleration concept . to achieve a large luminosity , such an accelerator would need to operate in the high beamstrahlung region , rendering experimentation at such a collider more challenging . studies so far indicate that this is not a substantial handicap , and the precision physics expected from an @xmath0 collider will be possible . the two - beam accelerator technology is not yet available today for use at a large scale collider . r&d on this technology will continue until 2006 at least , after which if no bad surprises emerge one can plan for a full technical design of such a collider . from the physics program side , a multi - tev collider has a large potential to push back the high energy horizon further , up to scales of 1000 tev , where if the higgs is light new physics can no longer hide from experiment . if no new scale is found by then we have to revise our understanding of nature . a multi - tev collider with high luminosity can be used for precision measurements in the higgs sector . it can precisely measure the masses and couplings of heavy sparticles , thereby completing the susy spectrum . if extra dimensions or even black holes pop up in the multi - tev range , such a collider will be a precision instrument to study quantum gravity in the laboratory . the physics reach , as envisioned today , for a multi - tev collider is summarized in table [ tab : sum ] . in short a collider with @xmath8 3 - 5 tev is expected to break new grounds , beyond the lhc and a tev class lc . , desy 2001 - 011 . , slac - r-571 . jlc-1 , jlc group , s matsumoto et al . , kek report 92 - 16 . p. burrows and r. patterson , _ lc expandability and upgradability _ , these proceedings .. m. battaglia , hep - ph/0103338 . the clic study team , _ a 3 tev e@xmath9e@xmath10 linear collider based on clic technology _ , cern 2000 - 008 . braun et al . , proc . of 18th international conference on high energy accelerators ( heacc2001 ) , 26 - 30 march 2001 , tsukuba , japan , and clic note 473 ; see also http://geschonk.home.cern.ch/geschonk/ r. corsini et al . , cern / ps 2001 - 030 ( ae ) , and 2001 particle accelerator conference ( pac2001 ) , chicago , illinois , usa , june 18 - 22 , 2001 d. asner et al . , hep - ex/0111056 v. telnov , _ photon colliders at multi - tev energies _ , these proceeedings . r. assmann and f. zimmerman , _ polarization at clic _ , these proceeedings . g.guignard , _ the clic study _ , these proceedings . d. schulte , _ machine - detector interface at clic _ , these proceedings + d. schulte , cern - ps-99 - 066 . r. settles , _ detector requirements at multi - tev lc _ , these proceedings . m. battaglia , in proceedings of the lcws2000 workshop , p831 . m. pohl and h.j . schreiber , _ simdet - a parametric monte carlo for a tesla detector _ , desy 99 - 030 . m. battaglia , adaption of the delphi pvec package . m. battaglia , e. boos , and w. yao , _ studying the higgs potential at the linear collider _ , hep - ph/0111276 . m. battaglia , a.de roeck , _ determination of the muon yukawa coupling at high energy @xmath0 linear colliders _ , these proceedings , hep - ph/0111307 . j. f gunion ( 1997 ) , hep - ph/9703203 . t. plehn and d. rainwater , phys . lett . * b520 * , 108 ( 2001 ) , hep - ph/017180 . marco battaglia et al . , hep - ph/0106204 . m. battaglia , a. kiiskinen and a. ferrari,_study of charged higgs bosons _ , these proceedings , hep - ex/0112015 . g. blair , w. porod , p.m. zerwas phys . rev . * d63 * ( 2001 ) 017703 , hep - ph/0007107 . g. moortgat - pick , _ physics opportunities with polarized @xmath11 and @xmath12 beams at a linear collider _ , these proceedings . g. wilson in proceedings of the lcws2000 workshop , p485 . m. battaglia , private communication . m. klasen , talk at the workshop on gamma - gamma colliders , chicago 2001 . a. ferrari , _ study of majorana neutrinos at clic _ , these proceedings . m. battaglia , s. riemann , s. de curtis and d. dominici , _ probing new scales at e+e- linear collider _ , these proceedings ; + battaglia et al . , hep - ph/0101114 . e. eichten , k lane and m. peskin , phys . lett * 50 * ( 1983 ) 811 ; h. kroha , phys . rev . * d46 * ( 1992 ) 58 . t. hambye and k. riesselmann , phys . * d55 * ( 1997 ) 7255 , hep - ph/9708416 . t. barklow , private communication . d. barger et al . , phys rev . * d52 * ( 1995 ) 3815 , phys rev . * d55 * ( 1997 ) 142 . m. butterworth , b.e . cox and j.r . forshaw , in preparation . a. dobado et al . , phys rev * d62 * ( 2000 ) 05501 . a. de roeck , _ ww scattering at clic _ , these proceedings . t. rizzo , hep - ph/0108235 . n. arkani - hamed , s. dimopoulos , and g. dvali , b429 263 1998 , and d59 086004 1999 ; i. antoniadis , n. arkani - hamed , s. dimopoulos , and g. dvali , b436 257 1998 . see , for example , i. antoniadis , b246 377 1990 ; i. antoniadis , c. munoz and m. quiros , b397 515 1993 ; i. antoniadis and k. benalki , b326 69 1994 and a15 4237 2000 ; i. antoniadis , k. benalki and m. quiros , b331 313 1994 . l. randall and r. sundrum , 83 3370 1999 . for an introduction to add phenomenology , see g.f . giudice , r. rattazzi and j.d . wells , b544 3 1999 ; 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the physics at an @xmath0 linear collider with a center of mass energy of 3 - 5 tev is reviewed . the following topics are covered : experimental environment , higgs physics , supersymmetry , fermion pair - production , @xmath1 scattering , extra dimensions , non - commutative theories , and black hole production .

currently popular theories of structure formation in the universe postulate that structure grows through the amplification by gravitational forces of initially small density fluctuations ( see white 1996 for a review ) . depending on the characteristics of the spectrum of fluctuations , small objects can be the first to collapse ; they then merge to form progressively larger systems giving rise to the complex structure we observe today . in this hierarchical structure formation scenario our galaxy , as a typical galaxy , should also have been formed in part by merging and accretion of smaller galaxies , or ` building blocks ' . these events should be imprinted in some of its present - day components , presumably as residual structure . for example , when a galaxy is disrupted it leaves trails of stars along its orbit . these could be superposed in a spheroidal component such as a stellar halo . in fact , numerous observations suggest substructure in the halo of the galaxy ( see majewski in this volume ) . in this paper , we attempt to describe what the signatures of different accretion events should be if indeed our galaxy formed as envisaged in current theories . should this merging history be observed in star counts , kinematic or abundance surveys of the galaxy ? how prominent or not would these substructures be ? how well - mixed are the stars that made up these progenitors ? what can we say about the properties of the accreted satellites from the observations we have today ? to tackle the questions we just posed we carry out n - body simulations of accretion of satellite galaxies , where we represent the milky way by a fixed , rigid potential and the satellite by a collection of particles . the self - gravity of the satellite is modelled by a monopole term as in white ( 1983 ) . the galactic potential is represented by two components : a disk described by a miyamoto - nagai potential , @xmath0 where @xmath1 , @xmath2 , @xmath3 , and a dark halo with a logarithmic potential , @xmath4 with @xmath5 and @xmath6 . the initial density distribution of the satellite is given by a plummer profile @xmath7 with @xmath8 , @xmath9 being the initial mass of the satellite and @xmath10 its scale length . its one - dimensional internal velocity dispersion is @xmath11 . we run several simulations which differ in their orbital parameters , which span a range in radial periods from 0.5 to 1.3 gyr , and have an apocentre to pericentric distance ratio of 5 to 10 ( fairly radial orbits ) . we have also imposed that the orbits pass close to the solar circle to compare the results of the experiments with the known properties of the stellar halo of the milky way . in all cases the satellite was represented by @xmath12 particles of equal mass . we find that the satellites become completely unbound after , at most , three pericentric passages . one process that will tend to erase any macroscopic correlation between the particles , making more difficult the detection of satellite debris , is phase - mixing . to quantify it we use the coarse - grained entropy defined as : @xmath13 = -\int \bar{f}\ln \bar{f } d^3x d^3v,\ ] ] where @xmath14 is the coarse - grained distribution function , that is , the average of the actual distribution function @xmath15 over small cells in phase - space . one of the interesting properties of @xmath14 is that it decreases as the system becomes phase - mixed . therefore , @xmath16 $ ] is expected to increase with time , as shown for our simulations in figure 1 . in practice , we replace the integral by a sum over cells , and @xmath14 by the fraction of particles in each cell . the spatial properties of the debris can be studied by plotting isodensity surfaces . these surfaces are indicative of how spread in its available configuration volume the system is , or equivalently how advanced the disruption is . we find that for the region of parameter space probed , these volumes are almost completely filled after a hubble time . in terms of the spatial distribution of the particles on the plane of the sky ( see helmi , zhao and de zeeuw , this volume , their figure 1 ) we do not find any strong correlations , contrary to what johnston , hernquist and bolte ( 1996 ) find in their simulations of accretion in the outer halo . we can understand this in terms of the short time scales and the strong flattening characteristic of the inner parts of our galaxy . the maximum densities of such debris are three to four orders of magnitude lower than the initial density of their progenitors , roughly comparable to the local density of the stellar halo . in order to reflect what observers can do in surveys of the local halo , in figure 2 we plot the kinematical properties of stars inside a box of 3 kpc on a side in different locations along the orbit . notice the strong correlations between the different components of the velocity vector inside any given box , and , in particular , the large velocity range in each component when close to the galactic centre . this shows that the debris can appear kinematically hot . this is the result of a combination of multiple streams within a given box ( clearly visible in figure 2 ) and strong gradients along each stream . at a given point along any particular stream the dispersions are usually very small . [ fig2 ] because the disruption of the satellite occurs very early in its history , it can be considered as an ensemble of test particles during most of its evolution . one of the distinguishing properties of this ensemble is that it initially had a very high density in phase - space , and by virtue of liouville s theorem , this is true at all times . at later times , however , this is no longer reflected by a strong concentration in configuration space . since the behaviour of a dynamical system is particularly simple in action - angle variables : @xmath17 we can find the evolution of the distribution function in the following way . we know the distribution function at the initial time @xmath18 . by a transformation of coordinates we may write it as a function of action - angle variables at that initial time : @xmath19 . eqs . ( [ eq : evol ] ) then give the distribution function at a later time @xmath20 in action - angle variables . if we now transform locally from @xmath21 back to @xmath22 , we obtain the distribution function , and thereby the velocity dispersions and the density behaviour , in the region of interest . in action - angle variables the system expands along three directions and contracts along the remaining three . this is directly associated with the equations of motion . any initial dispersion in the angles can only increase ( eqs . ( [ eq : evol ] ) ) , so that the system becomes a very elongated ellipsoid in phase - space as time passes by . the conservation of phase - space density ( liouville s theorem ) then forces the other directions to shrink . this is reflected in the projection onto observable space . it is possible to show ( see helmi & white 1998 for all the details ) that the velocity dispersions decrease on the average with time , and so the volume density also decreases with time as the system expands in the spatial directions . for example in the spherical case the dispersions and the central density behave as @xmath23 the velocity dispersion in the direction transverse to the plane of motion ( @xmath24 ) is constant , except for periodic variations due to the orbital phase . in the axisymmetric case , there no longer is a preferred orientation , so that also in the @xmath24-direction the velocity dispersion decreases , and therefore the density decreases as @xmath25 . our results suggest that fossil structure from an accretion event which took place at any time during the the history of the milky way should be visible in velocity space . a stream of stars is , most of the time , fairly cold . however , in particular in the inner parts of the galaxy , it is quite likely to find more than one stream from any particular disrupted satellite in a small region in configuration space . in that case , the apparent velocity dispersions can be much larger , although constrained by the initial dispersions in the integrals of motion . majewski , munn & hawley ( 1994 ) reported the discovery of a moving group near the ngp ( for details see majewski , this volume ) with large velocity dispersions ( greater than 30 @xmath26 ) , and with a mean motion very different from that of the other stars in the field . if we are to take these stars as satellite debris , we will have to invoke a multistream structure in order to explain their kinematics . indeed , there is some evidence of substructure in their distribution of angular momenta . this is to be expected if indeed there are multiple streams . with this in mind , we can use our simulations and analytic results to estimate the mass of the progenitor using the simulations , and estimates for its initial size and velocity dispersions . we find : @xmath27 , @xmath28 and @xmath29 . helmi , a. & white , s.d.m . 1998 , in preparation helmi , a. , zhao , h.s . & de zeeuw , p.t . 1998 , this volume johnston , k.v . , hernquist , l. & bolte , m. 1996 , , 465 , 278 majewski , s.r . , munn , j.a . & hawley , s.l . 1994 , , 427 , l37 majewski , s.r . 1998 , this volume white , s.d.m . 1983 , , 274 , 53 white , s.d.m . 1996 , in cosmology and large scale structure , les houches , session lx . amsterdam : elsevier , p. 349

we study numerical simulations of satellite galaxy disruption in a potential resembling that of the milky way . our goal is to assess whether a merger origin for the stellar halo would leave observable fossil structure in the phase - space distribution of nearby stars . we show how mixing of disrupted satellites can be quantified using a coarse - grained entropy . although after 10 billion years few obvious asymmetries remain in the distribution of particles in configuration space , strong correlations are still present in velocity space . we briefly describe how we can understand these effects based on the conservation of fine - grained phase - space density in an action - angle formalism . we also discuss the implications of our results on the known properties of the stellar halo .

first we need the concept of a reusable secure carrier @xcite , . a bell state like @xmath0 shared between alice(a ) and bob(b ) can be used as a reusable secure carrier between two parties as follows . alice entangles a qubit @xmath1 by the action of a cnot gate @xmath2 ( acting on the qubit @xmath3 and controlled by @xmath4 ) , which produces a state like @xmath5 at the destination bob disentangles the qubit by a cnot operation @xmath6 , leaving the carrier in its original state for reusing . during the transmission the qubit has been disguised in a highly mixed state . + any of the bell states [ bells ] |^_ab = ( |00|11)_ab,|^_ab = ( |01|10)_abcan be used as a carrier . + for three parties @xcite , a carrier shared between alice(a ) , bob(b ) and charlie(c ) can be a ghz state like @xmath7 or an even parity state like @xmath8 throughout @xcite , the comment @xcite and the present reply the subscripts @xmath9 and @xmath10 are used for the quibts shared by , or the local operators acted by , alice , bob and charlie respectively , while the subscripts @xmath3 and @xmath11 are used for the qubits sent to bob and charlie respectively . + it was shown in @xcite that by suitable local operations , alice can send a qubit @xmath12 to bob and charlie , by entangling it to the above carriers ( hence hiding it from eavesdroppers ) . in order to share the secret between bob and charlie , half of the bits ( the bits in the odd rounds ) were sent to bob and charlie , as states of the form @xmath13 which they could read without the help of each other and the other half ( the bits in the even rounds ) were sent to them in the form @xmath14 which they could use to decipher the value of @xmath12 only by their cooperation . note that @xmath15 . in order to be able to send both types of states in disguised form , alice needs to use two types of carriers , namely the @xmath16 carrier for the states @xmath17 and the @xmath18 carrier for the states @xmath19 . the interesting point is that the two types of carriers are transformed to each other at the end of every round by the local action of hadamard gates by the three parties , due to the following easily verified property an important property which requires careful attention is that the carrier alternates between the above two forms regardless of the value of the qubit @xmath12 which has been sent to bob and charlie by alice . + in @xcite the authors show that in the second round where a qubit say @xmath21 has been encoded as @xmath22 and entangled to the carrier @xmath18 , bob ( assuming that he has access to the channel between alice and charlie ) can intercept the qubit 2 sent to charlie ( assuming that he has access to the channel used between alice and charlie ) and perform a suitable unitary operation @xmath23 , on the state of the carrier and the two bits @xmath3 and @xmath11 , to split the carrier @xmath18 to two simple carriers of the type [ bells ] . this process is shown schematically in figure ( [ split ] ) . let us denote by @xmath24 the qubit sent by alice in the second round . bob keeps this qubit for himself and denotes it hereafter by @xmath25 , since it is now in possession of bob and plays a role as part of his new carriers . + it is important to note that the pattern of entanglement splitting depends on the value of this qubit @xmath24 as follows ( equation 3 of the comment ) : as it stands in @xcite , this does not harm the cheating strategy of bob , since as mentioned before any of the bell states can be used as a carrier between two parties . he then uses the above two pairs of entangled states for retrieving the qubits sent by alice on his own and sending counterfeit qubits to charlie in a clever way so that to avoid detection after public announcement of subsequence of the bits . + what is crucial in this attack is that bob acts by hadamard gates on his qubits @xmath27 and @xmath25 along with alice and charlie who are doing the same thing at the end of each round . in this way he almost maintains the pattern of the new carriers , which he has created in the second round , between himself and the other two parties . + the reason for `` almost '' is that the hadamard operations act as follows ( equation 4 of the comment ) : at first sight one may argue that alice and charlie who are no longer entangled after bob s trick , can detect their new disentangled situation ( i.e. by testing a bell inequality ) and hence detect bob s cheating . however this test requires statistical analysis which requires many measurements . in each measurement the carrier collapses and will not be usable anymore . being in conflict with the whole idea of reusable carrier , we do not follow this line of argument . instead we modify the protocol in a way which prevents bob s from entanglement splitting . + to this end we note that the operator @xmath31 is not the only operator which transforms the carriers @xmath16 and @xmath18 into each other . consider a unitary operator of the form @xmath32 where @xmath33 is an arbitrary parameter @xmath34 . for @xmath35 this is the usual hadamard operator . a simple calculation shows that a generalization of ( [ three ] ) is possible in the following form @xmath37 provided that @xmath38 therefore in the modified protocol alice , bob and charlie act alternatively by the operators @xmath39 , @xmath40 , and @xmath41 , and their inverses , on the qubits in their possession . the angles @xmath42 and @xmath43 can be announced publicly at the beginning of the protocol . we now show that after entanglement splitting , bob can not retain his pattern of carriers by any operator @xmath44 which he acts on his qubits @xmath25 and @xmath27 . we need the following + * proposition * : + * a : * the only operator @xmath45 which in conjunction with @xmath46 leaves invariant the state @xmath29 is the operator @xmath47 . + * b : * the only operator @xmath45 which in conjunction with @xmath46 transforms the state @xmath48 into @xmath49 is the operator @xmath50 , where @xmath51 means transpose . + * proof : * the proof is simply straightforward calculations . we highlight the basic steps . consider part * a*. we want an operator @xmath44 such that @xmath52 where we use @xmath53 as an abbreviations of @xmath54 and so forth . acting on both sides by @xmath55 we obtain @xmath56 we now rearrange both sides to the convenient form @xmath57 and effect the operators @xmath58 and @xmath59 on the right hand side by using ( [ ha ] ) . after comparing both sides in the basis @xmath60 we arrived at the stated assertion , namely that @xmath47 . + similar reasoning proves part @xmath27 . + we now come to our main conclusion . bob , being among the original legitimate parties knows the values of the angles , @xmath61 . however in order to scape detection he has to apply either the operator @xmath62 or @xmath63 at the end of each round . however his choice depends on the value of the second bit which he does not know . without this knowledge he can not retain the pattern of fraud carriers which he has constructed between him and the other two parties . this then introduces errors in half of the bits sent by alice and received by him and charlie , which in subsequent public announcement of substrings of bits reveals his cheating . incidentally we note that the equality @xmath64 holds only for @xmath65 , that is for the ordinary hadamard gate . s. bagherinezhad , v. karimipour , phys . rev . * a * , 67 , 044302 , ( 2003 ) . jian - zhong du et al . , entanglement split : comment on `` quantum secret sharing based on reusable greenberger - horne - zeilinger states as secure carriers [ phys . rev . a * 67 * , 044302 ( 2003 ) ] '' , quant - ph/0605088 . y. zhang , c. li and g. gao , phys . rev . * a * , 64 , 024302 , ( 2001 ) .

in a recent comment , it has been shown that in a quantum secret sharing protocol proposed in [ s. bagherinezhad , v. karimipour , phys . rev . * a * , 67 , 044302 , ( 2003 ) ] , one of the receivers can cheat by splitting the entanglement of the carrier and intercepting the secret , without being detected . in this reply we show that a simple modification of the protocol prevents the receivers from this kind of cheating . * reply to `` comment on quantum secret sharing based on reusable greenbergr - horne - zeilinger states as secure carriers '' * + v. karimipour + department of physics , sharif university of technology , + p.o . box 11365 - 9161 , + tehran , iran pacs numbers : 03.67.dd , 03.65.ud . to set up the context and the notations , it is appropriate to first review briefly the protocol itself @xcite and the basic feature of the attack or cheating suggested in @xcite .

@xmath1 is the low energy effective theory of the strong interactions . it is given as a power expansion of the external four - momenta of the pseudo - goldstone bosons @xmath13 , @xmath14 and @xmath15 on the scale @xmath161 gev . as a result , the expansion is typically valid up to @xmath17500 mev . however , the constraints coming from the spontaneous / explicit chiral symmetry are not restricted to the low energy region @xcite . in this work , we present a way of resummation of the @xmath1 series that in fact can be applied to any other system whose dynamics can be described by low energy chiral lagrangians . we describe the successfull application of such approach to meson - meson interactions which are well reproduced up to @xmath171.2 gev . let us a consider a partial wave amplitude @xmath18 with definite isospin ( @xmath19 ) . we use a matrix formalism in order to deal with coupled channels . in this way @xmath18 will be a matrix whose element @xmath20 represents the scattering of @xmath21 with angular momentum @xmath22 and isospin @xmath19 . if we consider only two body intermediate states unitarity with coupled channels reads in our normalization : @xmath23 where @xmath24 is a diagonal matrix with elements @xmath25 with @xmath26 the center mass three - momentum , @xmath27 and @xmath28 are the masses of the particles in the state @xmath29 and @xmath30 is the usual heaviside function . ( [ uni ] ) is a well known result and is the basis of the @xmath14 matrix formalism since all the dynamics is embodied in re@xmath5 which is @xmath31 . the former equation shows clearly that , when considering @xmath5 , unitarity is exactly satisfied with two body intermediate states . from the @xmath1 expansion of @xmath32 , where @xmath33 and @xmath34 are the @xmath3 and @xmath4 contributions respectively , we work out the expansion of @xmath5 . in this way we will obtain our approach for the @xmath14 matrix ( or re@xmath5 ) . @xmath35^{-1}= t_2^{- 1}\cdot [ 1 + t_4 \cdot t_2^{- 1}+ ... ]^{- 1}\nonumber \\ & = & t_2^{- 1}\cdot [ 1 - t_4 \cdot t_2^{- 1}+ ... ]=t_2^{-1}\cdot [ t_2-t_4]\cdot t_2^{-1}\end{aligned}\ ] ] inverting the former result , one obtains : @xmath36^{-1}\cdot t_2 \nonumber \\ k&=&t_2\cdot \left[t_2-\hbox{re}t_4 \right]^{-1}\cdot t_2\end{aligned}\ ] ] in @xcite we study the @xmath39 and @xmath40 partial waves . to make use of eq . ( [ t ] ) one needs the lowest and next to leading order @xmath41 amplitudes . in our case the @xmath42 and @xmath43 are taken from @xcite and the @xmath44 is also given in @xcite . our amplitudes depend on six parameters @xmath45 , @xmath46 , @xmath47 , @xmath48 , @xmath49 and @xmath50 which are fitted to the elastic @xmath37 @xmath51 and @xmath52 phase shifts . in the following table we show the resulting values for the @xmath53 coefficients comparing them with the @xmath1 values . .@xmath53 coefficients . [ cols="^,^,^",options="header " , ] we have presented a method of resummation of the @xmath1 series based in the expansion of @xmath5 . in this way unitarity is fulfilled to all orders and resonances are well reproduced . the method is rather general and could be applied to any system whose dynamics is described by chiral lagrangians . we have applied it successfully to describe the s and p - wave meson - meson amplitudes giving rise to the resonances : @xmath6 , @xmath7 , @xmath8 , @xmath9 , the octet contribution to the @xmath10 , @xmath11 and @xmath12 . 200 j. a. oller , e. oset and j. r. pelez , phys . ( 1998 ) 3452 . j. gasser and h. leutwyler , nucl . b 250 ( 1985 ) 465 , 517 , 539 . f. guerrero and j. a. oller , nucl . b 537 ( 1999 ) 459 . j. a. oller , e. oset and j. r. pelez , phys . d 59 ( 1999 ) 074001 . j. v. steele , h. yamagishi and i. zahed , nucl . phys . a 615 ( 1997 ) 305 ; m. r. pennington and j. portoles , phys . b 344 ( 1995 ) 399 . v. bernard , n. kaiser and u. g. meissner , nucl . b 357 ( 1991 ) 129 . g. ecker , j. gasser , a. pich and e. de rafael , nucl . b 321 ( 1989 ) 311 .

a non - perturbative method @xcite which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe meson - meson interactions up to @xmath0 gev , extending in this way the range of applicability of the information contained in chiral perturbation theory ( @xmath1 ) @xcite , since this perturbative series is typically restricted to @xmath2 mev . the approach uses the @xmath3 and @xmath4 @xmath1 lagrangians . the seven free parameters resulting from the @xmath4 lagrangian are fitted to the experimental data . the approach makes use of the expansion of @xmath5 instead of the amplitude itself as done in @xmath1 . the former expansion is suggested by analogy with the effective range approximation in quantum mechanics and it appears to be very useful . the results , in fact , are in good agreement with a vast amount of experimental analyses @xcite . the amplitudes develop poles corresponding to the @xmath6 , @xmath7 , @xmath8 , @xmath9 , the octet contribution to the @xmath10 , @xmath11 and @xmath12 @xcite . the total and partial decay widths of the resonances are also well reproduced .

a circulant graph of @xmath7 vertices is fully described by an @xmath7-by-@xmath7 symmetric circulant adjacency matrix @xmath67 defined as follows . @xmath68\end{aligned}\ ] ] where @xmath69 . obviously , every circulant matrix can be generated given any row of the matrix conventionally we use the first row of the matrix , denoted as @xmath70 . it is clear that @xmath67 has at most @xmath7 distinct eigenvalues which are given by @xmath71 , where @xmath72 and @xmath73 @xcite . if @xmath67 is singular , some of the eigenvalues of @xmath67 are zeros . the complete graph and complete bipartite graph are straightforward examples of circulant graphs with few distinct eigenvalues . there are also some other interesting examples of circulant graph such as self - complementary circulant graphs and paley graphs with prime order @xcite . both of these two families of graphs are also strongly regular graphs which have only three distinct eigenvalues . for example , the paley graph on 13 vertices has three distinct eigenvalues : 6 ( with multiplicity 1 ) and @xmath74 ( both with multiplicity 6 ) , and thus the diagonal unitary @xmath75 can be implemented efficiently . we note here it is required to implement qft ( and its inverse ) for the dimension of 13 , which does not have the form of @xmath27 . the qft on general dimensions can be implemented by means of amplitude amplification with extra qubit registers to perform the computation @xcite . alternatively , approximate versions of the qft on general dimensions have also been developed @xcite . we say that the eigenvalues of a circulant graph can be characterised efficiently , if they can be calculated efficiently classically . in other words , the eigenvalue matrix @xmath76 of the given circulant hamiltonian can be efficiently computed , and thus the diagonal unitary operator @xmath75 can be efficiently implemented @xcite . specifically , there exists a quantum circuit shown in figure [ diagonalunitarycircuit ] , which transforms a computational basis state @xmath77 , together with a @xmath16-qubit ancilla @xmath78 for @xmath79 , as @xmath80 where @xmath81 . note that here we assume @xmath82 can be expressed exactly as a rational number with @xmath16 bits of precision . if this is not the case , truncating @xmath82 to @xmath16 bits of precision will introduce an error which can be made arbitrarily small by taking large enough @xmath79 . the function @xmath83 returns @xmath84 for any given @xmath85 . @xmath84 is always a real number since the adjacency matrix is symmetric . for example , for the case of the cycle graph of @xmath27 vertices , there are essentially @xmath86 distinct eigenvalues simply given by @xmath87 , where @xmath81 . and then @xmath83 will be the cosine function that can be computed with a number of operations polynomial in @xmath4 , using a reversible equivalent of classical algorithms to compute trigonometric functions , e.g. the taylor approximation . in general , given a sparse circulant graph which has only @xmath37 @xmath88s in the first row @xmath70 of its adjacency matrix , an efficient function @xmath83 can be given as @xmath89 where @xmath90 is the set of positions for which the first row in nonzero . @xmath83 is a sum of @xmath91 numbers , taking @xmath33 time to compute . for a non - sparse circulant graph , its eigenvalues are still possible to be calculated efficiently classically . some straightforward examples are complete graph , complete bipartite graph @xmath92 and cocktail party graph . therefore , together with the quantum circuits of qft and the inverse of qft , we construct an efficient quantum circuit for implementing ctqw on the circulant graph whose eigenvalues can be computed efficiently classically . unlike the sampling problem we discussed in the main text , the scenario of `` swap test '' , where we compare two unitary processes @xmath36 and @xmath93 , could sometimes be easier for a classical computer . imagine we start each process in the state @xmath94 . then the overlap @xmath95 between the resulting output states approximated by the swap test satisfies @xmath96 where @xmath97 is the value at position @xmath85 on the diagonal of @xmath30 . @xmath95 can be approximated by a classical algorithm up to @xmath48 additive error . the algorithm simply takes the average of @xmath37 values of the product @xmath98 for uniformly random @xmath85 . for each @xmath85 , this value can be computed exactly in polynomial time . this highlights that the complexity of comparing @xmath99 and @xmath100 depends on the choice of input states @xmath101 and @xmath102 . in full generality , one could allow these to be arbitrary states produced by a polynomial - time quantum computation ; the state comparison problem would then be bqp - complete , but for rather trivial reasons . we expect that the problem would remain classically hard for choices of initial states relevant , for example , to quantum - chemistry applications . on the other hand , the swap test can still be used as in scenario ( b ) in the main text to compare the evolution of two hamiltonians , one of which is not circulant but is efficiently implementable . in this case , the comparison problem is also bqp - complete , and hence expected to be hard for a classical computer . we present the ideal and experimentally sampled probability distributions of ctqw with initial states @xmath58'$ ] , @xmath59'$ ] ( mentioned in the main text ) , @xmath103'$ ] , @xmath104'$ ] , @xmath105'$ ] , @xmath106'$ ] , in table i. the achieved average fidelities between ideal and experimental probability distributions are 96.68@xmath620.27% , 95.82@xmath620.25% , 92.61@xmath620.21% , 96.36@xmath620.16% , 98.76@xmath620.17% and 97.27@xmath620.24% respectively . in the main text , we reconstructed the density matrices for the two quantum states @xmath107 and @xmath108 , through performing quantum state tomography . here we also present the reconstructed density matrices for another two evolution states @xmath109 and @xmath110 , with the achieved fidelities of 88.63@xmath621.24% and 91.53@xmath620.53% respectively . see in figure [ densitym12 ] . the four reconstructed density matrices @xmath111 , @xmath112 , @xmath113 and @xmath114 for quantum states @xmath107 , @xmath108 , @xmath115 and @xmath116 are shown as follows .

the random walk formalism is used across a wide range of applications , from modelling share prices to predicting population genetics . likewise quantum walks have shown much potential as a framework for developing new quantum algorithms . in this paper , we present explicit efficient quantum circuits for implementing continuous - time quantum walks on the circulant class of graphs . these circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently . we also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer , assuming conjectures from computational complexity theory . this is a new link between continuous - time quantum walks and computational complexity theory and it indicates a family of tasks which could ultimately demonstrate quantum supremacy over classical computers . as a proof of principle we have experimentally implemented the proposed quantum circuit on an example circulant graph using a two - qubit photonics quantum processor . quantum walks are the quantum mechanical analogue to the well - known classical random walk and they have established roles in quantum information processing @xcite . in particular , they are central to quantum algorithms created to tackle database search @xcite , graph isomorphism @xcite , network analysis and navigation @xcite , and quantum simulation @xcite , as well as modelling biological processes @xcite . meanwhile , physical properties of quantum walks have been demonstrated in a variety of systems , such as nuclear magnetic resonance @xcite , bulk @xcite and fiber @xcite optics , trapped ions @xcite , trapped neutral atoms @xcite , and photonics @xcite . almost all physical implementations of quantum walk so far followed an analog approach as for quantum simulation @xcite , whereby the apparatus is dedicated to implement specific instances of hamiltonians without translation onto quantum logic . however , there is no existing method to implement analog quantum simulations with error correction or fault tolerance , and they do not scale efficiently in resources when simulating broad classes of large graphs . in this paper , we present efficient quantum circuits for implementing continuous time quantum walks ( ctqws ) on circulant graphs with an eigenvalue spectrum that can be classically computed efficiently . these quantum circuits provide the time - evolution states of ctqws on circulant graphs exponentially faster than best previously known methods @xcite . we report a proof - of - principle experiment , where we implement ctqws on an example circulant graph ( namely the complete graph of four vertices ) using a two - qubit photonics quantum processor to sample the probability distributions and perform state tomography on the output state of a ctqw . we also provide evidence from computational complexity theory that the probability distributions that are output from the circuits of this circulant form are hard to sample from using a classical computer , implying our scheme also provides an exponential speedup for sampling . efficient quantum circuit implementations of ctqws have been presented for sparse and efficiently row - computable graphs @xcite , and specific non - sparse graphs @xcite . however , the design of quantum circuits for implementing ctqws is in general difficult , since the time - evolution operator is time - dependent and non - local @xcite . a subset of circulant graphs have the property that their eigenvalues and eigenvectors can be classically computed efficiently @xcite . this enables us to construct a scheme that efficiently outputs the quantum state @xmath0 , which corresponds to the time evolution state of a ctqw on corresponding graphs . one can then either perform direct measurements on @xmath1 or implement further quantum circuit operations to extract physically meaningful information . for example the `` swap test '' @xcite can be used to estimate the similarity of dynamical behaviors of two circulant hamiltonians operating on two different initial states , as shown in figure [ cswaptest_sampling](a ) . this procedure can also be adapted to study the stability of quantum dynamics of circulant molecules ( for example , the dna mbius strips @xcite ) in a perturbational environment @xcite . on the other hand , when measuring @xmath1 in the computational basis we can sample the probability distribution @xmath2 that describes the probability of observing the quantum walker at position @xmath3an @xmath4-bit string , corresponding to the vertices of the given graph , as shown in figure [ cswaptest_sampling](b ) . sampling of this form is sufficient to solve various search and characterization problems @xcite , and can be used to deduce critical parameters of the quantum walk , such as mixing time @xcite . it is unlikely for a classical computer to be able to efficiently sample from @xmath5 . we adapt the similar methodology of refs . @xcite to show that if there did exist a classical sampler for a somewhat more general class of circuits , this would have the following unlikely complexity - theoretic implication : the infinite tower of complexity classes known as the polynomial hierarchy would collapse . this evidence of hardness exists despite the classical efficiency with which properties of the ctqw , such as the eigenvalues of circulant graphs , can be computed on a classical machine . for an undirected graph @xmath6 of @xmath7 vertices , a quantum particle ( or `` quantum walker '' ) placed on @xmath6 evolves into a superposition @xmath8 of states in the orthonormal basis @xmath9 that correspond to vertices of @xmath6 . the exact evolution of the ctqw is governed by connections between the vertices of @xmath6 : @xmath10 where the hamiltonian is given by @xmath11 for hopping rate per edge per unit time @xmath12 and where @xmath13 is the @xmath7-by-@xmath7 symmetric adjacency matrix , whose entries are @xmath14 , if vertices @xmath15 and @xmath16 are connected by an edge in @xmath6 , and @xmath17 otherwise @xcite . circulant graphs are defined by symmetric circulant adjacency matrices for which each row @xmath15 when right - rotated by one element , equals the next row @xmath18for example complete graphs , cycle graphs and mobius ladder graphs are all subclasses of circulant graphs . it follows that hamiltonians for ctqws on any circulant graph have a symmetric circulant matrix representation , which can be diagonalized by the unitary fourier transform @xcite , i.e. @xmath19 , where @xmath20 and @xmath21 is a diagonal matrix containing eigenvalues of @xmath22 , which are all real and whose order is determined by the order of the eigenvectors in @xmath23 . consequently , we have @xmath24 , where the time dependence of @xmath25 is confined to the diagonal unitary operator @xmath26 . the fourier transformation @xmath23 can be implemented efficiently by the well - known qft quantum circuit @xcite . for a circulant graph that has @xmath27 vertices , the required qft of @xmath7 dimension can be implemented with @xmath28 quantum gates acting on @xmath29 qubits . to implement the inverse qft , the same circuit is used in reverse order with phase gates of opposite sign . @xmath30 can be implemented using at most @xmath7 controlled - phase gates with phase values being a linear function of @xmath31 , because an arbitrary phase can be applied to an arbitrary basis state , conditional on at most @xmath32 qubits . given a circulant graph that has @xmath33 non - zero eigenvalues , only @xmath33 controlled - phase gates are needed to implement @xmath30 . if the given circulant graph has @xmath34 distinct eigenvalues , which can be characterised efficiently ( such as the cycle graphs and mobius ladder graphs ) , we are still able to implement the diagonal unitary operator @xmath30 using polynomial quantum resources . a general construction of efficient quantum circuits for @xmath30 was given by childs @xcite , and is shown in the appendix for completeness . thus , the quantum circuit implementations of ctqws on circulant graphs can be constructed , which have an overall complexity of @xmath33 , and act on at most @xmath29 qubits . compared with the best known classical algorithm based on fast fourier transform , that has the computational complexity of @xmath35 @xcite , the proposed quantum circuit implementation generates the evolution state @xmath1 with an exponential advantage in speed . consider a circuit of the form @xmath36 , where @xmath30 is a diagonal matrix made up of @xmath37 controlled - phase gates . define @xmath38 @xmath39 represents a family of circuits having the following structure : each qubit line begins and ends with a hadamard ( @xmath22 ) gate , and , in between , every gate is diagonal in the computational basis . this class of circuits is known as instantaneous quantum polynomial time ( iqp ) @xcite . it is known that computing @xmath40 for arbitrary diagonal unitaries @xmath30 made up of circuits of @xmath37 gates , even if each acts on @xmath41 qubits , is # p - hard @xcite . this hardness result even holds for approximating @xmath40 up to any multiplicative error strictly less than @xmath42 @xcite , where @xmath43 is said to approximate @xmath40 up to multiplicative error @xmath44 if @xmath45 towards a contradiction , assume that there exists a polynomial - time randomized classical algorithm which samples from @xmath46 . then a classic result of stockmeyer @xcite states that there is an algorithm in the complexity class fbpp@xmath47 which can approximate any desired probability @xmath5 to within multiplicative error @xmath48 . this complexity class fbpp@xmath47described as polynomial - time randomized classical computation equipped with an oracle to solve arbitrary np problems sits within the infinite tower of complexity classes known as the polynomial(-time ) hierarchy @xcite . combining with the above hardness result of approximating @xmath40 , we find that the assumption implies that an fbpp@xmath49 algorithm solves a # p - hard problem , so p@xmath50 would be contained within fbpp@xmath49 , and therefore the polynomial hierarchy would collapse to its third level . this consequence is considered very unlikely in computational complexity theory @xcite . we therefore conclude that a polynomial - time randomized classical sampler from the distribution @xmath46 is unlikely to exist . further , this even holds for classical algorithms which sample from any distribution @xmath51 which approximates @xmath46 up to multiplicative error strictly less than @xmath42 in each probability @xmath5 . it is worth noting that if the output distribution results from measurements on only @xmath52 qubits @xcite , or obeys the sparsity promise that only a @xmath37-sized , and a priori unknown , subset of the measurement probabilities are nonzero @xcite , it could be classically efficiently sampled . the proof of hardness here does not hold for the approximate sampling from @xmath46 up to small _ additive _ error . it is an interesting open question whether similar techniques to @xcite can be used to prove hardness of the approximate case , perhaps conditioned on other conjectures in complexity theory . as an experimental demonstration , we used a photonic quantum logic to simulate ctqws on the @xmath53 graph a complete graph with self loops on four vertices ( figure [ expsetup](a ) ) . complete graphs are a special kind of circulant graph , with an adjacency matrix @xmath13 where @xmath54 for all @xmath55 . the hamiltonian of a complete graph on @xmath7 vertices has only 2 distinct eigenvalues , 0 and @xmath56 . therefore , the diagonal matrix of eigenvalues of @xmath53 is @xmath57 . following the aforementioned discussion , we can readily construct the quantum circuit for implementing ctqws on @xmath53 graph based on diagonalization using the qft matrix . however , the choice of using the qft matrix as the eigenbasis of hamiltonian is not strictly necessary any equivalent eigenbasis can be selected . through the diagonalization using hadamard eigenbasis , an alternative efficient quantum circuit for implementing ctqws on @xmath53 graph is shown in figure [ expsetup](b ) , which can be easily extended to the complete graph on @xmath7 vertices . we built a configurable two - qubit photonics quantum processor ( figure [ expsetup](c ) ) , adapting the entanglement - based technique presented in @xcite , and implemented ctqws on @xmath53 graph with various evolving times and initial states . specifically , we prepared two different initial states @xmath58'$ ] and @xmath59'$ ] , which represent the quantum walker starting from vertex 1 , and the superposition of vertices 1 and 2 respectively . we chose the evolution time following the list @xmath60 , which covers the whole periodical characteristics of ctqws on @xmath53 graph . for each evolution , we sampled the corresponding probability distribution with fixed integration time , shown in figure [ expdata](a ) and ( b ) . to measure how close the experimental and ideal probability distributions are , we calculated the average fidelities defined as @xmath61 . the achieved average fidelities for the samplings with two distinct initial states are 96.68@xmath620.27% and 95.82@xmath620.25% respectively . through the proposed circuit implementation , we are also able to examine the evolution states using quantum state tomography , which is generally difficult for the analog simulations . for two specific evolution states @xmath63 and @xmath64 , we performed quantum state tomography and reconstructed the density matrices using the maximum likelihood estimation technique . the two reconstructed density matrices achieve fidelities of 85.81@xmath621.08% and 88.44@xmath620.97% respectively , shown in figure [ expdata](c ) and ( d ) . in this paper , we have described how ctqws on circulant graphs can be efficiently implemented on a quantum computer , if the eigenvalues of the graphs can be characterised efficiently classically . in fact , we can construct an efficient quantum circuit to implement ctqws on any graph whose adjacency matrix is efficiently diagonalisable , in other words , as long as the matrix of column eigenvectors @xmath23 and the diagonal matrix of the eigenvalue exponentials @xmath30 can be implemented efficiently . we have shown that the problem of sampling from the output probability distributions of quantum circuits of the form @xmath65 is hard for classical computers , based on a highly plausible conjecture that the polynomial hierarchy does not collapse . this observation is particularly interesting from both perspectives of ctqw and computational complexity theory , as it provides new insights into the ctqw framework and also helps to classify and identify new problems in computational complexity theory . for the ctqws on the circulant graphs of @xmath66 non - zero eigenvalues , the proposed quantum circuit implementations do not need a fully universal quantum computer , and thus can be viewed as an intermediate model of quantum computation . although the hardness of the approximate case of the sampling problem is unknown , the evidence we provided for the exact case indicates a promising candidate for experimentally establishing quantum supremacy over classical computers , and further evidence against the extended church - turing thesis . compared with other intermediate models such as the one clean qubit model @xcite , iqp and boson sampling @xcite , the quantum circuit implementation of ctqws is also more appealing due to available methods in fault tolerance and error correction , which are difficult to implement for other models @xcite . this may also lead onto other practical applications through the use of ctqws for quantum algorithm design . 10 farhi , e. & gutmann , s. quantum computation and decision trees . * 58 , * 915 ( 1998 ) . kempe , j. quantum random walks : an introductory overview . * 44 , * 307 - 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in circumstellar disks , the major sources of dust are thought to be minor bodies , like comets . both the stellar radiation drag ( poynting - robertson drag ) and stellar wind drag tend to induce dust inflow toward the star . as the dust passes by planets in its infall , it interacts with them , for example , by accumulating in planetary resonances ( liou & zook 1999 , ozernoy et al . the inner region of the @xmath0 pictoris dusty disk is tilted by a few degrees with respect to the outer disk ( burrows et al . 1996 , mouillet et al . 1997 , heap et al . 2000 ( for references , see the last paper ) . heap et al . ( 2000 ) concluded that the size and shape of the warp favors the presence of a planet(s ) in a slightly inclined orbit . the dynamics of interplanetary particles are determined by several effects , including stellar radiation pressure ; the poynting - robertson ( p - r ) and stellar wind drags ; resonance effects by planets ; and gravitational encounters with planets . to simulate the gravitational dynamics of comets and nonconservative dynamics of dust particles around a star , we use an implicit second - order integrator ( taidakova & gorkavyi , 1999 ) . in the absence of a planet , the surface density of dust between the star and the pericenter of dust sources is constant , while the number density of dust varies as @xmath2 , @xmath3 being heliocentric distance ( gorkavyi et al . the presence of a planet induces dramatic changes in the cometary and dust distribution . this is illustrated in fig . 1 , which shows a representative trajectory of dust particles . [ ! ht ] [ ! ht ] two algorithms for modeling the @xmath0 pictoris disk were considered . _ algorithm i _ : \1 . input an initial symmetric cometary disk . input the mass and orbital radius of the planet on an orbit inclined to the initial cometary disk . simulate the asymmetric dust distribution on a time scale of @xmath4 yrs . inclination of particles orbits to the plane of the initial cometary disk and asymmetry of dust is the result of precession of drifting particles around the planet s orbital plane ( see fig . 1 ) . simulate the dust - scattered light distribution . : \1 . input an initial symmetric cometary disk . input the mass and orbital radius of the planet on an orbit inclined to the initial cometary disk . determine the asymmetric distribution of comets due to orbital precession and gravitational scattering by the planet ( these processes can be realized without any drifts ) after @xmath5 yrs . simulation of the asymmetric dust distribution for short life times of particles . asymmetry of dust is mainly a result of an asymmetry in the initial cometary distribution . simulate the dust - scattered light distribution ( see fig . 2 ) . both alternatives produce a similar warp , but the second alternative seems to be more preferable due to : * a more realistic ( shorter ) lifetime of particles ; * accounting for gravitational interactions between comets and the planet . the stis images show the disk to be warped at small distances to the star in a sense that the inner disk is tilted by @xmath6 with respect to the outer disk ( heap et al . see fig . 2 to compare the stis observations with our modeling . asymmetric structures in the circumstellar disk indicate at least one planet embedded in the disk of @xmath0 pictoris .

our efficient numerical approach has been applied to modeling the asymmetric circumstellar dust disk around @xmath0 pictoris as observed with the hst / stis . we present a new model on the origin of the warping of the @xmath0 pic disk . we suggest that the observed warp is formed by the gravitational influence of a planet with a mass of about 10 masses of earth , at a distance of 70 au , and a small inclination ( @xmath1 ) of the planetary orbit to the main dust disk . results of our modeling are compared with the stis observations .

convection near solar surface has strongly non - local and dynamical character . hence numerical simulation provide useful information on the structure spatial scales by convection and help to construct consistent models of the physical processes underlying the observed solar phenomena . we investigate effects of compressibility and weak of magnetic field on formation non - local structure of convection using realistic physics and conservative tvd numerical scheme of godunov type . the previous simulations were confined by small computational domain and studied processes on scales order size of granulation [ @xcite ] . in order to investigate collective interaction of convective modes different scales and process of formation of supergranulation we conducted calculation in three dimensional computational box by size 30 mm in horizontal direction and by size 18 mm in vertical direction . we take distribution of the main thermodynamic variables by radius due to standard solar model [ @xcite ] with parameters @xmath0 , where @xmath1 and @xmath2 are hydrogen and helium abundance by mass , and @xmath3 is the ratio of mixing length to pressure scale height in convection region . we use opal opacities and equations of state for solar matter [ @xcite ] . we solve fully compressible nonideal magnetohydrodynamics equations : @xmath4 @xmath5 = \rho \vec g + \nabla \cdot \tau\ ] ] @xmath6\ ] ] @xmath7 @xmath8 where @xmath9 is the total energy , @xmath10 is the energy transferred by radiation and @xmath11 is viscous stress tensor . we assume that small scales are independent of resolved scales ( large eddy simulations ) and rate dissipation is defined from buoyancy and shear production terms [ @xcite ] . the numerical method that we used was an explicit godunov - type conservative tvd difference scheme [ @xcite ] @xmath12 where @xmath13 and operator @xmath14 is @xmath15 flux along each direction , for example x , was defined by local - characteristic method as follows @xmath16\ ] ] where @xmath17 is matrix whose columns are right eigenvectors of @xmath18 evaluated at generalized roe average for real gases of @xmath19 and @xmath20 . the @xmath21 is the matrix of numerical dissipation . term @xmath22 is accounted effect of gravitation forces and radiation . the one step of time integration is defined by runge - kutta method [ @xcite ] as @xmath23 @xmath24 @xmath25 the scheme is second order by space and time . for approximation viscous terms we used central differences . for evaluation radiative term in energy equation we used the diffusion approximation @xmath26\ ] ] we use uniform grid in x - y directions and nonuniform grid in vertical z one . we apply periodic boundary condition in horizontal planes and choose on the top and bottom as follows @xmath27 @xmath28 @xmath29 in initial moment magnetic field equal 50 g and has just one vertical component . for the magnetic diffusitvity we take constant value @xmath30@xmath31sec@xmath32 on the figures 1 - 4 results of development convection after 12 solar hr mhd numerical simulation are shown . we founded that magnetic field concentrate on the boundary of convective cells in forms magnetic flux and sheets . diverging of convective flows from centre supergranular expell weak magnetic field on the edges of convective cell . average size of supergranular celss is 10 - 20 mm with lifetime about 8 - 10 hours . we aplly procedure averaging by interval time two hour and find value of velocity from centre supergranular equal to 1 - 1.5 km / sec . in places action of strong magnetic field with strength 700 - 900 g we observe effect of suppression of convection and decreasing of fluctuation of temperature . magnetic pressure in regions concentration of magnetic flux prevent inflow of matter . transfer of radiation energy in these places is suppressed . we founded from simulation that maximum of value of magnetic field in computational domain equal to 1300 g. inside of supergranular we have usual picture of evolution of convection on scale of granulation with average sizes of cells about 1 - 2 mm and lifetimes about 10 minutes . here we see wider upflows of warm , low density , and entropy neutral matter and downflows of cold , converging into filamentary structures , dense material . we observe continuous picture formation and destruction of granules . granules with highest pressure grow and push matter against neighboring granules , that then shrink and disappear . ascending flow increases pressure in center of granule and upflowing fluids decelerates motion . this process reduce heat transport to surface and allow material above the granule to cool , become denser , and by action gravity to move down . we observe formation new cold intergranule lane splitting the original granule . from figure 4 we see distinctly existence three different regions development of convection . in near of solar surface to the depth 4 mm we founded zone of turbulent convection . in this region cold blobs of matter move down with velocity in maximum about 4 km / sec with maximum mach number equal 1 . the downdrafts has different and very complicate vertical structure . some ones travel small distance from surface and become weak enough to be broken up by the surrounding fluid motion . other ones conserve motion with high velocity and move on distance about 6 mm . we observe that different nature such behavior is due to initial condition of formation downdrafts . in place of confluence of convective cells to one point more energy is released . in region from 5 mm to 8 mm of depth we reveal more quiet character of convective flow than in turbulent zone . below 8 mm we see clear separate large scale density fluctuations and streaming flow of matter similar jets with average velocity about 1km / sec . the magnetic field in these places has values about 300 g . distance beetween different narrow jets gives size of supergranular cells . places of intersections of path jets with horizontal plane are vertices of huge convective cells . from distribution iso - surface of magnetic field with strength 500 g we have discovered that pumping of magnetic field occupy more part of all computational domain up to bottom boundary . magnetic field near solar surface in our numerical simulation has very complicate structure . inside supergranular cells we see formation , growth and evolution with time many arising to surface loops of magnetic field . there is places in vertices of huge cells with vorticity motion that provide quick rate magnetic helicity transport across solar photosphere(fig.5,6 ) . on the boundary supergranular cell magnetic field has just vertical component . in these parts we observe quick changing sign and big values of current helicity(fig.7 ) . i would like to thank gary zank and nikolai pogorelov from riverside university for financial support for participation me in conference astronum-2006 .

three - dimensional magnetohydrodynamical large eddy simulations of solar surface convection using realistic model physics is conducted . the effects of magnetic fields on thermal structure of convective motions into radiative layers , the range of convection cell sizes and penetration depths of convection is investigated . we simulate a some portion of the solar photosphere and the upper layers of the convection zone , a region extending 30 x 30 mm horizontally from 0 mm down to 18 mm below the visible surface . we solve equations of the fully compressible radiation magnetohydrodynamics with dynamical viscosity and gravity . for numerical simulation we use : 1)realistic initial model of sun and equation of state and opacities of stellar matter , 2 ) high order conservative tvd scheme for solution magnetohydrodynamics , 3 ) diffusion approximation for solution radiative transfer 4 ) calculation dynamical viscosity from subgrid scale modelling . simulations are conducted on horizontal uniform grid of 320 x 320 and with 144 nonuniformly spaced vertical grid points on the 128 processors of supercomputer mbc-1500 with distributed memory multiprocessors in russian academy of sciences .

atlas will be a particle physics experiment at the future large hadron collider ( lhc ) , which is being built at cern and is expected to start operation in 2007 . the pixel detector is the innermost component of the atlas inner tracker . in the barrel the detector modules are mounted on staves , while the modules in the end caps are organized in disk sectors . the pixel detector consists of 1774 detector modules ( barrel : 1456 modules ; discs : 318 ) . @xmath0 + the most important components of a detector module are : * 46080 individual pixel sensors with size of @xmath1 * 16 front end read out chips * 1 module controller chip the pixel stave is the module local support unit of the barrel section of the pixel detector . the components of a stave are the thermal management tile ( tmt ) , the stave carbon structure , and the stave cooling circuit . additionally , every stave has two geometrical reference marks ( ruby balls ) . the stave coordinate system is specified in figure [ fig : altube ] . the tmt itself consists of two parts . both parts have a shingled design with an angle of 1.1 degrees which are glued together . as material for the tmts , carbon - carbon ( c - c ) has been chosen . the reason for this is a thermal conductivity which is 10 - 100 times better than standard carbon fiber reinforced plastic ( cfrp ) , even in the transverse direction to the fibres . it has excellent mechanical properties , stability , and transparency to particles . the tmt is made of 1502 zv 22 c - c material from sgl ( augsburg , germany ) . the raw material is in the form of plates of about 6 mm thickness . the plates consist of 2-d roving fabric carbon fibres layers overlapped in a phenolic resin matrix , densified , and graphitized at high temperature to enhance the thermal properties . the raw tmts are machined to the final stepping shape with a cnc milling machine equipped with high speed spindle and diamond coated millers . the specific properties of the material are summarized in table [ tab : propertiesofsglcc1502zv22 ] . .properties of sgl cc 1502 zv 22 [ cols="<,<,<",options="header " , ] the stave cooling circuit is made of a thin aluminum tube ( see figure [ fig : altube ] ) , shaped to fit inside the inner cross section of the stave carbon structure . the material chosen is 6060 aluminum alloy . this material shows good extrusion properties at small thickness . the cooling system is based on the evaporation of fluorocarbon and provides an operating temperature of about @xmath2 . the stave carbon structure ( `` omega profile '' ) is made of three layers of unidirectional ultra high modulus ( uhm ) carbon fibre reinforced cyanate ester resin pre - preg ( preimpregnated ) . the adopted lay - up ( 0 - 90 - 0 ) , 0.3 mm thick , has been optimised through an extensive design and test program . the choice of the pre - preg material and of the lay - up with a central cross - layer has been made in order to match the longitudinal cte to that of the impregnated c - c , thus minimizing distortions resulting during cool - down . the 13 modules are arranged one after the other along the stave axis and they are partially overlapped in order to achieve the required coverage in the axial direction . thus , the surface of the stave in contact with the modules is stepped and the modules are arranged in a shingled layout . however , c - c materials have two main technological drawbacks limiting their application range : porosity and difficulty to achieve complex and accurate geometries due to the high temperature manufacturing process . to overcome the porosity of the c - c material , it was impregnated with resin such that infiltration by the thermal greases and carbon dust release could be avoided . for the assembly of modules on staves a custom made module loading machine was developed and built in wuppertal . the requirements of this machine are : * handling the modules with minimal stress * positioning of modules on the stave with an accurancy better than 50 microns * regular glue deposition + to control the applied stress the bow of each module is measured before and after loading . the main components of the module loading machine are the granite base of @xmath3 and a flatness of @xmath4 from johan fischer . on this base several linear guideways from schneebergertype monorail bm are mounted to allow movement of the central measurement unit , the microscope m 420 from leica . the microscope itself is connected to owismicrometric tables and allows movements in all dimensions . the movements are controlled by heidenhainsealed linear encoders . heidenhain digital readouts type nd 760 are used for displaying and storing the position of the m 420 using a personal computer . the module mounting head is connected to several linear guides , goniometer and rotary tables to reach any position . the module is fixed by vacuum to the mounting head and its position is always monitored by the microscope . for the deposition of the glue a computer controlled dispenser from efdtype 1502 the assembly time of each module is about 1 hour , the curing time of the glue is 2 hours . this leads to a production rate of 1 stave per week . the x , y , and z position of the glued modules of each stave is controlled with respect to the stave ruby balls . these provide the reference system for the module position and allow one to assess the accuracy of the loading procedure . as a typical result the z position measurement for 13 staves is provided in figure [ fig : z - deviation_modwise ] . for each stave the deviation from the nominal position is shown for each of the 13 modules . the stated module i d s are equivalent to defined locations on the stave . the tolerances are @xmath5 and are indicated in the figure by thicker lines . the plot shows that the accuracy of the z positioning is always within the tolerances of @xmath6 . in figure [ fig : z - deviation_distribution ] , the distribution of the z - deviation is given and demonstrates that 50% of the modules are glued with an accuracy which is even better than @xmath7 . one can also see that there is a systematic shift of 6 - 7@xmath8 . as mentioned previously , the difference between the bow of the module before and after loading is an indicator as to whether stress has been applied during the loading procedure . figure [ fig : bow ] shows the mean bow difference ( mean value ) , averaged over all 13 modules of one stave , as well as the standard deviation ( sd ) and the average of the absolute values ( mean of amounts ) . one can see , that the bow difference is always better than @xmath9 . this is interpreted to show that a minimum of stress is being applied to the modules during the loading procedure . a module loading machine for the atlas pixel detector has been successfully realized in wuppertal . all requirements of the mounting precision are fulfilled . the position of the modules after loading are well within the tolerances . the applied stress during loading is negligible . this work has been supported by the _ bundes - ministerium fr bildung , wissenschaft , forschung und technologie _ ( bmbf ) under grant number05 ha4px1/9 . atlas technical proposal cern / lhcc/94 - 43 , 15 december 1994 . pixel detector technical design report cern / lhcc/98 - 13 . atlas detector and physics performance technical design report cern / lhhc/99 - 14 . b - layer ( atl - ip - cs-0009 ) , layer 1 and 2 specifications ( atl - ip - cs-0007 ) . pitch based carbon fibre ys80 ( data sheet ) , nippon graphite fiber ( ngf ) . available from : http://plaza6.mbn.or.jp/~gf/english/products/space/ysa.html . cyanate ester resin system ex1515 ( data sheet ) , bryte technologies inc . available from : http://www.brytetech.com/pdf-ds/ex-1515.pdf .

the barrel part of the atlas pixel detector will consist of 112 carbon - carbon structures called `` staves '' with 13 hybrid detector modules being glued on each stave . the demands on the glue joints are high , both in terms of mechanical precision and thermal contact . to achieve this precision a custom - made semi - automated mounting machine has been constructed in wuppertal , which provides a precision in the order of tens of microns . as this is the last stage of the detector assembly providing an opportunity for stringent tests , a detailed procedure has been defined for assessing both mechanical and electrical properties . this note gives an overview of the procedure for affixation and tests , and summarizes the first results of the production . , , , , , , , , pixel detector , stave , mounting machine

vw ari ( hd 15165 , bds 1269 ) is a remarkable visual binary system consisting of two components : vw ari a ( v=6.@xmath671 , a - type ) and its companion ( v=8.@xmath633 , f - type ) . the primary vw ari a is a multiperiodic pulsating star ( probably of @xmath7 sct - type ) having non - radial modes . this star shows the spectrum typical of very metal - deficient stars . the rather high @xmath8 value found for this star , makes it difficult to derive accurate elemental abundances . a first attempt was undertaken by andrievsky et al . ( 1995 ) , who showed that calcium and iron are strongly deficient in the atmosphere of vw ari a , while the secondary component possesses a solar - like chemical composition . such a strange discrepancy between the metallicities of the two components can be explained by several hypotheses . for example , these stars possibly do not constitute a physical pair or , in case they do , such an unusual stellar system could be formed as a result of stellar capture . nevertheless , taking into account that 1 ) with a rather high probability vw ari is a binary system and 2 ) the probability of stellar capture in the field is too small , we propose that the difference in chemical composition of both components could appear simply due to the peculiar evolution of vw ari a as a @xmath2 boo - type star . the atmospheres of this type of stars are known to be strongly deficient in some heavy metals , while cno - elements exhibit solar - like abundances ( see e.g. strenburg , 1993 ) . to check this hypothesis , we performed a detailed spectroscopic analysis of vw ari ( primary component of the system ) based on the spectral synthesis technique . seven ccd spectra have been obtained on 21 november 1994 with the chelle spectrometer lynx ( modified version : 29 spectral orders with the length of each order @xmath9 60 ) on the 6-m telescope ( special astrophysical observatory of the russian academy of sciences , russia , northern caucasus ) . the detailed description of the spectrometer is given by panchuk et al . the resolving power was 24000 , s / n @xmath9 100 . the spectral region was 5035 - 7185 . the epochs at mid - exposures were the following : jd 2449670 + 1 ) 8.158 , 2 ) 8.165 , 3 ) 8.186 , 4 ) 8.215 , 5 ) 8.232 , 6 ) 8.247 , 7 ) 8.263 . all spectra have been reduced using the dech20 code ( galazutdinov , 1992 ) , which includes extraction of spectra from images , dark and cosmic hits subtraction , flat - field correction , wavelength calibration , etc . the effective temperature and gravity for vw ari a ( t@xmath0=7200 k , @xmath1=3.7 ) were estimated using the photometric indices @xmath10 and @xmath11 , and the calibration by kurucz ( 1991 ) . we adopted a microturbulent velocity of 3 kms@xmath12 , which is appropriate for a - f main - sequence stars , and @xmath13 kms@xmath12 was taken from abt ( 1980 ) . the starsp code ( tsymbal , 1996 ) was applied to derive the elemental abundances . the atmosphere model was interpolated from kurucz s ( 1992 ) grid . the input oscillator strengths of the investigated lines and blends were initially corrected by comparison of the solar synthetic spectrum ( solar model from kurucz s grid , @xmath14 kms@xmath12 and solar abundances from grevesse and noels , 1993 ) with the solar flux spectrum ( kurucz et al . 1984 ) . the resulting abundances were found by means of the optimal fitting of the synthetic spectrum to the observed one . they are given in table 1 . .abundances for vw ari a [ cols="<,^,^,^,^,^,^,^,^,^,^,^,^,^ " , ] the abundance pattern in the atmosphere of vw ari resembles that of @xmath2 boo - type stars ( see , e.g. strenburg , 1993 , andrievsky et al . , 1998 ) : normal abundances ( or slight underabundances ) of carbon and oxygen and strong deficiency of other elements . an additional confirmation that vw ari could be a @xmath2 boo star is its position in @xmath15 diagrams . this star possesses photometric characteristics which place it exactly in the region occupied by @xmath2 boo stars . supposing that vw ari belongs to the @xmath2 boo group , one can also easily explain the remarkable difference between the metallicities of this star and of its companion f - star with solar - like abundances ( andrievsky et al . , 1995 ) . abt , h.a . : 1980 , _ publ . _ , * 92 * , 796 andrievsky , s.m . , chernyshova , i.v . , usenko , i.a . , kovtyukh , v.v . , panchuk , v.e . , galazutdinov , g.a . : 1995 , _ publ . _ , * 107 * , 219 andrievsky , s.m . , chernyshova , i.v . , klochkova , v.g . , panchuk v.e . , 1998 , these proceedings galazutdinov , g.a . : 1992 , _ prepr . sao ras _ , * no.92 * , 1 grevesse , n. , noels , a. : 1993 , _ origin and evolution of the elements _ , eds . n. prantzos , e. vangioni - flam and m. cass , _ cambridge univ . press _ , 14 kurucz , r.l . : 1991 , _ precision photometry : astrophysics of the galaxy _ , + eds . a.g.d . philip , a.r . upgren and k.a . l. davis press _ , 1 kurucz , r.l . : 1992 , _ the stellar populations of galaxies _ , eds . b. barbuy , a. renzini , _ iau symp . 149 _ , 225 kurucz , r.l . , furenlid , i. , brault , i. and testerman l. : 1984 , _ the solar flux atlas from 296 nm to 1300 nm _ , national solar observatory panchuk , v.e . , klochkova , v.g . , galazutdinov , g.a . , ryadchenko , v.p . and chentsov , e.l . : 1993 , _ sov . _ , * 19 * , 11 paunzen , e. , weiss , w.w . , heiter , u. and north , p. : 1997 , _ astron . _ , * 123 * , 93 strenburg s. , 1993 , a&a 277 , 139 tsymbal , v. : 1996 , _ model atmospheres and spectrum synthesis _ , eds . s.j . adelman , f. kupka and w.w . weiss , _ asp conf . _ , * 108 * , 198

seven high - resolution and high s / n ccd spectra were used to derive elemental abundances in the atmosphere of vw ari a ( t@xmath0=7200 , @xmath1=3.7 ) which is the primary component of a visual binary system . the synthetic spectrum technique applied in the analysis allowed to reveal the following feature : the atmosphere of this star is strongly deficient in some metals , while light elements have solar - like abundances . taking into account these results , one can suggest that vw ari a is a @xmath2 boo - type star . another argument supporting this supposition is the following : on the diagrams `` @xmath3 '' , `` @xmath4 '' and `` @xmath5 '' ( paunzen et al . 1997 ) vw ari a falls exactly in the region occupied by the @xmath2 boo stars . note also , that a previous analysis ( andrievsky et al . 1995 ) has shown that the secondary component of vw ari has a normal metallicity . differences in chemical compositions of the two components appear to be due to the specific evolution of the primary vw ari a.

the radio far infrared ( fir ) correlation is one of the tightest observed correlations in astrophysics that connects several independent physical parameters in the interstellar medium ( ism ) . the radio luminosity and the fir luminosity of star - forming galaxies are observed to be correlated over five orders of magnitude for the global scale @xcite with dispersion less than a factor of 2 . the radio luminosity is typically measured at 1.4 ghz and the fir luminosity can be both monochromatic ( at 24 , 60 or 70@xmath1 m ) or bolometric ( between 40 and 120@xmath1 m or between 8 and 1000@xmath1 m ) . the radio fir correlation is well studied for galaxies in the local universe for several classes of galaxy morphology like spirals , ellipticals , dwarf irregulars , etc . it is known to hold good at global @xcite as well as at local scales ( few 100 pc to few kpc ) within galaxies @xcite . at the brightest end of fir luminosity , the relationship is observed to hold for ( ultra ) luminous infrared galaxies [ ( u)lirg ] and star - burst galaxies . at the faintest end it holds in dwarf galaxies @xcite . it is believed that star - formation connects the two regimes of emission . synchrotron ( also referred to as non - thermal ) emission in the radio band is caused by acceleration of cosmic ray electrons ( cres ) in the galactic magnetic field produced by supernova explosions of massive stars . in the fir , the emission originates due to dust re - radiation , heated by ultraviolet ( uv ) photons from massive ( @xmath13 ) , short lived ( @xmath14 yrs ) stars . however , the tightness seen in the correlation needs to be explained , as a number of independent physical quantities are responsible for the emission in each regime like , the magnetic field , number density of cres , energy losses of cres , star formation history , dust / gas density , dust absorption efficiency , etc . several models have been proposed to explain the tightness seen in the radio fir correlation ( see e.g. ; * ? ? ? * ; * ? ? ? * ; * ? ? ? more recent models by @xcite and @xcite have shown that the above mentioned factors conspire to maintain the tightness observed for the global radio fir correlation . observationally , it is important to assess the form of the radio fir correlation at high redshifts as it might depend on the evolution of ism parameters with redshift ( @xmath0 ) like synchrotron and inverse - compton losses , dust content , star formation rate , magnetic field strength and overall sed ( see e.g. ; * ? ? ? * ; * ? ? ? * ; * ? ? ? recently , @xcite predicted a modification of the form of the radio fir correlation , based on the observed relationship between magnetic field strength and star formation rate caused due to turbulent amplification of the magnetic field . a breakdown in the correlation is expected depending on the dominant energy loss mechanism of the cres in the radio domain , i.e. , synchrotron , inverse - compton , bremsstrahlung and/or ionization losses . typical ( 1@xmath15 ) sensitivity of most of the existing deep radio surveys are limited only to few tens of @xmath1jy ( see e.g. , @xcite [ vla - vvds ] ; @xcite [ vla - cosmos ] ; @xcite [ evla - stripe82 ] , etc . ) . however , a few deeper surveys exists reaching 1@xmath15 sensitivity @xmath16jy ( see e.g. , @xcite [ e - cdfs ] ; @xcite [ goods - n ] ) . these observations can detect normal galaxies ( @xmath17 ) up to redshift of @xmath18 at 1.4 ghz with @xmath19 sensitivity , making it difficult to study the radio fir correlation for such galaxies at higher redshifts . the correlation has been studied for ( u)lirgs with higher luminosity ( @xmath20 ) up to redshifts of @xmath21 @xcite . such galaxies can have significant contamination due to agns and compact nuclear starbursts . even in the case of relatively low optical depth , starburst related free free absorption can give rise to substantial obscuration @xcite that can affect the form of the correlation . it is therefore imperative to study the radio fir correlation for less extreme star - forming galaxies at _ high redshifts _ where the bulk of the radio and fir emission originates from star formation . in this paper , we study the properties of the radio fir correlation , both the slope and the traditionally defined ` @xmath22 ' parameter , for a flux limited and color selected sample in the xmm - lss field . we explore the correlation for blue star - forming galaxies up to @xmath3 employing the technique of image stacking . due to the inherent flux limitation of the parent sample , we detect normal star - forming galaxies up to @xmath23 and more luminous galaxies above that . for comparison , we study the correlation for luminous galaxies that are directly detected in this field up to @xmath24 0.95 . the paper is organized as follows : in section 2 , we describe our sample selection and data . we discuss the technique of image stacking at 0.325 ghz and 1.4 ghz in the radio and at 24 , 70 , 160 , 250 , 350 and 500 @xmath1 m in the fir and the @xmath5correction method in section 3 . we present our results in section 4 and discuss them in section 5 . throughout this paper , we assume a flat @xmath25cdm model with @xmath26 , @xmath27 and @xmath28 .

we study the radio far infrared ( fir ) correlation in `` blue cloud '' galaxies chosen from the prism multiobject survey ( primus ) up to redshift ( @xmath0 ) of 1.2 in the xmm - lss field . we use rest - frame emission at 1.4 ghz in the radio and both monochromatic ( at 70@xmath1 m ) and bolometric ( between @xmath2 m ) emission in the fir . to probe the nature of the correlation up to @xmath3 , where direct detection of blue star - forming galaxies is impossible with current technology , we employ the technique of image stacking at 0.325 and 1.4 ghz in the radio and in six infrared bands , viz . 24 , 70 , 160 , 250 , 350 and @xmath4 m . for comparison , we also study the correlation for more luminous galaxies that are directly detected . the stacking analysis allows us to probe the radio fir correlation for galaxies that are up to 2 orders of magnitude fainter than the ones detected directly . the @xmath5correction in the infrared wavebands is obtained by fitting the observed spectral energy distribution ( sed ) with a composite mid - ir power law and a single temperature greybody model . we find that the radio luminosity at 1.4 ghz ( @xmath6 ) is strongly correlated with monochromatic fir luminosity at 70 @xmath1 m ( @xmath7 ) having slope @xmath8 and with bolometric luminosity ( @xmath9 ) having slope @xmath10 . the quantity @xmath11)$ ] is observed to decrease with redshift as @xmath12 probably caused due to the non - linear slope of the radio fir correlation . within the uncertainties of our measurement and the limitations of our flux - limited and color - selected sample , we do not find any evolution of the radio fir correlation with redshift .

there is a serious question as to whether the specified gradients of rf cavities operating under vacuum would operate in the specified magnetic fields . this is under study by nfmcc collaboration @xcite and alternative designs using high pressure hydrogen gas , or open cell rf with solenoids in the irises , are being considered . the bunching and phase rotation will be optimized for the muon collider , instead of being copied from a neutrino factory . instead of the slow helices , a planar wiggler lattice is being studied that would cool both muon signs simultaneously , thus greatly simplifying the system . the use of more , but lower field ( e.g. , 35 t ) final cooling solenoids is also under study . experiments are underway to demonstrate two of the new technologies : mercury target @xcite , ionization cooling @xcite . further experimental studies are needed . although much work remains to be done , the scenario outlined here appears to be a plausible solution to the problems of capturing , manipulating , and cooling muons to the specifications for muon colliders with useful luminosities and energies , even up to 8 tev in the center of mass . 99 g. i. budker , quoted and translated in @xcite . d. cline , in _ physics potential and development of @xmath4 colliders : second workshop ; sausalito , ca 1994 _ , edited by d. cline ( american institute of physics , woodbury , ny , 1996 ) , pp . 36 . a. n. skrinsky , quoted and translated in @xcite ; v. v. parkhomchuk and a. n. skrinsky , in _ proceedings of the 12th international conference on high energy accelerators , 1983 _ , edited by f. t. cole and r. donaldson , 485 ; d. neuffer , fermilab report fn-319 , 1979 ; d. neuffer , part . * 14 * , 75 ( 1983 ) ; d. v. neuffer and r. b. palmer , in _ fourth european particle accelerator conference _ , edited by v. suller and ch . petit - jean - genaz ( world scientific , singapore , 1994 ) , p. 52 . the @xmath4 collaboration , reports bnl-52503 , fermi lab - conf . 96/092 , lbnl-38946 , 1996 . http://www.muonsinc.com h. g. kirk _ _ , _ a high - power target experiment at the cern ps _ pac07 , albuquerque , nm , ( mopas094 ) . y. alexahin and e. gianfelice - wendt , fermilab report beams - doc-2724-v1 , 2007 . url : http://beamdocs.fnal.gov/adpublic/docdb/documentdatabase d. neuffer , report nfmcc - doc-269-v1 , 2003 . url : http://nfmcc-docdb.fnal.gov/cgi-bin/documentdatabase/ icool , http://pubweb.bnl.gov/people/fernow/icool/readme.html j. s. berg _ et al . _ , phys . rev . beams * 9 * , 011001 ( 2006 ) . r. palmer _ et al . _ , phys . st accel . beams * 8 * , 061003 ( 2005 ) . amit klier , presentation at the low emittance muon collider workshop , fermilab ( 6 - 10 feb 2006 ) . url : http://www.muonsinc.com/mcwfeb06/ g. b. lubkin , phys . today 47n12 , 21 ( 1994 ) . http://www.superpower-inc.com/20070807.aspx s. a. kahn _ et al . _ , _ a high field hts solenoid for muon cooling _ pac07 , albuquerque nm , ( mopan118 ) . summers _ et al . _ , _ muon acceleration to 750 gev in the tevatron tunnel for a 1.5 tev @xmath5 collider _ , pac07 , albuquerque nm , ( thpms082 ) ; also arxiv:0707.0302 . m. zisman , _ status of the international muon ionization cooling experiment _ , pac07 , albuquerque nm , ( thpmn119 ) ; p. drumm , _ mice : the international muon ionisation cooling experiment _ , pac07 , albuquerque nm , ( roaa004 ) .

a complete scheme for production , cooling , acceleration , and ring for a 1.5 tev center of mass muon collider is presented , together with parameters for two higher energy machines . the schemes starts with the front end of a proposed neutrino factory that yields bunch trains of both muon signs . six dimensional cooling in long - period helical lattices reduces the longitudinal emittance until it becomes possible to merge the trains into single bunches , one of each sign . further cooling in all dimensions is applied to the single bunches in further helical lattices . final transverse cooling to the required parameters is achieved in 50 t solenoids . .5 in .parameters of three muon colliders . note 1 : depth is relative to any nearby low land , e.g. fox river at fnal . note 2 : survival is from the end of phase rotation to the collider ring . [ cols="<,^,^,^ " , ] [ tuneshift ] note that @xmath0 is larger at earlier cooling stages to allow for losses . the first order shifts can be corrected by increasing the focus strength , but tune spreads of half the shifts can not be corrected . before the merge , the shifts are small because the numbers of muons per bunch are small . the only 6d cooling stage with significant tune shift is the last ( # 8) . its tune accepted @xmath1 which is 5 times the calculated maximum full tune spread of @xmath2 7.3% , and is not expected to be a problem . the tune shifts in the 50 t cooling will be significant only during the reaccelerations , where we have assumed @xmath3s corresponding to 3 t focusing fields . the design of these lattices to accept such tune shifts appears possible , although we are clearly nearing the limit .

we are grateful to andrew przeworski for very helpful correspondence concerning his work , jeff weeks for many useful comments , and neil cornish for drawing our attention to the reference @xcite . we also thank faperj and cnpq for the grants under which this work was carried out . figure 1 : : the solutions curve of @xmath34 , as plots of @xmath0 ( vertical axis ) versus @xmath48 ( horizontal axis ) , with @xmath2 taken as @xmath10 ( upper curve ) and @xmath38 ( lower curve ) , respectively . the depth of the survey in both cases correspond to a redshift @xmath51 ( cmbr ) . included also is a dashed rectangular box , representing the relevant part , for our purposes , of the hyperbolic region of the parameter space given by recent observations . the undetectable region of the parameter space ( @xmath52 ) corresponding to each value of @xmath53 lies above the related curve . ellis , _ gen . * 2 * , 7 ( 1971 ) ; d.d . sokolov & v.f . shvartsman , _ sov . jetp _ * 39 * , 196 ( 1974 ) ; g.f.r . ellis & g. schreiber , _ phys . a _ * 115 * , 97 ( 1986 ) ; r. lehoucq , m. lachize - rey & j .- p . luminet , _ astron . astrophys . _ * 313 * , 339 ( 1996 ) ; b.f . roukema , _ mon . not . r. astron . _ * 283 * , 1147 ( 1996 ) ; g.f.r . ellis & r. tavakol , _ class . quantum grav . _ * 11 * , 675 ( 1994 ) ; n.j . cornish , d.n . spergel & g.d . starkman , _ proc . sci . _ * 95 * , 82 ( 1998 ) ; n.j . cornish & j.r . weeks , astro - ph/9807311 ( 1998 ) ; g.i . gomero , a.f.f . teixeira , m.j . rebouas & a. bernui , gr - qc/9811038 ( 1998 ) ; r. lehoucq , j .- luminet & j .- p . uzan , _ astron . astrophys . _ * 344 * , 735 ( 1999 ) ; j.p . uzan , r. lehoucq & j.p . luminet , _ astron . _ * 351 * , 776 ( 1999 ) ; h.v . fagundes & e. gausmann , _ phys . lett . a _ * 261 * , 235 ( 1999 ) ; m.j.rebouas _ int . j. mod . d _ * 9 * , 561 ( 2000 ) g.i . gomero , m.j . rebouas & a.f.f . teixeira , _ phys . a _ * 275 * , 355 ( 2000 ) ; g.i . gomero , m.j . rebouas & a.f.f . quantum grav . _ * 18 * , 1885 ( 2001 ) ; r. lehoucq , j.p . uzan & j.p . luminet , astro - ph/0005515 ( 2000 ) ; v. blanlil & b.f . roukema , eds . , in the proceedings of the _ cosmological topology in paris 1998 _ , astro - ph/0010170 . starkman , _ class . quantum grav . _ * 15 * , 2529 ( 1998 ) ; m. lachize - rey & j .- p . luminet , _ phys . rep . _ * 254 * , 135 ( 1995 ) ; ya . b. zeldovich & i.d . novikov , _ the structure and evolution of the universe _ , pages 633 - 640 . the university of chicago press , chicago ( 1983 ) . see also on page 637 of this book the references to earlier works by sveges ( 1966 ) , sokolov ( 1970 ) , paal ( 1971 ) , sokolov and shvartsman ( 1974 ) , and starobinsky ( 1975 ) . d. atkatz & h. pagels , _ phys . rev . d _ * 25 * , 2065 ( 1982 ) ; ya.b . zeldovich & a.a . starobinsky , _ sov . _ * 10 * , 135 ( 1984 ) ; y.p . goncharov & a.a . bystsenko , _ astrophysics _ * 27 * , 422 ( 1989 ) . a.e . _ , _ phys . d _ * 63 * , 042001 ( 2001 ) ; p. de bernardis _ et al . _ , in proceedings of the capp2000 conference , verbier , 17 - 28 july 2000 , astro - ph/0011469 ( 2000 ) ; j.r . et al . _ , in proceedings of neutrino 2000 ( elsevier ) , cita-2000 - 63 , eds . j. law & j. simpson , astro - ph/0011381 ( 2000 ) ; j.r . et al . _ , in proceedings of iau symposium 201 ( pasp ) , cita-2000 - 65 , astro - ph/0011378 ; a. balbi _ _ , _ astrophys . j. _ * 545 * , l1l4 ( 2000 ) . _ , _ astrophys . j. _ * 507 * 46 ( 1998 ) ; a.g . _ , _ astron . j. _ * 116 * , 1009 ( 1998 ) ; s. perlmutter _ _ , _ astrophys . j. _ * 517 * , 565 ( 1999 ) ; s. perlmutter , m.s . turner & m. white , _ phys . _ * 83 * , 670 ( 1999 ) .

using recent observational constraints on cosmological density parameters , together with recent mathematical results concerning small volume hyperbolic manifolds , we argue that , by employing pattern repetitions , the topology of nearly flat small hyperbolic universes can be observationally undetectable . this is important in view of the facts that quantum cosmology may favour hyperbolic universes with small volumes , and from the expectation , coming from inflationary scenarios , that @xmath0 is likely to be very close to one . it is well known that general relativity is a local metrical theory and therefore the corresponding einstein field equations do not fix the global topology of spacetime . this freedom has resulted in a great deal of interest in the possibility that the universe may possess compact spatial sections with a non - trivial topology , which do not necessarily have positive curvature ( see for example @xcite @xcite and references therein ) . interest in such spaces has also come from quantum cosmology , where the existence of the wave function of the universe may require finiteness of the spatial sections ( see for example @xcite ) . also , in the ` tunnelling from nothing ' scenario , manifolds with small compact spatial sections may be more likely to emerge @xcite . furthermore , there is a precise sense in which most compact @xmath1-manifolds are hyperbolic @xcite . together these facts have motivated the study of hyperbolic manifolds with non - trivial topology as possible models for our universe . there has also been two other important developments recently : one observational , the other mathematical . regarding the former , recent observations seem to indicate that the ratio of the total density to the critical density of the universe , @xmath0 , is likely to be very close to one @xcite , with a significant proportion of this energy being in the form of a dark component with negative pressure @xcite . regarding the latter , we first of all discuss briefly some preliminaries and recall that even though at present there is no complete classification of hyperbolic manifolds , a number of important results are known about them , including the two important theorems of mostow @xcite and thurston @xcite . according to the former , geometrical quantities of orientable hyperbolic manifolds , such as their ( finite ) volumes and the lengths of their closed geodesics , are topological invariants . according to the latter , there is a countable infinity of sequences of compact orientable hyperbolic manifolds , with the manifolds of each sequence being ordered in terms of their volumes @xcite , with an overall lower bound which is shown to be greater than 0.28151 @xcite . a natural way to characterize the shape of such manifolds is in terms of the sizes of their closed geodesics . a particularly useful indicator in this regard is the so called _ injectivity radius _ , @xmath2 , defined as the radius of the smallest sphere inscribable in @xmath3 . this in turn allows the definition of a related indicator that has often been utilized in most studies regarding searches for topological multiple images ( see , for example @xcite @xcite ) and references therein ) , namely the ratio of the injectivity radius to the depth @xmath4 of the astronomical survey up to a given redshift @xmath5 [ r_inj ] t_inj=. the crucial point regarding this indicator is that , in any universe for which @xmath6 , there would be no observed multiple images of either cosmic objects or spots of cosmic microwave background radiation ( cmbr ) , and therefore the topology would not be detectable observationally using pattern repetition , no matter how accurate the observations . despite the global inhomogeneity of hyperbolic manifolds this result is location independent and therefore applicable to any observer in the universe . similarly the set of universes for which @xmath7 are observationally detectable through pattern repetitions , at least in principle , for some observers . an important point regarding @xmath2 is that its lower bound in the set of all compact hyperbolic manifolds is zero . thus , no matter what the cosmological parameters ( and the resulting @xmath4 ) , there will always exist compact hyperbolic universes ( with small enough @xmath2 such that @xmath7 ) such that their topologies are detectable observationally , at least by some observers , even though their number will decrease drastically as @xmath8 @xcite . now given the potential importance of the small volume hyperbolic manifolds in connection , e.g. , with quantum cosmology , the question arises as to whether the existence of detectable topologies for all values of @xmath9 still holds if we restrict ourselves only to a set of small volume manifolds . surprisingly , the answer turns out to be in the negative . to see this , we recall an important set of recent mathematical results which show that very small values of @xmath2 do not occur in small volume hyperbolic manifolds , and that there is in fact a lower bound on the lengths of geodesics in any set of small volume closed orientable hyperbolic 3-manifolds @xcite . thus , for example , according to a theorem of przeworski @xcite , the shortest geodesic in closed orientable hyperbolic 3-manifolds with volume less than 0.94274 must have length greater than 0.09 , corresponding to a lower bound on @xmath2 of @xmath10 . an important point for our purposes here is that it can be shown that there are non - zero lower bounds to lengths of shortest geodesics in any set of closed orientable hyperbolic 3-manifolds , whose volumes are smaller than that of the first orientable cusped manifold by any @xmath11 @xcite . to study an important consequence of these results for cosmology , let us assume that the universe can be modelled by a @xmath12-manifold @xmath13 , with a locally hyperbolic isotropic and homogeneous friedmann - lematre - robertson - walker metric in the standard form [ flrw1 ] ds^2 = -c^2dt^2 + r^2 ( t ) . furthermore , let the @xmath1-space be a multiply connected compact quotient manifold of the form @xmath14 , where @xmath15 is a discrete group of isometries of @xmath16 acting freely on @xmath16 . now in order to have @xmath17 , we consider a survey of depth up to the redshift @xmath5 . in this cosmological setting the depth of the survey expressed in units of the curvature radius ( @xmath18 ) is given by is identified with the curvature radius of the spatial section of the universe at time @xmath19 , and thus @xmath20 can be interpreted as the distance of any point with coordinates @xmath21 to the origin of coordinates ( in @xmath16 ) , in units of curvature radius , which is a natural unit of length and suitable for measuring areas and volumes . throughout this letter we shall use this natural unit . ] @xmath22^{-1/2 } dx \ ; , \ ] ] where the current content of the universe is taken to be dust ( of density @xmath23 ) plus a cosmological constant @xmath24 , with @xmath25 , @xmath26 , @xmath27 , and where the index @xmath28 denotes evaluation at present time . now to examine the consequences of the above theorem in the light of recent cosmological observations , recall that as @xmath8 , the curvature radius increases , resulting in a decrease in @xmath4 , and as a result the set of topologies that would be observationally detectable would have to possess @xmath2 approaching zero in order to ensure @xmath29 . the above mathematical results , with their lower bounds on @xmath2 , have the consequence that the topology of small hyperbolic universes would be undetectable for values of @xmath0 close enough to one . the important point being that the range of @xmath0 for which the topology of such universes are undetectable turns out to be within the range of values of @xmath0 allowed by recent observations , and particularly those suggested by the inflationary scenarios . to quantify this , we proceed in the following way . the above theorem gives the lower bound on @xmath2 in a set of small volume manifolds ( those manifolds with volume less than 0.94274 , which includes at least the weeks manifold ) to be 0.045 . this allows bounds to be imposed on the ranges of cosmological parameters for which the topology is undetectable . we note that 0.045 is the best estimate available at present and the true lower bound on @xmath2 may be greater . a way of dealing with this possibility is to consider the first 51 smallest manifolds of the hodgson - weeks census of closed hyperbolic manifolds . this set contains all manifolds of the census with volumes smaller than the volume of the first cusped manifold . we note that the volumes of the last 7 manifolds in this set differ from the volume of the first cusped hyperbolic orientable manifold by a factor which is smaller than @xmath30 , thus giving an idea of the size of the above mentioned @xmath31 for the set of manifolds considered here . the manifold in this set with the lowest @xmath32 is the eighteenth manifold in the census , denoted by @xmath33 , with volume 1.58865 . figure 1 gives a plot of the solution curve of equation @xmath34 in the @xmath35@xmath36 plane for @xmath37 and @xmath38 , where a survey of depth @xmath39 ( corresponding to the redshift of the surface of last scattering , cmbr ) was used . also included in this figure is a dashed rectangular box , representing the relevant part ( for our purposes here ) of the hyperbolic region of the parameter space ( @xmath40 $ ] and @xmath41 $ ] ) given by recent observations @xcite . for each value of @xmath2 undetectablilty is ensured for the values of cosmological parameters ( region in the @xmath35@xmath42 plane ) which lie above the corresponding curve . thus for @xmath43 , all closed orientable hyperbolic manifolds ( universes ) with volumes less than 0.94274 would have undetectable topology , if the total density @xmath0 turned out to be higher than @xmath44 . on the other hand , for @xmath45 , the topology of none of the 51 manifolds of the census ( whose volumes range from 0.94271 to 2.02988 ( corresponding to the manifold @xmath46 ) , and which includes the weeks manifold ) would be detectable , if the total density @xmath0 turned out to be higher than @xmath47 . clearly , the actual precise bounds on @xmath0 depend on the precise value of the @xmath48 employed . the resulting allowed changes in the bounds on @xmath0 due to employing other values in the observed range of @xmath48 are , however , small , as can be seen from figure 1 . similarly , one can easily find the corresponding ranges of @xmath0 for any other particular manifold or finite set of small manifolds . the important point is the existence of a lower bound on @xmath2 for any finite set of small volume manifolds ( smaller , by any @xmath11 , than the volume of the first cusped orientable hyperbolic manifold ) , which in turn gives lower bounds on @xmath49 , such that the topology of the universe is not detectable with methods based on the search for pattern repetitions . , cornish _ et al . _ @xcite have argued that even for these large volume hyperbolic manifolds @xmath3 , it is very unlikely that the earth is in a region whose closed geodesics are as short as the shortest closed geodesics of @xmath3 . thus , according to @xcite the chances of detecting the topology of these ( large ) hyperbolic universes are also very low according to recent observations ( @xmath50 ) , even if cmbr is used . ] to conclude , if it turns out , as suggested by inflationary scenarios , that @xmath0 is very close to one , then our results are significant in implying that the topology of small hyperbolic universes , suggested , for example , by some arguments based on quantum cosmology , can be undetectable using pattern repetitions . this motivates the development of new strategies for looking for the topology of the universe , not based on the observation of repeated patterns .

we assume that the classical limit of the massive gluons is represented by the equation of motion with a mass : - d _ f _ - m^2 a _ = 0 , [ eqm ] where f_^a = _ a_^a - _ a_^a + g f_abc a_^b a_^c , and @xmath0 is the covariant derivative . the landau - gauge condition @xmath1 follows from this equation by applying @xmath2 on the equation . at the zeroth order in @xmath3 , we find the following solution & & a_0 = 0 , + & & a = ^-1(_2 t + _ 3 t ) h_0(z , r ) , [ h0 ] where h_0 = ( _ x , _ y , _ z - ( m^2 -^2 ) dz ) ( z , r ) , with @xmath4 and @xmath5 . the electric and magnetic field is e^a & = & -a_0^a - i g f_abca^b a_0^c - ^a , + b^a & = & a^a . this solution may be interpreted as having two point charges placed at @xmath6 and @xmath7 with the opposite signs . this electric field has no divergence @xmath8 except for the points on the charges with the magnitude @xmath9 . the electric flux looks like that of magnetic field in superconducting material . the color of the magnetic field and the electric field are 90 degrees different in the space of color , and the magnetic flux keeps inducing the electric flux . the shape of electric flux and magnetic field are shown in figure [ fig : em4 ] . the electric flux looks like a tube elongated in @xmath10-direction . when we pull the electric charges apart , the tube will get longer but it wo nt get thicker and be about @xmath11 . therefore , a constant tension will occur between the charges , which is quite consistent with stringy picture@xcite of confinement . . the mass @xmath12 . electric flux on the vertical plane and magnetic flux on a tube for the zero - th order classical solution are shown.,width=340 ] the zeroth - order solution above may be improved to all the orders perturbatively . the equation of motion ( [ eqm ] ) in a expanded form is a^a - _ _ a^a - m^2 a^a = g f_abc ^ a_^b a_^c + g f_abc a_^b f_^c . [ eqm2 ] we can perturbatively obtain the solution by repeatedly applying this equation . in addition , we have @xmath13 not only for the zeroth - order solution ( [ h0 ] ) but also to all the orders in @xmath3 . the right hand side of eq.([eqm2 ] ) gives zero if we apply @xmath14 on it , since the first term gives @xmath15 , and the second term @xmath16 will become ^ j_^a = ( ^ a^a ) ( _ a_^a - _ a_^a ) + a^a^ ( _ a_^a - _ a_^a ) + g ^ a^a f_abc a_^b a_^c . using symmetry , the equation of motion and jacobi s identity , we have ^ j_^a & = & g a^a f_abc ( _ a_^ba_^c + a_^b ( _ a_^c - _ a_^c ) + g a^b f_cde a_^d a_^e + m^2a^a ) & & + g ^ a^a f_abc a_^b a_^c = 0 . then @xmath17 follows at the @xmath18-th order , if @xmath17 holds at the @xmath19-th order in @xmath3 . this classical solution gives a picture that @xmath20 and @xmath21 are rotating within a color plane that includes @xmath22 and @xmath23 direction , and quark charges are rotating too . quantum mechanically , a quark must change its color after emitting a gluon . this should have been the reason why it was difficult to understand the static force between confined quarks in the analogy of electric force . further this picture clarifies why non - abelian nature is essential for confinement . in the solution of massive yang - mills theory such as weak theory , the solution does not form conserved flux tubes and its electric field vanishes at longer distance . the reason why we do nt have such a decaying solution is because we do nt have current conservation @xmath24 for the theory with broken global symmetry . this confinement picture will be valid for all the theories that have the same equation of motion classically , including real qcd and lattice qcd . here we additionally present a toy but quantum model , in which the mechanism presented in the previous section holds and easier to analyze . we consider a theory with its lagrangian : ( f_^a)^2 + |_- ig a_^a ^a |^2 - ( ^)^2 + ^ , and with a spontaneous symmetry break of _ ij , [ vev ] where @xmath25 is a complex valued @xmath26 matrix field , and its left index couples to the gauge field but its right index does not . the gauge symmetry is broken , but the global color - rotation symmetry would not be broken under the vacuum expectation value ( [ vev ] ) since the non - gauged ( right ) index of @xmath25 may be rotated together . using the faddeev - popov method , the lagrangian is l & - & ( _ a^a - i g m ( - ^ ) ) ^2 & + & i |c^a ( ( d)_ab + g m ( ^a ^b+ ^b^a ^ ) ) c^b . it is invariant under the brst transformation : _ ba^a _ & = & _ c^a + g f_abc a^b _ c^c , _ b _ ij & = & i g c^a^a_ik _ kj , _ b c^a & = & - g f_abc c^b c^c/2 , + _ b|c^a & = & i b^a , _ b b^a & = & 0 . this model gives the equation of motion ( [ eqm ] ) as the classical counterpart . under the spontaneous symmetry breakdown of eq.([vev ] ) , the gauge bosons and ghosts acquire mass , and massive scalar particles appear due to higgs mechanism . we may take the mass of the higgs particle large enough to make it physically irrelevant . it is easy to show existence of mass gap in this model . here @xmath27 is the full hamiltonian with @xmath28 shifted variables , and @xmath29 . for any eigenstate @xmath30 with its energy @xmath31 , we have e = e|h + h_m|e > e|h_m|e , and the right - hand side should be a positive value unless the number of the gluon is zero . in general , |e= |n_g = 0 + |n_g = 1 + |n_g = 2 + , where @xmath32 is a state with its gluon number @xmath33 . any energy eigenstate with quarks should include @xmath34 states . if it does not , ( h_0 + h_int + h_a)|e= e|e , where @xmath35 includes @xmath36 states and @xmath37 should only include @xmath38 and @xmath39 states but the right - hand side can not include @xmath34 states . due to nonbreaking of the brst symmetry , the quarks are confined in this model because no colored state may appear as follows . the color current is j_^a = f_abc a^b f_0^c(x ) + j_0^a + ( a_b)^a - i ( |cd_c ) + i ( _ |cc ) , where @xmath40 is the color current from the quarks and the higgs field @xmath41 , where @xmath42 . the maxwell equation d^f_^a + g j_^a = _ b^a - i g f_abc ( _ |c^b ) c^c , may be written as @xmath43 . under brst formalism , physical states must be annihilated by the generator @xmath44 @xcite . therefore @xmath45 for any physical states @xmath46 and @xmath47 , which means that ( ^f_^a + g j_^a ) |f= 0 inside the physical space . the operator on the left - hand side is the generator of color gauge transformation , and then this equation means that only color - neutral state can appear as a physical state . in this letter , we presented a new classical solution of qcd and discussed possible relation to confinement . further , we found that confinement and mass gap may occur in a model with a explicit mass introduction with higgs mechanism . dual meissner effect , i.e. massiveness of magnetic field , has mainly been considered to be the mechanism that confines color charged particles , i.e. quarks . however , the picture presented here shows that mass acquisition of electric field is rather appropriate to show the confinement string if the vector particle could acquire mass without breaking the conservation of color current . this mechanism will be valid in the real qcd because the lattice qcd , which is equivalent to the real qcd , dynamically acquires mass from analytical and lattice studies@xcite . further , we have another possibility that some of higgsless massive vector field theories @xcite works . in that case , the analyses in the latter sections would be useful . bogolubsky , e .- ilgenfritz , m. mller - preussker , a. sternbeck , lattice gluodynamics computation of landau - gauge green s functions in the deep infrared , phys.lett.b676:69-73,2009 [ arxiv:0901.0736 ]

recent researches on the solution of schwinger - dyson equations , as well as lattice simulations of pure qcd , suggest that the gluon propagator is massive . in this letter , we assume that the classical counterpart of this massive gluon field may be represented with the equation of motion for yang - mills theory with a mass term added . a new classical solution is given for this equation . it is discussed that this solution may have some role in confinement . these days , evidences are accumulating that the lattice qcd , which is equivalent to the real qcd , dynamically acquires mass from analytical and lattice studies@xcite ( and see @xcite for a list of references ) . the analytical studies with the schwinger - dyson equation ( sde ) nicely agree @xcite with the lattice data . those sde analyses are based on landau gauge . in this letter , the classical counterpart of massive gluons in the landau gauge is considered . in the next section , a new classical solution is given for the equation of motion , and its relation to confinement is discussed . the mechanism here will equally be valid as far as the theory has a mass but the color symmetry is unbroken . though this theory is intended to give insight into real qcd , a non - qcd toy model is additionally analyzed in section 2 . this model is not for the real world but for facilitating analysis in a toy world . this model shows interesting behavior of the mass gap and absence of colored states .

gw vir variables belong to the spectroscopic class of the pg 1159 stars ( wesemael , green & liebert 1985 ) , which is named after the prototype pg 1159@xmath0035 . these objects are strongly hydrogen - deficient post - agb stars which pass through the hottest stage of stellar evolution . their effective temperatures range between 75 000 and 200 000k , surface gravities vary from @xmath1 $ ] . the so - called born - again scenario ( a late thermal pulse which transferred these objects back to the agb followed by a second post - agb evolution , iben et al . 1983 ) is mainly accepted as an explanation for the h - deficiency and can reproduce well the observed abundances . pg 1159 stars have spectra which are dominated by lines of , , and ( werner et al . 2004 ) , their atmospheres show a typical surface composition of he : c : o = 33:50:17 by mass . beside these main constituents there are several lines of trace elements , such as neon , nitrogen , silicon , sulfur , phosphorus , and fluorine ( reiff et al . 2005 , werner et al . 2005 ) . presently 37 pg 1159 stars are known , eleven of them proved to be pulsators . the pulsating members of the pg 1159 class are referred as gw vir variables . they are non - radial g - mode pulsators with periods from 300s up to 1000s , in some cases exceeding even 2000s ( nagel & werner 2004 ) . the favored excitation mechanism for the pulsations is the @xmath2-mechanism associated with cyclic ionization of carbon and oxygen ( quirion , fontaine & brassard 2004 ) . in the @xmath3 diagram the gw vir variables are located among the pg 1159 stars in the so - called gw vir instability strip . spectral analyses of pulsating and non - pulsating pg 1159 stars were used by dreizler & heber ( 1998 ) to define empirically the edges of this instability strip . but it is still puzzling that also non - pulsating pg 1159 stars are located within the instability strip . in our analysis we try to find more characteristic properties to distinguish between pulsating and non - pulsating members of this class . for our analysis we selected pulsating and non - pulsating pg1159 stars for which high resolution ( r @xmath4 20 000 ) fuv spectra obtained with the far ultraviolet spectroscopic explorer ( fuse ) are available . the resulting sample comprises eleven objects . the fuse spectra are processed within the standard calfuse pipeline process . a log of all observations used for this analysis is listed in table [ tab : log ] . besides the fuv spectra we also used spectra obtained with stis , ghrs and iue as well as optical spectra . the model atmospheres and synthetic line profiles are computed with the tbingen model atmosphere package ( werner et al . 2003 , rauch & deetjen 2003 ) . the line - blanketed nlte model atmospheres are in radiative and in hydrostatic equilibrium . besides the main constituents of the atmospheres of pg 1159 stars , helium , carbon , and oxygen , our model atmospheres also contain neon and nitrogen . for the abundances of these elements we use atmospheric parameters taken from the literature which are summarized in table [ tab : parameters ] . for neon an abundance of 2% mass fraction was assumed for all models , according to werner & rauch ( 1994 ) and werner et al . although the abundances in the literature were mostly determined in analyses of optical spectra the synthetic spectra can also fit the fuv spectra well , which confirms the literature values for abundances in most cases . in fig.[fig : pg1159 ] we display the fuse spectrum of pg1159@xmath0035 together with our synthetic spectrum . as lines of sulfur and silicon were also identified in several objects we included those elements in the synthetic spectra , too . both were treated with line formation calculations without back - reaction on the atmospheric structure . we assumed solar abundances for both elements . l l r c object & observation i d & & aperture + rxj2117.1 + 3412 & p1320501 & 8232s & lwrs + pg1144 + 005 & p1320201 & 6859s & lwrs + pg1520 + 525 & p1320101 & 3648s & lwrs + pg1159@xmath0035 & q1090101 & 6321s & lwrs + k1@xmath016 & m1031010 & 11271s & hirs + hs2324 + 3944 & p1320601 & 4004s & lwrs + abell 78 & b1100101 & 9972s & lwrs + & b1100102 & 7894s & lwrs + ngc 7094 & p1043701 & 23183s & lwrs + abell 43 & b0520202 & 12150s & lwrs + pg1424 + 535 & p1320301 & 11132s & lwrs + pg1707 + 427 & p1320401 & 14599s & lwrs + silicon is detectable in at least three objects , which are pg 1159@xmath0035 , and the two cooler stars pg 1424 + 535 and pg 1707 + 427 . models with a solar si abundance can fit the doublets at 1122/1128 and 1393/1402 well . in all spectra sulfur lines are detected , but our preliminary fits also suggest abundances less than solar . in fig . [ fig : sis_lines ] we display part of the fuse spectrum of pg 1424 + 535 with a preliminary fit of the sulfur and silicon lines , both with solar abundances . in former analyses by dreizler & heber ( 1998 ) it was suggested that the nitrogen abundance is a characteristic difference between pulsating and non - pulsating pg 1159 stars , as nitrogen was detected in all gw vir pulsators with a rather high abundance of 1% by mass , while in stable pg 1159 stars no nitrogen could be detected , except for pg 1144 + 005 ( which is considered outside the instability strip ) . in order to confirm previously determined n abundances we tried to fit the n resonance doublet at 1238/1242 . for this purpose we also analysed the stis spectrum of pg 1159@xmath0035 , which has a high resolution ( 0.1 ) and high s / n . in this spectrum the interstellar component of the resonance doublet is clearly separated from the photospheric component . this allows to determine the n abundance much more precisely than before and it seems to turn out that the n abundance is also significantly lower , about 0.1% by mass , than suggested by dreizler & heber ( 1998 ) . [ fig : n_comparison ] shows the n resonance doublets of three objects , the pulsators pg 1159@xmath0035 and pg 1707 + 427 and the non - pulsator pg 1424 + 535 . while the comparison of pg 1707 + 427 and pg 1424 + 535 seems to confirm the characteristic difference in the n abundance , the new fit to the photospheric components in the stis spectrum of pg 1159@xmath0035 shows that the n abundance is only 0.1% by mass , but still higher than in the non - pulsator pg 1424 + 535 . further analyses are necessary to confirm these preliminary results . l r c r c r r r c object & @xmath5 & @xmath6 & & he & & & & puls . + & @xmath7kk@xmath8 $ ] & ( cgs ) & & + rxj2117.1 + 3412 & 170 & 6.0 & & 38.0 & 56.0 & & 6.0 & @xmath9 + pg1144 + 005 & 150 & 6.5 & & 39.0 & 58.0 & 1.5 & 1.6 & + pg1520 + 525 & 150 & 7.5 & & 44.0 & 39.0 & & 17.0 & + pg1159@xmath0035 & 140 & 7.0 & & 33.0 & 49.0 & 1.0 & 17.0 & @xmath9 + k 1@xmath016 & 140 & 6.4 & & 33.0 & 50.0 & & 17.0 & @xmath9 + hs2324 + 3944 & 130 & 6.2 & 21.0 & 41.0 & 37.0 & & 1.0 & @xmath9 + abell 78 & 110 & 5.5 & & 33.0 & 50.0 & 2.0 & 15.0 & + ngc 7094 & 110 & 5.7 & 36.0 & 43.0 & 21.0 & & & + abell 43 & 110 & 5.7 & 36.0 & 43.0 & 21.0 & & & @xmath9 + pg1424 + 535 & 110 & 7.0 & & 50.0 & 44.0 & & 6.0 & + pg1707 + 427 & 85 & 7.5 & & 43.0 & 38.5 & 1.5 & 17.0 & @xmath9 +

gw vir variables are the pulsating members in the spectroscopic class of the pg 1159 stars . in order to understand the characteristic differences between pulsating and non - pulsating pg1159 stars , we analyse fuse spectra of eleven objects , of which six are pulsating , by means of state - of - the - art nlte model atmospheres . the numerous metal lines in the fuv spectra of these stars allow a precise determination of the photospheric parameters . we present here preliminary results of our analysis .

the broad emission iron lines are well - known features found in about two dozens of spectra of active galactic nuclei and black hole binaries . they are supposed to originate close to the black hole by the reflection of the primary radiation on the accretion disc . the spin of the black hole plays an important role in the forming of the line shape . especially , it determines the position of the marginally stable orbit which is supposed to confine the inner edge of the accretion disc ( see figure [ intro ] ) . the innermost stable orbit occurs closer to a black hole with a higher spin value . however , the spin affects also the overall shape of the line . over almost two decades the most widely used model of the relativistic disc spectral line has been the one by , which includes the effects of a maximally rotating kerr black hole . in other words , the laor model sets the dimensionless angular momentum @xmath1 to the canonical value of @xmath0 so that it can not be subject of the data fitting procedure . have relaxed this limitation and allowed @xmath1 to be fitted in the suite of ky models . other numerical codes have been developed independently by several groups ( , , ) and equipped with similar functionality . however , the laor model can still be used for evaluation of the spin if one identifies the inner edge of the disc with the marginally stable orbit . in this case the spin is actually estimated from the lower boundary of the broad line . the comparison of the laor and model is shown in the right panel of figure [ intro ] . the other parameters of the relativistic line models are inclination angle @xmath2 , rest energy of the line @xmath3 , inner radius of the disc @xmath4 , outer radius of the disc @xmath5 , emissivity parameters @xmath6 , @xmath7 with the break radius @xmath8 . the emissivity of the line is given by @xmath9 for @xmath10 and @xmath11 for @xmath12 . the angular dependence of the emissivity is characterized by limb darkening profile @xmath13 in the laor model . the model enables to switch between different emission laws . we used further two extreme cases , the with the same limb - darkening law as in the laor model and * with the limb - brightening law @xmath14 . the aim of this paper is to compare the two models applied to the current data provided by the xmm - newton satellite , and to the artificial data generated for the on - coming x - ray mission . for this purpose we have chosen two sources , mcg-6 - 30 - 15 and gx 339 - 4 , which exhibit an extremely skewed iron line according to recently published papers ( ) . and marginally stable orbit @xmath15 . right : comparison of the laor ( black , solid ) and ( red , dashed ) model for two values of the spin @xmath16 ( top ) and @xmath17 ( bottom ) . the other parameters of the line are @xmath18kev , @xmath19 , @xmath20.,scaledwidth=98.0% ] and marginally stable orbit @xmath15 . right : comparison of the laor ( black , solid ) and ( red , dashed ) model for two values of the spin @xmath16 ( top ) and @xmath17 ( bottom ) . the other parameters of the line are @xmath18kev , @xmath19 , @xmath20.,title="fig:",scaledwidth=98.0% ] + and marginally stable orbit @xmath15 . right : comparison of the laor ( black , solid ) and ( red , dashed ) model for two values of the spin @xmath16 ( top ) and @xmath17 ( bottom ) . the other parameters of the line are @xmath18kev , @xmath19 , @xmath20.,title="fig:",scaledwidth=98.0% ] we used the sas software version 7.1.2 ( http://xmm.esac.esa.int/sas ) to reduce the xmm - newton data of the sources . further , we used standard tools for preparing and fitting the data available at http://heasarc.gsfc.nasa.gov ( ftools , xspec ) the galaxy mcg-6 - 30 - 15 is a nearby seyfert 1 galaxy ( @xmath21 ) . the skewed iron line has been revealed in the x - ray spectra by all recent satellites . the xmm - newton observed mcg-6 - 30 - 15 for a long 350ks exposure time during summer 2001 ( revolutions 301 , 302 , 303 ) . the spectral results are described in . we joined the three spectra into one using the ftool mathpha . the black hole binary gx 339 - 4 exhibited a strong broadened line in the 76ks observation in 2002 ( ) when the source was in the very high state ( for a description of the different states see ) . the observation was made in the _ burst mode _ due to a very high source flux . the 97@xmath22 of photons are lost during the reading cycle in this mode , which results into 2.25ks total exposure time . we rebinned all the data channels in order to oversample the instrumental energy resolution maximally by a factor of 3 and to have at least 20 counts per bin . the first condition is much stronger with respect to the total flux of the sources @xmath23erg@xmath24s@xmath25 in 210kev ( @xmath26cts ) for mcg-6 - 30 - 15 and @xmath27erg@xmath24s@xmath25 in 210kev ( @xmath28cts ) for gx 339 - 4 . [ cols="^,^,^ " , ] we investigated the iron line band for two representative sources mcg-6 - 30 - 15 ( active galaxy ) and gx 339 - 4 ( x - ray binary ) . the iron line is statistically better constrained for the active galaxy mcg-6 - 30 - 15 due to a significantly longer exposure time of the available observations for comparison of count rates of the sources see table 3 . the spectra of both sources are well described by a continuum model plus a broad iron line model . we compared modeling of the broad iron line by the two relativistic models , laor and . the model leads to a better defined minimum of @xmath29 for the best fit value . the confidence contour plots for @xmath30 versus other model parameters are more regularly shaped . this indicates that the model has a smoother adjustment between the different points in the parameter space allowing for more reliable constraints on @xmath30 . the laor model has a less accurate grid and is strictly limited to the extreme kerr metric . the discrepancies between the and laor results are within the general uncertainties of the spin determination using the skewed line profile when applied to the current data . however , the results are apparently distinguishable for higher quality data , as those simulated for the xeus mission . we find that the laor model tends to overestimate the spin value and furthermore , it has insufficient energy resolution which affects the correct determination of the high - energy edge of the broad line . the discrepancies in the overall shape of the line are more visible especially for lower values of the spin @xmath30 . as a side - product , we have found that the correct re - binning of the data with respect to the instrumental energy resolution is crucial to obtain statistically the most relevant results . arnaud , m. , barcons , x. , barret , d. , bautz , m. , bellazzini , r. , xeus : the physics of the hot evolving universe , _ experimental astronomy _ , tmp , 24a , 2008 beckwith , k. , done , c. , iron line profiles in strong gravity , _ monthly notices of royal astronomical society _ , 352 , 353 , 2004 brenneman , l. w. , reynolds , c. s. , constraining black hole spin via x - ray spectroscopy , _ astrophysical journal _ , 652 , 1028 , 2006 ade , a. , calvani , m. , relativistic emission lines from accretion discs around black holes , _ monthly notices of royal astronomical society _ , 363 , 177 , 2005 doviak , m. , karas , v. , yaqoob , t. , an extended scheme for fitting x - ray data with accretion disc spectra in the strong gravity regime , _ astrophysical journal supplements _ , 153 , 205 , 2004 fabian , a. c. , vaughan , s. nandra , k. , iwasawa , k. , ballantyne , d. r. et al . , a long hard look at mcg-6 - 30 - 15 with xmm - newton , _ monthly notices of royal astronomical society _ , 335 , l1 , 2002 gallo e. , corbel s. , fender r. p. , a transient large - scale relativistic radio jet from gx 339 - 4 , _ monthly notices of royal astronomical society _ , 347l , 52 g , 2004 laor , a. , line profiles from a disk around a rotating black hole , _ astrophysical journal _ , 376 , 90 , 1991 miller , j. m. , fabian , a. c. , reynolds , c. s. , nowak , m. a. , homan , j. et al . , evidence of black hole spin in gx 339 - 4 : xmm - newton / epic - pn and rxte spectroscopy of the very high state , _ astrophysical journal _ , 606 , l131 , 2004 miller , j. m. , homan , j. , steeghs , d. , rupen , m. , hunstead , r. w. et al . , a long , hard look at the low / hard state in accreting black holes , _ astrophysical journal _ , 653 , 525 , 2006 miller , l. , turner , t. j. , reeves , j. n. , an absorption origin for the x - ray spectral variability of mcg-6 - 30 - 15 , _ astronomy & astrophysics _ , 483 , 437 , 2008 reis , r. c. , fabian , a. c. , ross , r. , miniutti , g. , miller , j. m. , reynolds , c. s. , a systematic look at the very high and low / hard state of gx 339 - 4 : constraining the black hole spin with a new reflection model , _ arxiv:0804.0238 _ , 2008 remillard , r. a. and mcclintock , j. e. , x - ray properties of black hole binaries , _ annual review of astronomy & astrophysics _ , 49 , 2006 vaughan , s. , fabian , a. c. , a long hard look at mcg-6 - 30 - 15 with xmm - newton - ii . detailed epic analysis and modelling , _ monthly notices of royal astronomical society _ , 348 , 1415 , 2004

the analysis of the broad iron line profile in the x - ray spectra of active galactic nuclei and black hole x - ray binaries allows us to constrain the spin parameter of the black hole . we compare the constraints on the spin value for two x - ray sources , mcg-6 - 30 - 15 and gx 339 - 4 , with a broad iron line using present relativistic line models in xspec laor and . the laor model has the spin value set to the extremal value @xmath0 , while the model enables direct fitting of the spin parameter . the spin value is constrained mainly by the lower boundary of the broad line , which depends on the inner boundary of the disc emission where the gravitational redshift is maximal . the position of the inner disc boundary is usually identified with the marginally stable orbit which is related to the spin value . in this way the laor model can be used to estimate the spin value . we investigate the consistency of the laor and models . we find that the spin values evaluated by both models agree within the general uncertainties when applied on the current data . however , the results are apparently distinguishable for higher quality data , such as those simulated for the international x - ray observatory ( ixo ) mission . we find that the laor model tends to overestimate the spin value and furthermore , it has insufficient resolution which affects the correct determination of the high - energy edge of the broad line . +

taking into account the recent technological advances , and needs of our modern society , the study of the magnetic properties of new materials is of fundamental importance to develop devices for different applications such as , for example , memory structures.@xcite in view of their characteristics , amorphous silicon ( _ a_-si ) thin films seems to be good candidates for such a purpose.@xcite an interesting way of studying the _ a_-si thin films magnetic response is to focus on the properties of the neutral dangling - bonds ( d@xmath3 ) present in these materials . neutral dangling - bonds are paramagnetic centers that are excellent probes for the investigation of _ a_-si thin films . moreover , silicon dangling - bonds are charge trapping centers@xcite that are more stable under the diamagnetic d@xmath5 form.@xcite in the present work we have studied the behaviour of the paramagnetic defects d@xmath3 in amorphous silicon nitride thin films doped with various rare - earth elements , _ a_-sin : re ( re = rare - earths : y , la , pr , nd , sm , gd , tb , dy , ho , er , yb , and lu ) . depending on the re dopant , these thin films present a relative strong and narrow light emission , even at room temperature.@xcite,@xcite as a consequence , re - doped _ a_-sin thin films are expected to be ideal candidates to develop photonic devices . towards this end , the study of their magnetic properties will certainly contribute to decide about the potential applications of these materials . all films were prepared in a high vacuum chamber ( base pressure @xmath6 torr ) , by radio frequency ( @xmath7 mhz ) sputtering a si ( @xmath8 % pure ) target covered at random with small pieces of metallic re ( @xmath9 % pure ) elements . polished crystalline ( _ c_-)si wafers and high - purity quartz plates were used as substrates in every deposition run . during deposition , the substrates were kept at @xmath10 @xmath11c under a constant total pressure of @xmath12 torr consisting of a mixture of high - purity ar + n@xmath13 gases . the mean thickness of the films was @xmath14 nm . the atomic composition of the _ a_-sin : re films ( @xmath15 si , @xmath16 n , @xmath17 re ) were determined by _ rutherford _ backscattering spectrometry ( rbs ) in the case of si and re and by nuclear reaction analysis ( nra ) for n. a non - intentionally amount of hydrogen of @xmath18 h was detected by elastic recoil detection ( erd ) analysis in all _ a-_sin : re films . the density of the films was estimated to be @xmath19 at . the optical bandgap of these films were determined through optical transmission measurements in the visible - ultraviolet range using a commercial spectrophotometer and stays around @xmath21 ev.@xcite room-@xmath22 _ raman _ scattering measurements , using the @xmath23 nm line of an ar@xmath24 _ laser _ , were also performed and confirmed the amorphous structure of the films . the electron spin resonance ( esr ) experiments were carried out in a _ bruker _ x - band ( @xmath25 ghz ) spectrometer using a room-@xmath26 te@xmath27 cavity . all mesuarements have been taken at room temperature . this work presents a new approach in the study of the d@xmath3 density of _ a_-sin thin films doped with res . our main finding was the depletion of the density of d@xmath3 in the _ a_-sin matrix caused by the presence of magnetic re species . we have observed that the insertion of magnetic re species dramatically suppresses the number of esr active d@xmath3 states and that such a decrease approximately scales with the spin component of the re magnetic moment . table i displays the atomic concentrations [ re ] , [ si ] , [ n ] and [ h ] as determined from rbs , nra , and erd for all the films investigated in this work . from the d@xmath3 esr intensity measurements , and using as standard a kcl - pitch sample , we have estimated the [ d@xmath0 of each film . the d@xmath3 esr parameters and [ d@xmath0 are also given in table i. as can be seen from table i , the average density of d@xmath3 magnetic defects in these films was of , typically , @xmath28 @xmath29 . figure @xmath30 shows the room-@xmath26 esr normalized spectra of d@xmath3 in _ a_-sin films doped with different re elements ( notice the different intensities ) . from a lorentzian lineshape fitting of the resonances for all the _ a_-sin : re thin films we have obtained approximately the same peak - to - peak linewidth , @xmath31 @xmath32 g , and field for resonance , @xmath33 g ( corresponding to @xmath34 ) . an early esr study on undoped _ a-_si@xmath35n@xmath36 films pointed out a very weak d@xmath3 esr signal with @xmath37 and @xmath38 g.@xcite a comparison of these data with our larger linewidth and higher [ d@xmath1 suggests that the present _ a-_sin : re films are more disordered . this is probably associated to the higher n / si ratio ( @xmath39 in our films.@xcite figure @xmath40 shows [ d@xmath0 for the various re elements investigated in this work . it is noted that the magnetic res cause a dramatic depletion of [ d@xmath41 and the strongest suppressing effect is found for gd@xmath42 , at the middle of the re - series . within our experimental accuracy , the non - magnetic re elements do not cause a systematic change in [ d@xmath0 . the inset of fig . @xmath40 presents the drop of [ d@xmath0 , or in another words , the number of inactive esr d@xmath3 , [ d@xmath3(re@xmath43)]@xmath44[d@xmath3(re@xmath45 ) ] , due to the presence of the magnetic re@xmath45 s relative to the average value for the non - magnetic re@xmath43 s . notice that the minimum in fig . @xmath40 correlates quite well with the re s de gennes factor , @xmath46 , and/or the @xmath47 factor . the striking result of figure @xmath40 suggests that the mechanism responsible for the depletion of [ d@xmath0 involves the spin part of the re magnetic moment and may be attributed to a strong exchange - like coupling , @xmath48 , between the re@xmath42 spin , @xmath49 , and the spin of the d@xmath3 , @xmath50 . such a strong exchange coupling may probably shift and/or broaden the d@xmath3 resonance beyond the detection limit of our esr experimental facilities . it is then possible that a coupling of this kind leads to a [ d@xmath0 decrease involving the de gennes factor , @xmath46 . the existence of this factor has been largely confirmed in re - doped type ii superconductor compounds through the decrease of the superconducting temperature , @xmath4 , ( @xmath51 ) due to the cooper - pairs breaking property of the re ions . @xcite @xcite @xcite at this point , we should also mention that the depletion of [ d@xmath0 could be approximately described by the spin part of the re - magnetic moment , @xmath47 , that also takes its highest value at the gd@xmath42 ion ( @xmath52 ) . these two analyses are showed in the inset of fig . @xmath40 . rare - earth doped amorphous silicon - nitrogen films were prepared by co - sputtering and investigated by means of different experimental techniques ( esr , @xmath53-susceptibility , ion - beam analyses , and _ raman _ scattering ) . the main experimental results can be summarized as : @xmath54 a strong depletion in the density of d@xmath3 states induced by the presence of magnetic reions , and @xmath55 the correspondence between this depletion and the re s de gennes factor , @xmath46 , and/or the re s @xmath47 factor . these results led us to propose a mechanism involving a strong exchange - like coupling between the re@xmath42 magnetic moment and the spin of the silicon dangling - bond d@xmath3 . this strong coupling may cause a large shift and/or broadening of the d@xmath3 resonance which are beyond the limit of detection of our esr spectrometer . this work has been supported by fapesp , capes and cnpq . table i - atomic composition of the a - sin : re films considered in this work , as determined from rbs ( _ rutherford _ backscattering spectrometry ) and nra ( nuclear reaction analysis ) . @xmath56 , @xmath57 , @xmath58 , and [ d@xmath0 stand for the line - width , resonance field , @xmath58-value , and neutral si dangling - bond concentration , respectively . _ _ @xmath59_n.a . _ means not available and `` * '' means minimum detectable value . @xmath60$]_@xmath61$]_@xmath62$]_@xmath63h_pp@xmath63h_r@xmath63g@xmath64 ^ 0@xmath65 \\ & ( at.\% ) & ( at.\% ) & ( at.\% ) & ( g ) & ( g ) & - & ( cm$]^-3@xmath66a@xmath6740.0@xmath6358.0@xmath630.0@xmath6316(2)@xmath633378(2)@xmath632.004(1)@xmath633.210 ^ 20@xmath68a@xmath6940.0@xmath6358.0@xmath630.7@xmath6320(2)@xmath633378(2)@xmath632.004(1)@xmath634.210 ^ 20@xmath68a@xmath7041.0@xmath6357.6@xmath630.4@xmath6318(2)@xmath633378(2)@xmath632.005(1)@xmath632.710 ^ 20@xmath68a@xmath7140.0@xmath6358.0@xmath630.6@xmath6316(2)@xmath633379(2)@xmath632.004(1)@xmath631.910 ^ 20@xmath68a@xmath7239.0@xmath6359.7@xmath630.8@xmath6316(2)@xmath633378(2)@xmath632.005(1)@xmath639.610 ^ 19@xmath68a@xmath7338.0@xmath6359.2@xmath630.8@xmath6315(2)@xmath633378(2)@xmath632.004(1)@xmath639.210 ^ 19@xmath68a@xmath7439.0@xmath6359.3@xmath630.7@xmath63n.a.@xmath63n.a.@xmath63n.a.@xmath752.510 ^ 17@xmath68a@xmath7639.0@xmath6359.3@xmath630.7@xmath6319(2)@xmath633377(2)@xmath632.005(1)@xmath631.610 ^ 20@xmath68a@xmath7738.0@xmath6359.6@xmath630.4@xmath6317(2)@xmath633377(2)@xmath632.005(1)@xmath631.710 ^ 20@xmath68a@xmath7840.0@xmath6358.0@xmath630.6@xmath6316(2)@xmath633379(2)@xmath632.004(1)@xmath631.710 ^ 20@xmath68a@xmath7938.0@xmath6359.5@xmath630.5@xmath6316(2)@xmath633379(2)@xmath632.004(1)@xmath631.710 ^ 20@xmath68a@xmath8039.0@xmath6359.4@xmath630.6@xmath6321(2)@xmath633378(2)@xmath632.004(1)@xmath632.410 ^ 20@xmath68a@xmath8141.0@xmath6357.7@xmath630.3@xmath6320(2)@xmath633377(2)@xmath632.005(1)@xmath634.710 ^ 20@xmath82

amorphous silicon - nitrogen thin films doped with rare - earth elements ( _ a_-sin : re ; re = y , la , pr , nd , sm , gd , tb , dy , ho , er , yb , and lu ) have been prepared by co - sputtering and studied by means of electron spin resonance ( esr ) . it was found that the neutral dangling - bond density [ d@xmath0 of _ a_-sin films decreases with the presence of magnetic res and the drop of [ d@xmath1 approximately scales with the spin and/or the de gennes factor of each rare - earth element . these results suggest that a strong exchange - like interaction , @xmath2 , between the spin of the magnetic res and d@xmath3 may be responsible for this behaviour , similarly to the decrease of @xmath4 in re - doped superconductors .

since the early fifties it is known from optical polarisation studies , that magnetic fields are constituents of the galactic interstellar medium . the magnetic field strength is about a few @xmath2 g . radio continuum observations clearly indicate synchrotron radiation originating high above the galactic plane . thus , magnetic fields and cosmic rays are obviously constituents of the galactic halo . but what is about the gas within the galactic halo ? already parker ( 1966 ) showed , that magnetic fields are always associated with the gaseous phase . investigations in the uv - range show that highly ionised gas is common within the halo , but it is a long way from a pencil beam to the whole volume of the galactic halo . recent investigations of the soft x - ray background data indicated the existence of a pervasive x - ray emitting plasma ( @xmath3k ) with a vertical scale height of about 4.4kpc ( pietz et al . 1998 ) within the halo . moreover , a sensitive analysis of the leiden / dwingeloo survey gave evidence for a emission component with a high velocity dispersion of 60 @xmath4 ( kalberla et al . 1998 ) also detectable across the entire sky . the discovery of both gas components within the galactic halo encouraged us to study the hydrostatic equilibrium model of the milky way once again . for this approach we studied recent all - sky surveys of gas , soft x - ray radiation , high energy @xmath0-ray emission , and radio - continuum emission . to describe the large - scale properties of the milky way we used the approach of a hydrostatic halo model , as proposed by parker ( 1966 ) . to describe the gaseous disk - halo system , we identified 3 main constituents of the galactic interstellar medium , namely : the neutral interstellar gas with @xmath5 = 400 pc ( dickey & lockman , 1990 ) , the diffuse ionised gas ( dig ) with @xmath5 = 950 pc ( reynolds , 1997 ) , and halo gas with @xmath5 = 4.4 kpc ( kalberla et al . 1998 , and pietz et al . 1998 ) . the major difference to the previous studies of the hydrostatic equilibrium of the milky way ( e.g. bloemen 1987 , boulares & cox 1990 ) is the detailed knowledge about the gas phase in the galactic halo . in particular , the x - ray plasma in combination with the high - velocity dispersion component adds major physical parameters to our model . 1 displays the vertical density distributions of the gas phases ( diffuse neutral and ionised gas as well as the x - ray plasma ) in the solar vicinity . 2 gives an impression on the radial density distribution represented by the parameter @xmath6 according to taylor & cordes ( 1993 ) with @xmath7 kpc . following parker s ( 1966 ) suggestion , we studied whether gas , magnetic fields and cosmic rays in the galactic halo may be in pressure equilibrium . indeed , hydrostatic equilibrium models fit the all - sky - averaged observations best . in detail we tested the hydrostatic equilibrium model by modelling the galactic synchrotron emission at 408 mhz as observed by haslam et al . ( 1982 ) , the @xmath0-ray emission as observed with _ egret _ at energies @xmath8 100 mev ( fichtel et al . 1994 ) as well as by modelling the galactic x - ray plasma distribution deduced from the all - sky survey data ( pietz et al . a detailed discussion of the model calculations and a quantitative comparison with the observations are beyond the scope of this contribution ; for details we refer to kalberla & kerp ( 1998 ) . here we summarise the main features of the model . we found a pressure equilibrium between gas , magnetic fields and cosmic rays within the galactic halo . the magnetic field of the galactic halo is globally regularly ordered and orientated parallel to the galactic plane . in contrast to the halo the magnetic field within the disk is highly irregular and has only 1/3 of the gas pressure . for a galaxy in hydrostatic equilibrium the 3-d distributions of gas pressure , density and gravitational potential are identical in size and shape . accordingly , we can utilise our parameterisation of the milky way to deduce the gravitational potential _ and _ the dark matter content . in a simple view , the galaxy consists of 3 main parts : the galactic bulge , the stellar disk with a radial scale length of 4.5 kpc and the gaseous halo as described above . assuming that the gaseous halo traces the dark matter distribution we optimised the density of the gaseous halo component until the rotation velocity of the modelled distribution was in quantitative agreement with the observed rotation velocities ( i. e. fich el al . , 1990 ) within galactocentric radii 3 @xmath9 25 kpc . 3 shows the corresponding rotation curve . the total mass of the galaxy within @xmath10 = 50 kpc derived from our model is m=@xmath11 , consistent with m=@xmath12 ( little & tremaine , 1987 ) and also within the uncertainties with the results of kochanek ( 1996 ) of m=@xmath13 . in fig . 4 we show the gravitational acceleration @xmath14 in the solar neighbourhood as a function of @xmath15 deduced from our model in comparison to that of kuijken & gilmore ( 1989 ) and bienam et al . ( 1987 ) . within vertical distances of @xmath16 kpc our model ( solid line ) is in excellent agreement with @xmath14 derived by kuijken & gilmore ( 1989 ) ( dotted line ) and bienam et al . ( 1987 ) ( dashed line ) . the differences at larger @xmath17 distance is because of different model assumptions on the dark matter distribution . the turn - over of our model about 5 kpc above the disk is because of the radial dependence of @xmath14 , as shown in fig.5 ( the solar radius is marked by the dotted line ) . the large scale properties of the galactic halo are very well modelled assuming that the main constituents of the interstellar matter , the gas , the magnetic fields , and the cosmic rays are in hydrostatic equilibrium . we analysed recent all - sky surveys of gas , soft x - ray radiation , high energy @xmath0-rays and synchrotron radiation to test the model assumptions . in general we find good quantitative agreement between model and data . the assumption that the gaseous halo traces the dark matter in the galaxy leads to a total mass which is consistent with the observed rotation curve . bienaym o. , robin a.c . , crz m. , 1987 , a&a 180 , 94 bloemen j.b.g.m . , 1987 , apj 322 , 694 boulares a. , cox d.p . , 1990 , apj 365 , 544 ( b&c ) buote d.a , canizares c.r . , 1996 , apj 457 , 565 dickey j.m . , lockman f.j . , 1990 , ara&a , 28 , 215 fich m. , blitz l. , stark a.a . , 1990 , apj 342 , 272 fichtel c.e . , bertsch d.l . , chiang , j. , et al . , 1994 , apjs 94 , 551 haslam c.g . , stoffel h. , salter c.j . , wilson w.e . , 1982 , a&as 47 , 1 kalberla p.m.w . , kerp j. , 1998 , a&a 339 , 745 kalberla p.m.w . , westphalen g. , mebold u. , hartmann dap . , burton w.b . , 1998 , a&a 332 , l61 little b. , tremaine s. , 1987 , apj 320 , 493 kochanek c.s . , 1996 , apj 457 , 228 kuijken k. , gilmore g. , 1989 , mnras 239 , 605 little b. , tremaine s. , 1987 , apj 320 , 493 parker e.n . , 1966 , apj 145 , 811 pietz j. , kerp j. , kalberla p.m.w . , et al . , 1998a , a&a 332 , 55 reynolds r.j . 1997 , in proc . of 156 . we - heraeus - seminar on `` the physics of galactic halos '' , eds . lesch et al . , akademie verlag , berlin , 57 taylor j.h . , cordes j.m . , 1993 , apj 411 , 674 leo blitz : i m concerned about the reality of the 60 km / s component . first , i do nt see how it s possible to have a static ism with such highly supersonic velocities . second , the component is not seen in the bell labs survey which has very good instrumental sidelobe response . i can understand how baselines can introduce features in a spectrum , but i do nt see how a bad baseline can coincidentally remove a feature from all over the sky . peter kalberla : the reality of the 60 km / s component was discussed in detail by kalberla et al . ( 1998 , a&a 332 , l61 ) . for a comparison between the bell labs and leiden / dwingeloo surveys concerning broad emission lines see kalberla et al . ( 1997 , in proceedings of the iau colloquium no . 166 `` the local bubble and beyond '' , eds . d. breitschwerdt , m.j . freyberg , j. trmper , lecture notes in physics 506 , 475 ) . the fact that the observed line width of 60 km / s exceeds the thermal hi line width significantly does not imply that the hi gas is in supersonic motion . the hi gas in the halo has a volume filling factor of 0.12 only . one has to consider the motion of individual hi eddies with respect to the surrounding plasma . since the sound velocity of this plasma is more than twice as high as the typical hi eddy velocity of 60 km / s , the motions of the hi clumps are clearly _ sub_sonic . dissipative cloud - cloud collisions are of little relevance in a multiphase halo .

we investigated a hydrostatic equilibrium model of the milky way following parker ( 1966 ) , to constrain the large scale properties of the interstellar medium . in our approach we found an excellent agreement between our simple hydrostatic equilibrium model of the milky way and the recent all - sky survey data rangeing from the @xmath0-ray to the radio regime . on large scales the galactic disk - halo system is found to be stable against parker - instabilities . pressure support from the galactic disk is essential to stabilise the halo . in particular the diffuse ionised gas layer acts as a disk - halo interface . assuming that the distribution of the soft x - ray emitting plasma traces the gravitational potential , we derived the dark matter content of the milky way to be about @xmath1 . our findings are consistent with the rotation curve of the galaxy .

many of the x - ray sources in the rosat all - sky survey have been identified optically in the hamburg objective prism survey ( hagen et al . 1995 ) , among which are several cataclysmic variables ( cvs ) ( jiang et al . the source rxj0944.5 + 0357 (= 1rxsj094432.1 + 035738 ; hereafter rxj0944 ) , in the constellation sextans , was observed spectroscopically by jiang et al . and found to have hi and hei emission lines typical of a cv . further spectroscopic study by mennickent et al . ( 2002 ) showed the presence of absorption bands in the red , characteristic of a secondary with a spectral type near m2 . observations by the vsnet group have identified two dwarf nova - like outbursts , in january and june 2001 , during which rxj0944 rose to v @xmath0 13 from its quiescent magnitude of v @xmath0 16.2 . mennickent et al . confirmed the spectroscopically determined orbital period ( @xmath1 ) of 0.1492 d ( 3.581 h ) reported to them by thorstensen & fenton . mennickent et al . also provided the first high speed photometry of rxj0944 in which large amplitude variations ( @xmath0 0.5 mag ) were found on time scales of 10 min to 2 h. they did not report any coherent signals in their photometry . we have used the university of cape town ccd photometer ( odonoghue 1995 ) , attached to the 74-in and 40-in telescopes at the sutherland site of the south african astronomical observatory , to observe rxj0944 at time resolutions down to 6 s. table 1 gives the log of our photometric observations and figure [ fig1 ] shows the resulting light curves . .observing log . [ cols="^,^,^,^,^,^,^ " , ] notes : ` : ' denotes an uncertain value , @xmath2 is the integration time . [ tab1 ] a fourier transform ( ft ) of the entire data set shows no power at the spectroscopic period or its first harmonic , so we deduce that rxj0944 is of quite low inclination . from the radial velocity amplitude of 75 km s@xmath3 mennickent et al . reasoned that the inclination probably lies in the range @xmath4 ; our result indicates that it is probably at the lower end of this range . a low inclination is also compatible with the weakness of the emission lines in the spectrum . it was obvious early in our work that rxj0944 has a repetitive brightness modulation with a period @xmath0 2000 s. with further observations it could be seen that the feature is a double humped profile , with the two humps varying independently and rapidly in amplitude . in figure [ fig2 ] we show the light curve of run s6324 on a larger scale , with the cyclic modulation marked , and its highly variable pair of peaks . the ft for this run discloses a fundamental period at @xmath0 2220 s plus its first harmonic . there are only six cycles of this modulation in the light curve , so the uncertainty of the period is large ( at least @xmath0 40 s ) . the mean light curve , folded on the fundamental period of 2162 s as derived below , is given in figure [ fig3 ] and shows the double humped nature of the profile , and that the humps sit on plateaux with only short - lived dips between them . ( we removed the strong flare seen at hjd 2452356.418 in figure [ fig2 ] as being not representative ; it probably resulted from a sudden short - lived surge of mass transference . ) in the mean light curve , the two peaks occur at about phases 0.26 and 0.68 , respectively . the peaks on the plateau appear as flares of variable width , so that adding more observations tends to even out their contributions , with the result that the mean light curve for the entire data set ( using the period of 2162 s ) , shown in figure [ fig4 ] , has largely lost the evidence for the doubling of the profile . the ft for the full set of observations is given in figure [ fig5 ] , and shows clearly the humps of power near the @xmath0 2000 s fundamental and its first and second harmonics . there is a great deal of complicated fine structure in the ft , beyond what is produced by the window pattern ; this is caused by the rapid amplitude modulation of the fundamental and its harmonics . it is not possible to select unambiguous frequencies from the forest of aliases . however , the highest peak in the neighbourhood of the fundamental modulation is at 2162 s and the highest peak at the first harmonic is 1079 s , which supports the choice of a fundamental period near 2160 s. there are other humps of power in the total ft , but by subdividing our data ( in particular , treating the march and april data sets separately ) we find that the ft is non - stationary only the 2160 s modulation and its harmonics are persistent features . given the high activity in the light curves ( figure [ fig1 ] ) it is not surprising that the ft is also very variable . we find no evidence for rapid oscillations in brightness ( dwarf nova oscillations typically with periods in the range 550 s : see warner 1995 ) , but in run s6341 we find a quasi - periodic oscillation ( qpo ; see warner 1995 ) with a mean period of 351 s and amplitude 0.013 mag . this is clearly seen in the light curve and maintains coherence for about 6 cycles between each major change of phase . the presence of two distinct coherent periodicities in a cv is the recognised signature of an intermediate polar ( ip ) in which the non - orbital modulation is the spin period ( @xmath5 ) of the white dwarf primary , or its orbital side band ( see , e.g. , warner 1995 ) . x - ray emission is another common feature of ips , resulting from accretion from the inner edge of the accretion disc onto the magnetic pole(s ) of the white dwarf . we therefore conclude that rxj0944 is most probably an ip with highly variable two - pole accretion . with @xmath1 = 3.581 h and @xmath5 = 36.0 min , rxj0944 is quantitatively similar to canonical ips such as fo aqr and tv col . however , the double - humped light curve and other properties make it most similar to yy dra , as can be seen from the following brief review of the latter s properties . yy dra is a dwarf nova at v @xmath0 16.0 quiescent magnitude with a mean outburst interval of 870 d and amplitude 5.5 mag , a @xmath1 of 3.96 h and a @xmath5 of 529.2 s. both the spin period and the orbital sideband ( at 550 s ) have been detected in the optical region ( patterson et al . yy dra is the x - ray source 3a1148 + 719 and the spin modulation is seen in the x - ray emission ( patterson & szkody 1993 ) . an m - type spectrum of the secondary is visible in the red , which is not normal for cvs with @xmath1 @xmath0 4h , suggesting a lower luminosity disc , probably the result if its central truncation by the magnetosphere of the primary . hst observations of yy dra ( haswell et al . 1997 ) show that the uv emission line profiles are modulated at half the spin period , and that there is simultaneous presence of broad red and blue wings in civ emission , which is interpreted as evidence for two - pole accretion . this is in accord with the double - humped pulse profiles in the optical and x - ray regions , and the occasional variations in height of the two peaks ( though yy dra is also notable for the near equality of its accretion pole luminosities most of the time ) . during an outburst of yy dra x - ray emission greatly increased and the 529 s oscillation was usually visible , but near maximum disappeared , which is interpreted as possible due to the equality of accretion onto two extended poles ( szkody et al . 2002 ) . there are other ips with evidence of two - pole accretion : v405 aur ( haberl et al . 1994 ) is similar in having its principal optical modulation at the first harmonic rather than the 545 s fundamental ( allan et al . 1996 ) ; the 1wga j1958.2 + 3232 ( @xmath5 = 1467 s ) has a double peaked profile which shows reversal of circular polarization between the peaks , confirming that it is a two - pole accretor ( norton et al . 2002 ) and still , duck & marsh ( 1998 ) have found spectroscopic evidence that rx j0558 + 5353 is a two - pole accretor . the basic similarity of the optical photometric properties of rxj0944 and yy dra is evident , so we conclude that the same model , namely two - pole accretion , is the most probable description of rxj0944 , though with more variable and independent accretion rates onto the two poles . the phases of the two peaks determined from the mean light curve ( figure [ fig3 ] ) are not half a cycle apart , indicating that the magnetic poles are not diametrically opposite on the surface of the primary . for an ip , however , the strengths of the heii and ciii / niii emission lines at 4686 and 4650 ( mennickent et al . 2002 ) are relatively weak but the fact that they are seen at all is uncharacteristic of an ordinary dwarf nova . rxj0944 has the spectroscopic and photometric characteristics of an ip and would be worth studying in a pointed x - ray observation , in order to detect any modulation and thereby determine whether the 36.0 min periodicity in the optical is the white dwarf spin period or an orbital sideband . a time - resolved spectroscopic study with the hst should also be undertaken . rxj0944 also has interest as a dwarf nova there are other intermediate polars that show full dwarf nova outbursts ( xy ari is an example ) and others that have abbreviated outbursts ( e.g. v1223 sgr ) . high speed photometry during an outburst of rxj0944 could help to reveal the interaction between disc and magnetosphere as the rate of mass transfer increases and decreases . we thank drs s. potter and p. rodriguez - gil for allowing us to use their light curve of rxj0944 . paw is supported by funds from the university of cape town and the national research foundation ; bw is supported by funds from the university .

from optical photometry the cataclysmic variable rxj0944.5 + 0357 is shown to have a double - peaked pulse profile with a period @xmath0 2160 s. the two peaks vary rapidly in relative amplitude . often most of the optical power is concentrated in the first harmonic of the 2160 s modulation ; rxj0944.5 + 0357 therefore probably belongs to the relatively rare class of two - pole accreting intermediate polars exemplified by yy dra and v405 aur .

within the standard model framework , the strong interaction is described by quantum chromodynamics ( qcd ) , which suggests the existence of the unconventional hadrons , such as glueballs , hybrid states and multiquark states . the establishment of such states remains one of the main interests in experimental particle physics . decays of the @xmath4 particle are ideal for the study of the hadron spectroscopy and the searching for the unconventional hadrons . in the decays of the @xmath4 particle , several observations in the mass region 1.8 gev / c@xmath7 - 1.9 gev / c@xmath7 have been presented in different experiments@xcite@xcite , such as the @xmath8@xcite@xcite , @xmath9@xcite@xmath10@xcite , @xmath11@xcite@xmath10@xcite and @xmath12@xcite . recently , using a sample of @xmath13 @xmath4 events@xcite collected with besiii detector@xcite at bepcii@xcite , the decay of @xmath2 was analyzed@xcite , and the @xmath0 was observed in the @xmath1 mass spectrum with a statistical significance of @xmath5 . . the dots with error bars are data ; the histogram is phase space events with an arbitrary normalization . [ m6pi],scaledwidth=60.0% ] the @xmath1 invariant mass spectrum is shown in fig . [ m6pi ] , where the @xmath0 can be clearly seen . the parameters of the @xmath0 are extracted by an unbinned maximum likelihood fit . in the fit , the background is described by two contributions : the contribution from @xmath14 and the contribution from other sources . the contribution from @xmath14 is determined from mc simulation and fixed in the fit ( shown by the dash - dotted line in fig . [ m6pi_fit ] ) . the other contribution is described by a third - order polynomial . the signal is described by a breit - wigner function modified with the effects of the detection efficiency , the detector resolution , and the phase space factor . the fit result is shown in fig . [ m6pi_fit ] . the mass and width of the @xmath0 are @xmath15 mev / c@xmath7 and @xmath16 mev , respectively ; the product branching fraction of the @xmath0 is @xmath17 . in these results , the first errors are statistical and the second errors are systematic . . the dots with error bars are data ; the solid line is the fit result . the dashed line represents all the backgrounds , including the background events from @xmath18 ( dash - dotted line , fixed in the fit ) and a third - order polynomial representing other backgrounds . [ m6pi_fit],scaledwidth=60.0% ] figure [ comp_mw ] shows the comparisons of the @xmath0 with other observations at besiii@xcite . the comparisons indicate that at present one can not distinguish whether the @xmath0 is a new state or the signal of a @xmath1 decay mode of an existing state . , title="fig:",scaledwidth=67.0% ] ( -137 , 138 ) ( -137 , 123.5 ) ( -137 , 109 ) ( -137 , 94.5 ) ( -137 , 80 ) with the same data sample , the decay of @xmath6 was searched for@xcite . the mass spectrum of the @xmath1 is shown in fig . [ m6pi ] , where no events are observed in the @xmath19 mass region . with the feldman - cousins frequentist approach@xcite , the upper limit of the branching fraction is set to be @xmath20 at the 90% confidence level , where the systematic uncertainty is taken into account . with a sample of @xmath13 @xmath4 events collected at besiii , the decay of @xmath21 was analyzed@xcite . the @xmath0 was observed in the @xmath1 invariant mass spectrum . the mass , width and product branching fraction of the @xmath0 are @xmath15 mev / c@xmath7 , @xmath16 mev and @xmath17 , respectively . the decay @xmath22 was searched for . no events were observed in the @xmath19 mass region and the upper limit of the branching fraction was set to be @xmath20 at the 90% confidence level . 00 j. z. bai _ et al . _ [ bes collaboration ] , phys . lett . * 91 * , 022001 ( 2003 ) . j. p. alexander _ et al . _ [ cleo collaboration ] , phys . d * 82 * , 092002 ( 2010 ) . m. ablikim _ et al . _ [ besiii collaboration ] , phys . lett . * 108 * , 112003 ( 2012 ) . m. ablikim _ et al . _ [ bes collaboration ] , phys . lett . * 95 * , 262001 ( 2005 ) . m. ablikim _ et al . _ [ besiii collaboration ] , phys . lett . * 106 * , 072002 ( 2011 ) . m. ablikim _ et al . _ [ bes collaboration ] , phys . lett . * 96 * , 162002 ( 2006 ) . m. ablikim _ et al . _ [ besiii collaboration ] , phys . d * 87 * , 032008 ( 2013 ) . m. ablikim _ et al . _ [ besiii collaboration ] , phys . lett . * 107 * , 182001 ( 2011 ) . m. ablikim _ et al . _ [ besiii collaboration ] , chin . c * 36 * , 915 ( 2012 ) . m. ablikim _ et al . _ [ besiii collaboration ] , nucl . instrum . a * 614 * , 345 ( 2010 ) . j. z. bai _ et al . _ [ bes collaboration ] , nucl . instrum . a * 458 * , 627 ( 2001 ) . m. ablikim _ et al . _ [ besiii collaboration ] , arxiv:1305.5333 [ hep - ex ] . g. j. feldman and r. d. cousins , phys . d * 57 * , 3873 ( 1998 ) .

observation of the @xmath0 in the @xmath1 invariant mass in @xmath2 at besiii is reviewed . with a sample of @xmath3 @xmath4 events collected with the besiii detector at bepcii , the @xmath0 is observed with a statistical significance of @xmath5 . the mass , width and product branching fraction of the @xmath0 are determined . the decay @xmath6 is searched for , and the upper limit of the branching fraction is set at the 90% confidence level . observation of the @xmath0 at besiii

the colour dipole model has proven to be very successful in describing a wide variety of small-@xmath4 inclusive and diffractive processes at hera . this talk @xcite is based on work done on this subject in collaboration with h. kowalski and l. motyka @xcite . r0.5 [ fig : diagram ] the amplitude for an exclusive diffractive process , @xmath5 , shown in fig . [ fig : diagram ] , such as vector meson production , @xmath6 , or deeply virtual compton scattering ( dvcs ) , @xmath7 , can be expressed as @xmath8\cdot\boldsymbol{\delta}}\;\frac{\mathrm{d}\sigma_{q\bar q}}{\mathrm{d}^2\boldsymbol{b}},\end{gathered}\ ] ] up to corrections from the real part of the amplitude and from skewedness ( @xmath9 ) . here , @xmath10 is the fraction of the photon s light - cone momentum carried by the quark , @xmath11 is the transverse size of the @xmath12 dipole , while @xmath13 is the impact parameter , that is , @xmath14 is the transverse distance from the centre of the proton to the centre - of - mass of the @xmath12 dipole ; see fig . [ fig : diagram ] . the transverse momentum lost by the outgoing proton , @xmath15 , is the fourier conjugate variable to the impact parameter @xmath13 , and @xmath16 . the forward overlap function between the initial - state photon wave function and the final - state vector meson or photon wave function in is denoted @xmath17 , while the factor @xmath18 $ ] in originates from the non - forward wave functions . taking the imaginary part of the forward scattering amplitude immediately gives the formula for the total @xmath19 cross section : @xmath20 the dipole picture therefore provides a unified description of both exclusive diffractive processes and inclusive dis at small @xmath4 . the unknown quantity common to and is the @xmath14-dependent dipole proton cross section , @xmath21 where @xmath22 is the imaginary part of the dipole proton scattering amplitude , which can vary between zero and one , where @xmath23 is the unitarity ( `` black disc '' ) limit . the scattering amplitude @xmath22 is generally parameterised according to some theoretically motivated functional form , with the parameters fitted to data . we will consider two such parameterisations . the first parameterisation is based on lo dglap evolution of an initial gluon density , @xmath24 , with a gaussian @xmath14 dependence , @xmath25 . we refer to this parameterisation as the `` b - sat '' model @xcite : @xmath26 where the scale @xmath27 , @xmath28 gev@xmath29 is fixed from the @xmath30-slope of exclusive @xmath1 photoproduction , and the other three parameters ( @xmath31 , @xmath32 , @xmath33 ) are fitted to zeus @xmath34 data with @xmath35 and @xmath36 $ ] gev@xmath37 . the second parameterisation is a modified version of the colour glass condensate ( cgc ) dipole model of iancu , itakura and munier : @xmath38 where a gaussian impact parameter dependence is introduced into the saturation scale : @xmath39^{\frac{1}{2\gamma_s}}.\ ] ] we refer to the parameterisation given by and as the `` b - cgc '' model @xcite . the parameter @xmath40 gev@xmath29 is fixed from the @xmath30-slope of exclusive @xmath1 photoproduction , while the other four parameters ( @xmath41 , @xmath42 , @xmath43 , @xmath44 ) are fitted to zeus @xmath34 data with @xmath35 and @xmath45 $ ] gev@xmath37 . the optimum fitted value of the anomalous dimension at the saturation scale , @xmath46 , is close to the value of @xmath47 determined from numerical solution of the balitsky kovchegov equation . however , the value of @xmath48 obtained from the fit is lower than the perturbatively calculated value of @xmath49 , and suggests that the saturation scale comprises significant non - perturbative dynamics . r0.4 it is customary to define a saturation scale @xmath50 , that is , the momentum scale at which the dipole proton scattering amplitude @xmath22 becomes sizable such that non - linear effects start to become important . there is no unique definition of @xmath50 and various choices are used in the literature . we define the saturation scale @xmath51 , where the saturation radius @xmath52 is the dipole size where the scattering amplitude @xmath53 note that we use lower - case @xmath54 and upper - case @xmath55 to distinguish between the two scales defined by and respectively . the model - independent saturation scale @xmath50 is shown in fig . [ fig : q2sx ] : it is generally less than @xmath56 gev@xmath37 in the hera kinematic regime for the most relevant impact parameters @xmath57@xmath58 gev@xmath59 . l0.4 [ fig : apom ] a wealth of hera data exists on exclusive diffractive vector meson ( @xmath2 , @xmath1 , @xmath60 , @xmath61 ) production and dvcs . it is therefore a significant challenge for an essentially parameter - free model to describe all aspects of the @xmath62 , @xmath63 and @xmath30 dependence . extensive comparison of the b - sat and b - cgc model predictions with hera data on exclusive processes has been made in refs . @xcite . in general , both models describe almost all features of the available data . here we focus on only two aspects of the data which differentiate the models . in fig . [ fig : apom ] we show the effective pomeron trajectory @xmath64 vs. @xmath65 , where @xmath64 is determined by fitting @xmath66}$ ] . the b - cgc model gives a better description of @xmath67 , where @xmath68 . this suggests that the b - cgc dipole cross section better models the interplay between the @xmath4 and @xmath14 dependence . in fig . [ fig : crossw ] we show the @xmath63 dependence of the total cross sections for exclusive @xmath1 , @xmath60 and @xmath61 meson production . the @xmath63 dependence of @xmath1 photoproduction is much better described by the b - sat model than by the b - cgc model . this difference can be traced to relatively small differences in the form of the dipole cross sections . vs. @xmath63 for exclusive @xmath1 , @xmath60 and @xmath61 meson production compared to predictions from the b - sat and b - cgc models @xcite.,title="fig:",scaledwidth=33.0% ] vs. @xmath63 for exclusive @xmath1 , @xmath60 and @xmath61 meson production compared to predictions from the b - sat and b - cgc models @xcite.,title="fig:",scaledwidth=33.0% ] vs. @xmath63 for exclusive @xmath1 , @xmath60 and @xmath61 meson production compared to predictions from the b - sat and b - cgc models @xcite.,title="fig:",scaledwidth=33.0% ] [ fig : crossw ] r0.45 @xmath69 ( nb ) & @xmath70 ( nb ) + tevatron & @xmath71 & @xmath72 + lhc & @xmath73 & @xmath74 + + @xmath75 & @xmath69 ( pb ) & @xmath70 ( pb ) + tevatron & @xmath76 & @xmath77 + lhc & @xmath78 & @xmath79 + + @xmath3 & @xmath69 ( fb ) & @xmath70 ( fb ) + tevatron & @xmath80 & @xmath81 + lhc & @xmath82 & @xmath83 + the equivalent - photon approximation allows predictions to be made for the rapidity distributions of exclusive photoproduced @xmath1 and @xmath2 mesons , and @xmath3 bosons , expected at the tevatron and lhc . a given rapidity @xmath84 corresponds to a photon energy @xmath85 . the hadron hadron cross sections are obtained from the photon hadron cross sections by multiplying by the flux @xmath86 of quasi - real photons . we neglect the possible interference between photon pomeron and pomeron photon fusion . we also neglect absorptive corrections from soft rescattering . both these effects should be largely washed out for cross sections integrated over final state momenta , in which case the rapidity gap survival factor is expected to be @xmath87@xmath88 . in table [ tab : results ] we present @xmath89 at @xmath90 and the total cross sections integrated over rapidity . the @xmath1 and @xmath2 predictions have been scaled by factors 1.08 and 2.96 , respectively , in order to give the best agreement with the existing hera data . h. kowalski , l. motyka and g. watt , phys . rev . d * 74 * ( 2006 ) 074016 [ arxiv : hep - ph/0606272 ] . g. watt and h. kowalski , phys . d * 78 * ( 2008 ) 014016 [ arxiv:0712.2670 [ hep - ph ] ] . l. motyka and g. watt , phys . d * 78 * ( 2008 ) 014023 [ arxiv:0805.2113 [ hep - ph ] ] .

we discuss two different models for the impact parameter dependent dipole cross section : one based on dglap evolution and the other inspired by the balitsky kovchegov equation . the parameters are determined from fits to data on the total @xmath0 cross section measured at hera . the impact parameter dependent saturation scale is extracted . predictions are then confronted with hera data on exclusive diffractive vector meson production and deeply virtual compton scattering . finally , predictions are given for the cross sections of exclusive photoproduced @xmath1 and @xmath2 mesons , and @xmath3 bosons , expected at the tevatron and lhc .

lifetime distribution represents an attempt to describe , mathematically , the length of the life of a system or a device . lifetime distributions are most frequently used in the fields like medicine , engineering etc . many parametric models such as exponential , gamma , weibull have been frequently used in statistical literature to analyze lifetime data . but there is no clear motivation for the gamma and weibull distributions . they only have more general mathematical closed form than the exponential distribution with one additional parameter . + recently , one parameter lindley distribution has attracted the researchers for its use in modelling lifetime data , and it has been observed in several papers that this distribution has performed excellently . the lindley distribution was originally proposed by lindley @xcite in the context of bayesian statistics , as a counter example of fudicial statistics which can be seen that as a mixture of exp(@xmath0 ) and gamma(2 , @xmath0 ) . more details on the lindley distribution can be found in ghitany et al . + a random variable x is said to have lindley distribution with parameter @xmath0 if its probability density function is defined as : + @xmath1 with cumulative distribution function @xmath2 some of the advances in the literature of lindley distribution are given by ghitany et al . @xcite who has introduced a two - parameter weighted lindley distribution and has pointed that lindley distribution is particularly useful in modelling biological data from mortality studies . mahmoudi et . @xcite have proposed generalized poisson lindley distribution . bakouch et al . @xcite have come up with extended lindley ( el ) distribution , adamidis and loukas @xcite have introduced exponential geometric ( eg ) distribution . shanker et . @xcite have introduced a two - parameter lindley distribution . zakerzadeh et al.@xcite have proposed a new two parameter lifetime distribution : model and properties . hassan @xcite has introduced convolution of lindley distribution . ghitany et al.@xcite worked on the estimation of the reliability of a stress - strength system from power lindley distribution . elbatal et al.@xcite has proposed a new generalized lindley distribution . + risti @xcite has introduced a new family of distributions with survival function given by @xmath3 in this paper we introduce a new family of distribution generated by a random variable @xmath4 which follows one parameter lindley distribution . the survival function of this new family is given as : @xmath5 where @xmath6 and @xmath7 is a cumulative distribution function(cdf ) which we use to generate a new distribution . the cdf @xmath8 is referred to as a transformer and the corresponding probability density function ( pdf ) is given by @xmath9 we consider the transformer to follow exponential distribution with cdf @xmath10 . hence the survival function of the new distribution is given by @xmath11 with corresponding density given by @xmath12 we refer the random variable with survival function ( 4 ) as lindley - exponential(l - e ) distribution with parameters @xmath0 and @xmath13 which we denote by l - e(@xmath14 ) . the aim of this paper is to study the mathematical properties of the l - e distribution and to illustrate its applicability . the contents are organized as follows . the analytical shapes of the pdfin equations ( 5 ) are established in section 2 . the quantile function presented in section 3 . the expressions for the moment generating function and moments corresponding to equation ( 5 ) are given in section 4 . limiting distribution of sample statistics like maximum and minimum has been shown in section 5 . in section 6 , entropy of l - e distribution is presented . the maximum likelihood estimation procedure is considered in section 7 . the performance of the maximum likelihood estimators for small samples is assessed by simulation in section 8 . section 9 gives estimation of stress - strength parameter r by using maximum likelihood estimation method . finally we conclude the paper by showing applicability of the model to the real data sets . here , the shape of pdf ( 5 ) follows from theorem 1 . + * theorem 1 : * the probability density function of the l - e distribution is decreasing for @xmath15 and unimodel for @xmath16 . in the latter case , mode is a root of the following equation : @xmath17 _ proof : _ the first order derivative of @xmath18 is @xmath19 where , @xmath20 . for @xmath21 , the function @xmath22 is negative . so @xmath23 for all @xmath24 . this implies that @xmath25 is decreasing for @xmath26 . also note that , @xmath27 and @xmath28 . this implies that for @xmath16 , @xmath29 has a unique mode at @xmath30 such that @xmath31 for @xmath32 and @xmath33 for @xmath34 . so , @xmath35 is unimodal function with mode at @xmath36 . the pdf for various values of @xmath13 and @xmath0 are shown in figure 1 . @xmath37 and @xmath0.,scaledwidth=90.0% ] we , now , consider the hazard rate function ( hrf ) of the l - e distribution , which is given by @xmath38 + * proposition 1 * : for @xmath39 the hazard rate function follows relation @xmath40 . + * proof : * the proof is straight forward and is omitted . + in figure 2 , hazard function for different values of parameters @xmath41 and @xmath42 . @xmath37 and @xmath0.,scaledwidth=90.0% ] the cdf , @xmath43 , can be obtained by using eq.([4 ] ) . further , it can be noted that @xmath44 is continuous and strictly increasing so the quantile function of @xmath45 is @xmath46 , @xmath47 . in the following theorem , we give an explicit expression for @xmath48 in terms of the lambert @xmath49 function . for more details on lambert @xmath50 function we refer the reader to jodr @xcite . * theorem 2 : * for any @xmath51 , the quantile function of the l - e distribution @xmath45 is @xmath52 where @xmath53 denotes the negative branch of the lambert w function . + + _ proof : _ by assuming @xmath54 , the cdf can be written as @xmath55 for fixed @xmath56 and @xmath57 , the @xmath58 quantile function is obtained by solving @xmath59 . by re - arranging the above , we obtain @xmath60 taking exponential and multiplying @xmath61 on both sides , we get + @xmath62 by using definition of lambert - w function ( @xmath63 , where @xmath64 is a complex number ) , we see that @xmath65 is the lambert @xmath49 function of the real argument @xmath66 . thus , we have @xmath67 moreover , for any @xmath51 it is immediate that @xmath68 , and it can also be checked that @xmath69 since @xmath57 . therefore , by taking into account the properties of the negative branch of the lambert w function , we have @xmath70 also by substituting @xmath54 in cdf and solving it for @xmath71 , we get @xmath72 @xmath73 further the first three quantiles we obtained by substituting @xmath74 in equation ( 11 ) . @xmath75 the moment generating function of the random variable @xmath76 follow l - e distribution is given as + @xmath77 where , @xmath78 and @xmath79 known as digamma function . + hence the first and second raw moments can be obtained by @xmath80 and @xmath81 respectively . + @xmath82 where @xmath83 is eulergamma constant = 0.577216 . + table 1 displays the mode , mean and median for l - e distribution for different choices of parameter @xmath13 and @xmath0 . it can be observed from the table that all the three measures of central tendency decrease with increase in @xmath13 and increase with an increase in @xmath0 . also for any choice of @xmath13 and @xmath0 it is observed that mean @xmath84 median @xmath84 mode , which is an indication of positive skewness .

in this paper , we introduce a new distribution generated by lindley random variable which offers a more flexible model for modelling lifetime data . various statistical properties like distribution function , survival function , moments , entropy , and limiting distribution of extreme order statistics are established . inference for a random sample from the proposed distribution is investigated and maximum likelihood estimation method is used for estimating parameters of this distribution . the applicability of the proposed distribution is shown through real data sets . * keyword : * lindley distribution , entropy , stress - strength reliability model , maximum likelihood estimator . + * ams 2001 subject classification : * 60e05

the action evaluation , including the lagrange multipliers , is implemented directly in the discrete setting , which gives discrete variants of eq . ( [ eq.hamilton_rho_eom ] ) , along with the boundary conditions . in the numerical implementation , time and space are discretized , and @xmath4 is kept at points @xmath145 in 1d , and @xmath146 in 2d . we start by describing the method in 2d , and then discuss the simplifications which occur in 1d . the action , eq . ( [ eq : action ] ) , is discretized as @xmath147 where @xmath148 is the value of @xmath37 associated with the time interval @xmath149 $ ] . this allows for the time resolution to vary . for each @xmath150 separately , @xmath148 is evaluated as @xmath151 where @xmath152 . @xmath153 corresponds to the bond connecting @xmath154 to @xmath155 ( and similarly for other half - integer indices ) . let @xmath156 . then @xmath153 is given by@xmath157 with @xmath158 , @xmath159 , and a similar expression for @xmath160 . the currents @xmath161 are constrained to satisfy a discretized version of the continuity equation , eq . ( [ eq : conserve ] ) , @xmath162 where @xmath163 , and @xmath164 are the ( constant ) spacings in the @xmath165- and @xmath166-directions . to minimize the currents subject to eq . ( [ eq : kirchoff ] ) , we define @xmath167 . differentiating @xmath168 with respect to the currents gives@xmath169 with a similar expression for @xmath170 . this is a discrete variant of @xmath71 @xmath72 . substituting eq . ( [ eq : appendix_j ] ) into eq . ( [ eq : kirchoff ] ) , one obtains a linear set of equations for the @xmath69-variables , which corresponds to eq . ( [ eq.hamilton_rho_eom ] ) . these are solved to find the @xmath69-variables . note that on boundary sites eq . ( [ eq : kirchoff ] ) involves only three currents ( or two at corners of the lattice ) , which is equivalent to setting @xmath171 for @xmath172 outside the lattice . this corresponds to the boundary conditions @xmath173 in the continuum . given the @xmath69 values , the final expression for @xmath37 is obtained by combining eqs . ( [ eq : appendix_del_s]),([eq : appendix_sx ] ) and ( [ eq : appendix_j ] ) , and reads@xmath174{c}\sigma\left ( \rho_{i+1/2,j}\right ) \left ( \frac{\hat{\rho}_{i+1,j}-\hat{\rho}_{i , j}}{\delta x}\right ) ^{2}\\ + \sigma\left ( \rho_{i , j+1/2}\right ) \left ( \frac{\hat{\rho}_{i , j+1}-\hat{\rho}_{i , j}}{\delta y}\right ) ^{2}\end{array } \right ] \ , \ ] ] which serves as the discrete analog of @xmath65 = \frac{1}{2}\int dtd\mathbf{x}\sigma\left ( \rho\right ) \left ( \mathbf{\nabla}\hat{\rho}\right ) ^{2}$ ] . this concludes the evaluation of the action @xmath37 for a given @xmath4 . this procedure is used as a building block in the optimization algorithm , where @xmath37 is evaluated for different histories @xmath6 , see the main text . in 1d the above scheme is somewhat simplified . of course , only terms in the @xmath165 direction appear . the continuity eq . ( [ eq : kirchoff ] ) is now @xmath175 , so @xmath176 , where @xmath177 is independent of the position @xmath178 ( but may depend on time ) . summing over eq . ( [ eq : appendix_j ] ) , and using @xmath179 we find @xmath180 where @xmath177 is fixed by requiring that the boundary condition @xmath181 holds . as an additional tool to improve accuracy , it is possible to interpolate @xmath6 onto a finer grid in @xmath182 before evaluating the action . this simple step improves accuracy and stability at low resolutions . in the example presented below , we use this technique to double the time resolution . the algorithm was tested in 2d against the model @xmath183 and @xmath77 . this model is a particular case of the open boundary zero range process @xcite , and its large deviation is given by@xmath46 = \int d^{2}x\left ( \rho_{f}\ln\frac{\rho_{f}}{\bar{\rho}}+\bar{\rho}-\rho_{f}\right ) \ .\ ] ] @xmath184 $ ] was calculated for @xmath85 in fig . [ fig : ni_2d_low_rez](a ) . fig . [ fig : ni_2d_low_rez](b ) shows a comparison of the numerical method with the exact result at a relatively low resolution , with @xmath185 divisions in each space dimension and @xmath186 divisions in time , starting from @xmath187 . the profiles were interpolated onto a grid with twice the time resolution before the action evaluation . the relative error in @xmath184 $ ] was @xmath188 .

we study rare events in systems of diffusive fields driven out of equilibrium by the boundaries . we present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions . using this technique , we show that the probability density of a slowly varying configuration can be captured with a small number of long wave - length modes . for a configuration which varies rapidly in space this description can be complemented by a local equilibrium assumption . in many cases the typical size of fluctuations in a physical system with @xmath0 degrees of freedom is of order @xmath1 . larger fluctuations are rare , and their probability scales as @xmath2 \sim\exp\left ( -n\phi\left [ \rho\right ] \right ) \,$ ] , where @xmath3 is an intensive function of the state @xmath4 . the function @xmath5 $ ] is known as the _ large - deviation _ _ function _ ( ldf ) and is of fundamental interest in statistical mechanics . in equilibrium systems , @xmath3 is equal to the free - energy density . away from equilibrium , a simple expression for @xmath3 is in general not known , and it may be affected by details of the system s dynamics . besides its fundamental interest for non - equilibrium physics , the function @xmath3 is important in various applications , e.g. for calculating escape rates from metastable states , with applications ranging from chemistry and population dynamics to cosmology @xcite . in a non - equilibrium steady - state , to compute the probability of a rare - event , one must calculate the dynamics leading up to that event @xcite . this is in general a difficult task , even more so for spatially extended systems , where only a handful of analytical solutions exist @xcite . if a general understanding is to emerge , additional methods beyond exact solutions need to be considered . indeed , recent years have seen a considerable effort to develop numerical techniques to calculate the ldf in a variety of systems @xcite . in this letter , we study the ldf in bulk - conserving diffusive systems , which are driven out of equilibrium by the boundaries . these describe a broad range of transport phenomena , including electronic systems , ionic conductors , and heat conduction @xcite . we show that the ldf in such systems can be efficiently evaluated numerically for a _ general _ interacting system in one and two dimensions , giving us access to previously unavailable information . this is done by searching for the most probable history @xmath6 of the conserved density function @xmath4 leading to a rare state @xmath7 . importantly , using the numerical technique we show that for many non - trivial cases , the ldf of a slowly varying configuration @xmath7 can be calculated by considering only histories @xmath6 which are slowly varying in space , i.e. which are given by the sum of only a few long wave - length modes . this implies that the long wave - length structure of the ldf can be understood using an _ effective finite - dimensional theory _ , instead of the full infinite dimensional one . in addition , we find that a local equilibrium assumption can capture much of the short wave length structure . this could suggest a simple framework to treat the ldf in these systems . in bulk conserving diffusive systems , the conserved density @xmath8 , representing e.g. charge or energy density , is related to the current @xmath9 by@xmath10 where the current is given by @xmath11 @xmath12 is a density - dependent diffusivity function , while @xmath13 controls the size of the white noise @xmath14 , which in @xmath15 dimensions satisfies @xmath16 and @xmath17 . the prefactor @xmath18 in the noise variance results from the fact that we have scaled distances by @xmath19 the system size , and time by @xmath20 . after this rescaling the noise is small as a consequence of the coarse graining . @xmath21 and @xmath22 are related via a fluctuation - dissipation relation ( nyquist noise in electronic systems ) , which for particle systems reads @xmath23 where @xmath24 is the compressibility @xcite . here we study a system on a domain @xmath25 connected to reservoirs which fix the density at the boundary @xmath26 , @xmath27 if the boundary density is not constant a current is induced through the system , driving it out of equilibrium . the average , or most probable density profile for the system @xmath28 , is obtained by solving @xmath29 = 0 $ ] , with @xmath30 at the boundaries . in equilibrium ( i.e. when @xmath31 is constant ) , the steady - state probability of any other density profile @xmath32 is easy to obtain : the large deviation functional @xmath5 $ ] is then given by the free - energy , which is local in @xmath4 . by contrast , the steady - state probability distribution away from equilibrium is notoriously hard to compute . in general , it is known that despite the local nature of the dynamics , @xmath5 $ ] is non - local in @xmath4 , leading to generic long - range correlations @xcite . analytical results for @xmath5 $ ] are known only for a few models of interacting systems , corresponding to specific choices of @xmath21 and @xmath22 , and almost exclusively in one dimension ( 1d ) . the only known example in higher dimensions is the zero - range process , which admits a trivial product measure @xcite . hence , despite the central role that @xmath5 $ ] plays in the understanding of non - equilibrium phenomena , little is known about its properties . to compute the large deviation for the model described above , we first note that the probability of a noise realization @xmath14 is gaussian , @xmath33 . using this expression together with eq . ( [ eq : j_def ] ) , the probability of a history @xmath34 during time @xmath35 is @xmath36 , where the action @xmath37 is given by @xmath38 ^{2}}{2\sigma\left ( \rho\left ( \mathbf{x},t\right ) \right ) } \ .\label{eq : action}\ ] ] as the noise is small , the system spends most of the time close to @xmath39 , the unique fixed point of the diffusion equation at zero noise . to calculate the steady - state probability of a rare event , @xmath40 , we consider trajectories @xmath41 starting from @xmath28 in the distant past @xmath42 and ending at @xmath43 at @xmath44 . for large @xmath0 , its probability @xmath45 \right\ } $ ] is given by @xcite@xmath46 = \inf_{\rho,\mathbf{j}}s\ , \label{eq : phi_min_s}\ ] ] where the infimum is over histories satisfying eq . ( [ eq : conserve ] ) , with initial and final conditions @xmath47 , @xmath48 , and the boundary conditions , eq . ( [ eq : boundaries ] ) . we now describe a numerical method which utilizes this formulation to evaluate the large deviation @xmath49 $ ] . to calculate numerically the large deviation , we directly minimize the action , eq . ( [ eq : action ] ) . we present a simple algorithm , which efficiently finds minima of the action for such systems . the algorithm is based on starting with a problem where the solution is known and gradually modifying it while maintaining a minimizing solution . specifically , we start with a problem where the initial and final states are identical , @xmath50 . in the exact solution @xmath51 ; here we take a sufficiently early time @xmath52 , before any significant evolution has begun , and check for convergence . eq . ( [ eq : action ] ) has a unique minimum to this problem , @xmath53 and @xmath54 , for which the action vanishes , hence @xmath55 = 0 $ ] . we now gradually change the final condition : define a series of gradually changing profiles @xmath56 , @xmath57 , with @xmath58 , and @xmath59 . we call the series @xmath60 the _ final - state trajectory_. the solution for the problem with @xmath61 is known . in the next iteration we solve the same problem as above , only with final conditions @xmath62 , using as an initial guess @xmath41 as obtained from the previous iteration . this procedure is iterated until we reach the final condition @xmath63 . standard algorithms can be used for the minimization at each step ; we have experimented with different algorithms , and the final results did not depend on this choice , but computational efficiency did . since @xmath37 is a sum of squares , non - linear least - squares methods are applicable and were found to be efficient . within each iteration , we minimize the action @xmath64 = \inf_{\rho}\tilde{s}\left [ \rho\right ] $ ] , where @xmath65 \equiv\inf_{\mathbf{j}}s\left [ \rho , \mathbf{j}\right ] $ ] . to evaluate @xmath65 $ ] we take into account the constraint eq . ( [ eq : conserve ] ) , by introducing a lagrange multiplier @xmath66 , and optimizing @xmath67 with respect to @xmath68 and @xmath69 . @xmath70 gives @xmath71 @xmath72 , which together with eq . ( [ eq : conserve ] ) reads @xmath73 with boundary conditions @xmath74 @xcite . this is a linear equation for @xmath66 in terms of @xmath8 , which can easily be solved numerically . substituting the expression for @xmath68 into eq . ( [ eq : action ] ) , we find that @xmath65 = \frac{1}{2}\int dtd\mathbf{x}\sigma\left ( \rho\right ) \left ( \mathbf{\nabla}\hat{\rho}\right ) ^{2}$ ] . in practice this is carried out numerically by discretizing the equations , as is described in detail in the appendix . for reference below , we note that on the minimal path @xmath75 also holds , which yields an equation of motion for @xmath69:@xmath76 note that the @xmath69 field is the momentum conjugate to @xmath4 in a hamiltonian formulation of the problem @xcite . in the context of boundary driven - diffusive systems numerical techniques were used to study current large deviations ( and similar quantities ) @xcite . algorithms have also been devised to calculate generating functions in related systems @xcite . however , both of these quantities do not yield direct information on the probability density at a specific state . * * * * our algorithm directly minimizes the action , as do @xcite . a key feature of our algorithm is the gradual change of the final state , which makes it both stable and insensitive to the choice of optimization algorithm . the algorithm is easy to implement . as a further advantage , the algorithm is easily modified to use only a small number of modes , as explored below . the numerics were tested against the known 1d and two dimensional ( 2d ) models for which analytical expressions for large deviation and the trajectory minimizing the action exist . as a first demonstration , we consider the simple symmetric exclusion process ( ssep ) in 1d @xcite . the model describes a lattice gas with hard - core exclusion , and in the continuum limit leads to @xmath77 , @xmath78 with @xmath79 . we take the domain @xmath80 , and the boundary conditions are @xmath81 . when @xmath82 the system is driven out of equilibrium . the most probable state is @xmath83 . fig . [ fig : ssep_numerics ] shows an example of a path @xmath84 minimizing the action for the ssep , with a given final state @xmath85 . in this case it is known @xcite that there is a unique local minimizer for the action , and indeed we find a single solution , independent of the different final state trajectories tested . shown is the trajectory from the initial state @xmath28 to the final state @xmath85 at different times , compared with the numerical solution , showing close agreement . the inset shows the contribution to the large deviation ( the action integral , eq . ( [ eq : action ] ) ) , integrated up to time @xmath86 . the numerics where carried out with @xmath87 space divisions and @xmath88 time divisions . in order to capture the time evolution more exactly , the size of the time intervals @xmath89 was taken to be a geometric series , where the last division is @xmath90 times smaller than the first . the initial time was @xmath91 . as is clear from the inset , contributions from earlier time are negligible . the relative error in the large deviation is @xmath92 . by taking @xmath93 the error is reduced to @xmath94 . [ ptb ] ssep_numerics.eps we now show that the dynamics of the large deviations of slowly varying configurations can be _ captured by a small number of variables _ , which describe the long wave - length behavior . this provides an effective large - scale description of @xmath3 in terms of a small number of degrees of freedom . to this end we define a family of functions @xmath95 which span the function space , ordered such that @xmath96 is the slowest varying in space , followed by @xmath97 , etc .. we then consider an approximation in which the configurations leading to @xmath85 are restricted to be linear combinations of a finite number of the slowest - varying @xmath98,@xmath99 for @xmath100 this recovers the exact extremal solutions . for finite @xmath101 , when @xmath85 is itself of the form of eq . ( [ eq.finite_sum ] ) the solutions give upper bounds for the exact value of @xmath102 $ ] , since the minimization is only on a subset all histories @xmath6 . below we are interested in how well they approximate the exact solutions . a natural choice of the functions @xmath103 are the normal modes of the linearized hamilton evolution , eqs . ( [ eq.hamilton_rho_eom ] ) and ( [ eq.hamilton_rho_hat_eom ] ) , linearized around @xmath104 and @xmath105 @xcite . these are obtained by substituting @xmath106 , @xmath107 and keeping only linear terms in @xmath108 and @xmath109 @xmath110 with boundary conditions @xmath111 . the solution @xmath6 of these equations is the optimal trajectory of eq . ( [ eq : action ] ) for small fluctuations of @xmath4 around @xmath28 . these equations admit two types of solutions . in one type , @xmath112 vanish identically . these solutions correspond to the zero - noise evolution , and do not satisfy the initial condition at @xmath113 ( except in the trivial case @xmath114 ) . the other set of solutions is obtained by first solving eq . ( [ eq : modes_eom2 ] ) , which is an eigenvalue problem for @xmath112 , independently of @xmath98 . the resulting @xmath115 are then substituted into eq . ( [ eq : modes_eom1 ] ) , and @xmath108 is solved for . as a convention , we take all @xmath98 functions to be normalized with @xmath116 , and in 1d have a positive slope at @xmath117 . as a first example we return to the profile @xmath85 given in fig . [ fig : ssep_numerics ] , which is of the form @xmath118 , where @xmath119 are the two lowest eigenvalues , @xmath120 , and @xmath121 , @xmath122 . the modes @xmath98 , for @xmath123 are shown in fig . [ ssep_1d_modes_err_evolution_v5](a ) . we now minimize the action with histories constrained to be of the form of eq . ( [ eq.finite_sum ] ) , with @xmath124 . fig . [ ssep_1d_modes_err_evolution_v5](b ) shows the histories for @xmath125 ( dashed lines ) . even for @xmath125 , the large deviation is obtained to within 2% , see fig . [ ssep_1d_modes_err_evolution_v5](c ) , suggesting that even at this level the system s behavior can be captured by an effective model with only _ two degrees of freedom_. such a small error is striking considering the highly non - linear nature of the problem ( as @xmath126 is far from @xmath28 ) , which is generically expected to mix higher modes in significant amounts . by comparison , a local equilibrium approximation ( where a space - dependent chemical potential is set to reproduce @xmath28 ) gives a relative error of 16% , whereas extending the linearized dynamics to the full evolution @xcite gives an error in the large deviation of 67% ( mostly due to the long - range gaussian corrections ) . this highlights both the importance of non - linearities in this problem , and the success of the truncated approximation . the mode approximation can also be used as a high precision numerical method . as shown in fig . [ ssep_1d_modes_err_evolution_v5](c ) , for @xmath127 , the relative error is reduced to @xmath128 , well below the error obtained by a straightforward discretization of space . indeed similar approaches have been used as numerical tools to improve accuracy in @xcite . [ ptb ] ssep_1d_modes_err_evolution_v5.eps the low mode approximation is also useful in cases where an exact analytical solution does not exist . for example , our method allows us to study two - dimensional ( 2d ) systems . in 2d analytic solutions are only known for a set of models which exhibit no long - range correlations . we used one such model , with @xmath77 and @xmath129 , corresponding to a model of non - interacting particles , as a benchmark for our method , and found agreement between the numerics and the exact solution ( see the appendix ) . in what follows we present results for an interacting system , the ssep in 2d , for which an exact expression for the large deviation is not known . this exhibits the real power of the numerics . to show the generality of the low mode approximation , we take a somewhat arbitrary choice of boundary conditions , @xmath130 , on the square domain @xmath131 ^{2}$ ] , see fig . [ fig:2d_ssep_combined ] . the most probable density profile @xmath28 is shown in fig . [ fig:2d_ssep_combined](a ) , and we present results for the profile @xmath85 shown in fig . [ fig:2d_ssep_combined](b ) , which , as in the 1d discussion , is of the form @xmath132 , where @xmath133 are the lowest modes in this system , and @xmath134 . similar results were obtained for other profiles . fig . [ fig:2d_ssep_combined](c ) shows the growth of the modes for @xmath135 . the first two modes give the exact large deviation to within @xmath136 , as estimated by @xmath137 -\phi_{14}\left [ \rho_{f}\right ] \right ) /\phi_{14}\left [ \rho_{f}\right ] $ ] , see fig . [ fig:2d_ssep_combined](d ) . once more , as in 1d , this means that the evolution is well described by a two - parameter space @xmath138 , despite the non - linear nature of the problem . interestingly , a local equilibrium approximation gives a relatively low error of 1.2% . [ ptb ] 2d_ssep_combined.eps we have shown so far that the large deviation function is well - approximated using only a few modes , provided that @xmath85 itself is a slowly - varying function of space . here we discuss how to extend these results to cases where @xmath85 is not necessarily slowly varying , but has some high - mode content . recalling that the bulk behavior is governed by equilibrium dynamics , one might expect that small , high - mode perturbations around the low mode behavior would be captured by a local equilibrium theory . in particular , define a local free - energy density @xmath139 . in equilibrium , when all boundary densities are equal , this is precisely the free - energy density . we then expect @xmath46 -\phi\left [ \rho_{f , m}\right ] \simeq\int\left [ f_{eq,\bar{\rho}}\left ( \rho_{f}\right ) -f_{eq,\bar{\rho}}\left ( \rho _ { f , m}\right ) \right ] dx\ , \label{eq : local_eq}\ ] ] where @xmath140 is @xmath85 projected to the subspace spanned by @xmath141 . in other words , the error due to truncation of the high modes is approximately accounted for by a local equilibrium theory . we now show that this is indeed the case in an example on the kipnis marchioro presutti ( kmp ) model for heat transfer @xcite , whose continuum limit @xcite gives @xmath77 and @xmath142 ( similar results are obtained for other models ) . in fig . [ fig : local_eq ] , we take @xmath85 of the form @xmath143 . for this profile , the lhs of eq . ( [ eq : local_eq ] ) for @xmath125 equals -0.03667 and the rhs equals -0.03623 . thus eq . ( [ eq : local_eq ] ) is satisfied with relative accuracy of 1.2% . hence , for profiles with high mode content the effective low mode description can be corrected for using eq . ( [ eq : local_eq ] ) . [ ptb ] local_eq.eps in summary , our findings suggest that the evolution leading to a smooth rare event is smooth : the continuous diffusion @xmath144 , makes an enduring high frequency perturbation highly unlikely . indeed we show that even when the evolution leading to the rare event is restricted to profiles involving just a few modes , good quantitative agreement with the exact large deviation may be found . this means that the large deviation is well - described in a space involving just a few variables . finally , we note that in general the action may have more than a single local minimum , an effect which is well - known in finite - dimensional systems @xcite . while this does not happen in the well - known models used above in our comparisons , it does in fact exist in other models , and can be studied using the numerical method described here by considering various different final - state trajectories . for example , when two solutions are present , different choices of final - state trajectories will lead to the different local minima @xcite . a detailed account of this issue and its physical implications is beyond the scope of the present work , and will be disscussed elsewhere @xcite . 99 p. g. bolhuis , d. chandler , c. dellago , p. l. geissler , annu . rev . phys . chem . 53 , 291 - 318 ( 2002 ) a. kamenev and b. meerson , phys . rev . e. 77 , 061107 ( 2008 ) s. coleman , phys . rev . d 15 , 29292936 ( 1977 ) f. moss and p. v. e. mcclintock , ed . , noise in nonlinear dynamical systems , cambridge university press , cambridge ( 1989 ) d. g. luchinsky , p. v. e. mcclintock , and m. i. dykman , rep . prog . phys . , 61(8):889 - 997 ( 1998 ) r. s. maier and d. l. stein , phys . rev . e , 48(2):931 - 938 ( 1993 ) r. graham and t. tl , phys . rev . lett . 52 , 912 ( 1984 ) m.i . dykman , m.m . millonas and v.n . smelyanskiy , phys . lett . a , 195 ( 1994 ) , 53 h. touchette , r. j. harris , large deviation approach to nonequilibrium systems , in r. klages , w. just , c. jarzynski ( eds ) , nonequilibrium statistical physics of small systems : fluctuation relations and beyond , wiley - vch , weinheim ( 2012 ) m. i. freidlinand a. d. wentzell , random perturbations of dynamical systems , springer - verlag ( 1984 ) b. derrida , j. stat . mech . p07023 ( 2007 ) c. giardin , j. kurchan , and l. peliti , phys . rev . lett . 96 , 120603 ( 2006 ) v. lecomte and j. tailleur , j. stat . mech . p03004 ( 2007 ) j. tailleur and v. lecomte , aip conf . proc . 1091 , 212 - 219 ( 2008 ) c. giardina , j. kurchan , v. lecomte , j. tailleur , j. stat . mech . 45 4 ( 2011 ) d. passerone and m. parrinello , phys . rev . lett . 87 , 108302 ( 2001 ) . w. e , w. ren and e. vanden - eijnden , commun . pure appl . math . 57 , 637 ( 2004 ) . x. wan , j. comp . phys . 230 ( 2011 ) 86698682 . f. bouchet , j. laurie and o. zaboronski , j. phys . conf . ser . 318 ( 2011 ) 022041 ya . m. blanter and m. bttiker , physics reports , 336 , 1 - 2 ( 2000 ) , w. dieterich , p. fulde and i. peschel , adv . in phys . 29 , 527 - 605 ( 1980 ) c. kipnis , c. marchioro and e. presutti , j. stat . phys . 27 65 ( 1982 ) c. kipnis and c. landim , scaling limits of interacting particle systems ( springer , new york , 1999 ) l. bertini , a. de sole , d. gabrielli , g. jona - lasinio , and c. landim , phys . rev . lett . 87 , 040601 ( 2001 ) l. bertini , a. de sole , d. gabrielli , g. jona - lasinio , and c. landim , j. stat . phys . 107 , p07014 ( 2002 ) a. n. jordan , e. v. sukhorukov and s. pilgram , j. math . phys . 45 4386 - 4417 ( 2004 ) j. tailleur , j. kurchan and v. lecomte , j. phys . a : math . theor . 41 505001 ( 2008 ) p. i. hurtado and p. l. garrido , phys . rev . lett . 107 , 180601 ( 2011 ) p. i. hurtado et . al . , proc . natl . acad . sci . usa . 108(19 ) 77047709 ( 2011 ) v. elgart and a. kamenev , phys . rev . e 70 , 041106 ( 2004 ) g. bunin , y. kafri , d. podolsky , in preparation . every history which locally minimizes the action will be found by a final state trajectory which follows this history . h. spohn , j. phys . a : math . gen . 16 4275 ( 1983 ) b. derrida , j. l. lebowitz , and e. r. speer , j. stat . phys . 107 775 - 810 ( 2002 ) other choices of modes , such as simple plane waves were also tested , and also give good results , but with slower convergence . l. bertini , d. gabrielli and j. lebowitz , j. stat . phys . 121 843 ( 2005 )

the new availability of wide - field images from schmidt telescopes in the 1940 s meant that astronomers no longer had to make educated guesses about where to look to find new and interesting phenomena but were now spoilt for choice . the advent of synoptic surveys presents more extreme opportunities ; as an illustration , consider the sdss which over the course of 5 years represents a factor of a million increase in information over previous surveys ; however , the ( large sky synoptic telescope , tyson ( 2002 ) ) will amass a sdss every 3 nights . although overviews of synoptic surveys are riddled with cliches concerning undiscovered countries and uncharted waters , the exploration of the temporal domain results in data sets that are not just more voluminous than before , but far richer and more complex ( paczynski 2001 ; djorgovski et al . this presents challenges to all aspects of astronomy : data gathering , distribution , reduction , analysis , storage , archiving , dissemination and mining . vo technologies are being designed precisely to meet these types of challenges , but to use them requires changes in survey design philosophies . the is a major new survey being undertaken by caltech , yale , jpl and indiana university employing the world s largest astronomical camera and the recently refurbished oschin schmidt telescope at palomar to observe a third of the sky ( @xmath1 sq . deg . between @xmath2 ) a minimum of 8 times in 7 passbands to nominally twice the depth of sdss . the quest camera consists of 112 ccds arranged in four filter strips . each ccd has 2400 @xmath5 600 13@xmath6 m @xmath5 13@xmath6 m pixels , giving a total of 161 @xmath5 10@xmath7 pixels . at the prime focus of the oschin schmidt , quest covers a sky area of 4.6@xmath8 3.6@xmath3 ( the effective area is @xmath9 sq . deg ) and in a night can survey @xmath10 sq . two filter sets are used : johnson @xmath11 and gunn @xmath12 , with a doubling of gunn @xmath13 to afford extra depth . the data rate is 2.45mb / s and with a monthly average of 10 nights observing , quest produces @xmath4 tb of data / month . some of the immediate science goals are searching for high redshift quasars , strong gravitational lensing , supernovae and grbs , and near - earth asteroids and trans - neptunian objects . obviously once there is a sufficient body of repeat observations , searching for new types of variable object and phenomena will play a dominant part ; in particular , a rapid response mechanism to transients ( see section 4 ) is planned . as this survey is one of the first of the new breed of synoptic surveys , it is being used as a testbed for the vo technologies which will enable astronomers to exploit such surveys to the full . there are currently four areas of attention : different groups want to process the raw data in different ways to optimize the detection of specific types of object . access requirements to the data are also either near real - time or delayed . data distribution must be secure , fault tolerant ( error checking , multiply redundant ) and accountable ( transaction logging ) . the nature of the data is extremely well suited to parallelization , either on a multi - processor machine or in a more general distributed computing environment , e.g. an advanced highly cpu - intensive pipeline would be a suitable grid - level application . the identification of variable objects poses many problems : * associating different observations under different conditions ( e.g. seeing ) with the same identification ; * handling objects which only appear once ( e.g. supernovae ) * handling moving objects ( e.g. asteroids ) * optimally characterizing the variability of an object ( periodic / aperiodic ) * determining the best sampling strategy to maximize the range of temporal baselines covered other federated data sets will be employed in the data analysis to assist identification , e.g. sdss , dposs , 2mass . the deployment of quest as a federated data set needs to support both interactive and batch mode access . access to data products also needs to be transparent to the access rights of different users : quest survey team , collaborators and the general astronomy community . to illustrate how quest will make use of vo technologies in an integrated fashion , consider one of the pipeline systems under construction ( see fig . 1 for a cartoon depiction ) : this will produce real time ( within four minutes of the data being taken ) alerts of transient events ( e.g. supernovae ) . the specific processes which need to mesh are : * _ distribution : _ every 140s , 112 @xmath5 3.1 mb raw fits files are produced at palomar and streamed to caltech ( at 10mb / s ) where the cit data broker distributes the data to other sites , the raw image archive and the reduction pipeline * _ processing : _ the cit fast pipeline computes a real - time flat and extracts objects - each field produces @xmath1410000 objects * _ analysis : _ variable and transient objects are detected by comparing the latest observations with the fiducial sky ( composed from all quest observations and possibly other data sets ) in the master archive . they are processed to determine whether they might be asteroids and checked against lists of known variables . source classification is attempted using other federated data archives . * _ dissemination : _ the alert decision engine decides whether an alert should be issued based on decision algorithms and all available data and posts results to the website . palomar - quest is the prototype vo - integrated synoptic sky survey and marks the beginning of an exciting new era in astronomy : the characterization of the variable optical sky . djorgovski , s. g. et al . 2001 , in virtual observatories of the future , ed . r. j. brunner , s. g. djorgovski & a. s. szalay ( asp conf . 225 ) , 52 paczynski , b. 2000 , , 112 , 1281 tyson , j. a. 2002 , spie , 4836 , 10

the advent of wide - area multicolour synoptic sky surveys is leading to data sets unprecedented in size , complexity and data throughput . vo technology offers a way to exploit these to the full but requires changes in design philosophy . the palomar - quest survey is a major new survey being undertaken by caltech , yale , jpl and indiana university to repeatedly observe @xmath0 of the sky ( @xmath1 sq . deg . between @xmath2 ) in seven passbands . utilising the 48-inch oschin schmidt telescope at the palomar observatory with the 112-ccd quest camera covering the full 4@xmath3 x 4@xmath3 field of view , it will generate @xmath4 tb of data per month . in this paper , we review the design of quest as a vo resource , a federated data set and an exemplar of vo standards .

because of their large masses , charm quarks are produced very early and propagate through the quark - gluon plasma formed in relativistic heavy ion collisions . any modifications of charm quark spectrum thus carry information on the properties of the quark - gluon plasma . although charmed hadrons are at present not directly observable in central nucleus - nucleus collisions at the relativistic heavy ion collider ( rhic ) , experimental data on the transverse momentum spectrum of electrons from their decays have already provided useful information on the interaction of charm quarks in the quark - gluon plasma . for example , the transverse momentum spectrum of these electrons is found to be insensitive to the charm final - state interactions as results from both the pythia model and the blastwave hydrodynamic model are consistent with the experimental data @xcite . on the other hand , the large elliptic flow of these electrons is consistent with the prediction of the coalescence model @xcite which assumes that charm and light quarks are in thermal equilibrium and have same elliptic flow . in the present talk , we discuss in the framework of the ampt model @xcite the mechanism for the generation of charm quark elliptic flow and the dependence of its value on the charm scattering cross section in the quark - gluon plasma @xcite . the ampt model has four components : initial conditions , parton cascade , hadronization , and hadron cascade . for studying charm elliptic flow , we use the version with string melting , in which hadrons that are generated from the hijing model @xcite are converted to partons according to their valence structures with a formation time that is determined by the transverse momentum of the parent hadron , in order to simulate the evolution of the energy stored in initial strings and the effects of particle production from the coherent color field . the space - time evolution of resulting partonic system is modeled by the zpc model @xcite , which includes elastic scatterings between partons with a cross section given by the leading pqcd and regulated by a screening mass that is taken as a parameter to adjust the magnitude of the cross section . after the partonic system freezes out , closest quarks and anti - quarks are recombined into hadrons with their subsequent evolution simulated by the art model @xcite . using parton cross sections @xmath0-@xmath1 mb , the ampt model with string melting can give a good description of measured low transverse momentum particle spectrum @xcite , elliptic flow @xcite , higher - order anisotropic flows @xcite , and the pion interferometry @xcite . charmed particles are rare particles even at rhic as only about two pairs are produced in the mid - rapidity region of central au+au collisions at available top energies . to simulate charm particles efficiently , we use the perturbative method @xcite by introducing an enhancement factor for their production from initial hard scattering , so that each charmed particle carries a probability given by the inverse of corresponding enhancement factor , and neglects the effects due to charmed particle scattering on un - charmed particles . using the power law parametrization of d meson spectrum measured in d+au collisions by the star collaboration @xcite , we first generate the transverse momentum distribution of d mesons between rapidity of -2 and + 2 with their distribution in the transverse plane according to the positions of initial nucleon - nucleon collisions . the initial phase - space distribution of charm quarks is then obtained by dissociating d mesons into their valence quarks after a formation time given by inverse of the d meson transverse momentum . the charm scattering cross section with other partons in the quark - gluon plasma is taken to be the same as the cross section for collisions between light quarks . both cross sections of 3 mb , which is similar to that given by the perturbative qcd , and 10 mb that is needed for describing observables related to light quarks , are used in present study . at the freeze - out of partons , charm quarks are combined with light quarks into d mesons according to the coordinate - space coalescence model used in the ampt model . for the scattering of charmed mesons with other hadrons , their cross sections are simply taken to be the same as the charm - parton cross section as their effect on the charmed meson spectrum is insignificant . from their transverse momentum spectra at mid - rapidity , charm quarks are found to approach thermal equilibrium when their scattering cross sections increase . this result is reminiscent of the transition from the charm spectrum obtained from the pythia to that of the blastwave hydrodynamic model . as in ref.@xcite , the spectrum of electrons from the decay of final charmed mesons is not very sensitive to charm final - state interactions and is compatible with experimental data @xcite for both cross sections . for elliptic flows , results from the ampt model are shown in fig . [ fig : v2pt2 ] . it is seen from panels ( a ) and ( b ) that the magnitude of charm quark elliptic flow increases with increasing parton scattering cross section . for both parton cross sections , there is , however , a strong mass ordering of quark elliptic flows with charm quark elliptic flow saturating to about the same value at a larger transverse momentum compared with that of light quarks . the elliptic flows of d mesons and their decay electrons are shown in panels ( c ) and ( d ) . both are seen to follow essentially that of charm quarks as the momentum of a charmed meson is largely given by that of charm quark when light quarks have only bare masses as in the ampt model . a larger charmed meson elliptic flow of about 10% at @xmath2 gev / c is obtained if an isotropic instead of screened coulomb cross section is used for charm quark scattering as suggested recently in ref.@xcite that charm quark scattering is dominated by the formation of charmed meson resonances in the quark - gluon plasma . to explain the large charm elliptic flow of more than 10% in the available data @xcite thus requires effects beyond the perturbative qcd in the quark - gluon plasma . we have not included in the present study electrons from the decay of mesons consisting of bottom quark . their contribution is expected to become important at @xmath3 gev / c . also , the effect of radiative energy loss on charm quark elliptic flow , which becomes non - negligible as the charm quark transverse momentum increases , is not considered . for charm quarks with high transverse momentum , charm meson production will be mainly from fragmentation instead of recombination . these effects need to be included for a more complete study of heavy quark elliptic flow at high transverse momentum . our results are , nevertheless , consistent with other recent studies of charm collective flow @xcite , i.e. , charm elliptic flow is sensitive to charm final - state interactions and a large elliptic flow seen in available data requires a charm scattering cross section larger than that given by the perturbative qcd . j. adams _ et al . _ [ star collaboration ] , phys . rev . lett . 94 ( 2005 ) 062301 . a. tai [ star collaboration ] , j. phys . g 30 ( 2004 ) s809 . l. ruan [ star collaboration ] , j. phys . g 30 ( 2004 ) s1197 . adler _ et al . _ [ phenix collaboration ] , phys . lett . 94 ( 2005 ) 082301 . h. van hees and r. rapp , phys . c 71 ( 2005 ) 034907 . adler [ phenix collaboration ] , phys . c 72 ( 2005 ) 024901 . f. laue [ star collaboration ] , j. phys . g 31 ( 2005 ) s27 . l.w . chen and c.m . ko , j. phys . g 31 ( 2005 ) s49 . d. molnar , j. phys . g 31 ( 2005 ) s421 . bratkovskaya , w. cassing , h. stocker and n. xu , phys . c 71 ( 2005 ) 044901 . moore and d. teaney , phys . c 71 ( 2005 ) 064904 . m. djordjevic , m. gyulassy , r. vogt and s. wicks , arxiv : nucl - th/0507019 .

using the perturbative method for the simulation of charmed particles , the dynamical origin of charm quark elliptic flow is studied in the framework of a multi - phase transport ( ampt ) model . besides the expected ordering relative to that of light quarks according to quark masses , charm quark elliptic flow is seen to be sensitive to the parton scattering cross section . to describe the observed large elliptic flow of electrons from the decay of charmed mesons , a charm quark elastic scattering cross section much larger than that estimated from the perturbative qcd is required .

considerable interest has been recently devoted in finding exact solutions to schrdinger equations involving known potentials when the mass is position - dependent ( pdm ) . among them , one may mention the morse and coulomb potentials @xcite . moreover , it has been recently shown @xcite that to lowest order of perturbation theory , there exists a whole class of hermitian position - dependent - mass hamiltonians that are associated with pseudo - hermitian hamiltonians . a great deal of interest has been paid to the interplay between these pseudo - hermitian pt - symmetric hamiltonians and their equivalent hermitian representations @xcite . in particular , mostafazadeh @xcite has considered the transition to the classical limit by showing that the relevant classical hamiltonian for the pt - symmetric cubic anharmonic oscillator plus a harmonic term , produces a behavior similar to a point particle with position - dependent - mass interacting with a quartic harmonic oscillator . indeed , many physical settings exist in which the effective mass can in principle depend on position . for example , wang et al . @xcite have recently shown that the schrdinger equation for a thin charged shell moving under the influence of its own gravitational field may be viewed as a position - dependent - mass problem . displacement operators have already been introduced for systems with position - dependent - mass , for null or constant potentials from which generalized forms of the momentum operator have been obtained @xcite . in this contribution , we demonstrate the possibility of transforming via similarity transformations , a position dependent mass hamiltonian into a hamiltonian with constant ( unity ) mass . by doing so , these hamiltonians can then be solved ( if integrable ) using well - known techniques from quantum mechanics . if on the other hand the potentials are not solvable , perturbative methods may be applied for their solution . in order to achieve this objective , we use aspects associated with some non - classical states of the harmonic oscillator , namely , squeezed states @xcite . for squeezed states , the uncertainty may be `` squeezed '' in one of the quadratures , while in the other canonical conjugate variable the uncertainty increases . in what follows , we will first show how the constant mass may be eliminated from the kinetic energy in a hamiltonian . in this regard , consider the hamiltonian @xmath0 where the mass particle is @xmath1 and @xmath2 . this hamiltonian is in turn transformed using the squeeze unitary operator @xcite @xmath3.\ ] ] to find how the operator @xmath4 transforms the position and the momentum operators , the hadamard lemma @xcite is used ; i.e. , that @xmath5 + \frac{1}{2!}\left [ \hat{a},\left [ \hat{a},\hat{b}\right ] \right]+ \frac{1}{3!}\left [ \hat{a},\left [ \hat{a},\left [ \hat{a},\hat{b}\right]\right ] \right]+ ... $ ] , from which we obtain that @xmath6 as a result , the transformed hamiltonian takes the form @xmath7 and thus the mass has been effectively eliminated from the kinetic energy term . based on this latter possibility , one could ask if the mass can also be eliminated from the kinetic energy via a proper transformation , even if it is position dependent . there is always some uncertainty as to the actual form of the kinetic energy term in a hamiltonian , when the mass is position dependent . this is because @xmath8 no longer commutes with the momentum . there are consequently several ways to write the kinetic part of the hamiltonian that must be kept hermitian ; for instance @xmath9 on the other hand , by choosing @xmath10 , we arrive to the ordering proposed by bendaniel and duke @xcite , @xmath11 while with the choice @xmath12 , @xmath13 , we get @xmath14.\ ] ] although there is no apparent reason in selecting any particular ordering for the kinetic position - dependent - mass hamiltonian , here we will choose to work with the bendaniel and duke proposal . physical arguments supporting this choice were put forward by lvy - leblond @xcite . we now consider the complete quantum hamiltonian of a particle with position - dependent mass @xmath15 we then use the transformation @xmath16 with @xmath17 \right\rbrace,\ ] ] where @xmath18 is a well behaved function that will depend on position . using the hadamard lemma @xcite , one can show that the momentum operator transforms according to @xmath19,\ ] ] where @xmath20 for which @xmath21 on the other hand , for the position operator , we obtain @xmath22 where @xmath23 with @xmath24 from equation ( [ 11 ] ) , we note that @xmath25 from the above equations , we can then write @xmath26 where the transformed potential @xmath27 is given by @xmath28,\ ] ] and where @xmath29 up to this point , we have succeeded in eliminating the position dependency of the mass . note that both hamiltonians , @xmath30 and @xmath31 have the same sets of eigenvalues since they are related by a similarity transformation . therefore , by finding the eigenvalues of @xmath31 we can directly obtain the eigenvalues corresponding to the position dependent mass hamiltonian @xmath30 . let us consider a mass that decays with the position in an exponential - like fashion ; i.e. , let @xmath32 figure 1 , depicts this mass dependence on position when @xmath33 , and for three different values of the parameter @xmath34 . ) for @xmath33 , and @xmath35 . ] this particular dependence of the mass on position suggests the auxiliary function @xmath36 , in which case the similarity transformation takes the form @xmath37 .\ ] ] from here one finds that @xmath38 and @xmath39 that is consistent with @xmath40 . + with this particular choice for a position dependent mass ( [ 20 ] ) , we also choose the following potential @xmath41 with real arbitrary coefficients . if @xmath42 , @xmath43 , and @xmath44 , the transformed potential function @xmath27 is given by the morse potential @xmath45 ^ 2,\ ] ] where @xmath46 and @xmath47 . + in figure 2 , we plot the original potential ( [ 24 ] ) as a function of the position for the same values as in figure 1 , when @xmath48 . ) for @xmath33 , @xmath35 , and @xmath48 . ] the solution of the transformed equation , can now be obtained given that the mass is constant and the potential involved is of the morse type that is known to admit analytical solutions . by means of a squeeze - like unitary transformation , we have related a position dependent mass hamiltonian to a hamiltonian with constant mass . by doing so , we can use standard methods for analyzing quantum mechanical problems of this type . importantly , the eigenvalues of the transformed hamiltonian are the same as those associated with the original position dependent problem . meanwhile the eigenfunctions of these two hamiltonians are related by a similarity transformation - given by the squeeze - like operator ( [ 10 ] ) . a. de souza dutra and c. a. s. almeida , phys . lett . a 275 , 25 ( 2000 ) . b. bagchi , a. banerjee , c. quesne , czech . 56 , 893 ( 2006 ) . b. roy and p. roy , j. phys . a 35 , 3961 ( 2002 ) . a. d. alhaidari , phys . a 66 , 042116 ( 2002 ) . l. dekar , l. chetouani , and t. f. hammann , j. math . 39 , 2551 ( 1998 ) . v. milanovic and z. ikonic , j. phys . a 32 , 7001 ( 1999 ) b. bagchi , p. gorain , c. quesne , and r. roychoudhury , mod . lett . a 19 , 2765 ( 2004 ) . c. quesne and v. m. tkachuk , j. phys . a 37 , 4267 ( 2004 ) . j. yu , s .- h . dong , and g .- h . sun , phys . lett . a 322 , 290 ( 2004 ) . g. chen and z. chen , phys . lett . a 331 , 312 ( 2004 ) . a. r. plastino , a. puente , m. casas , f. garcias , and a. plastino , rev . 46 , 78 ( 2000 ) . c. quesne , k. a. penson , v. m. tkachuk revisiting maths - type q - deformed coherent states in : proceedings of the 8th international conference on squeezed states and uncertainty relations . puebla , mexico - june 9 - 13 , 2003 . h. moya - cessa , r. juregui , s. hacyan and o. castaos . 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we provide a squeeze - like transformation that allows one to remove a position dependent mass from the hamiltonian . methods to solve the schrdinger equation may then be applied to find the respective eigenvalues and eigenfunctions . as an example , we consider a position - dependent - mass that leads to the integrable morse potential and therefore to well - known solutions .

i am very grateful to pauchy hwang and the organizers for their invitation and warm hospitality . i also thank pauchy hwang and bingkan xue for the collaborated results in this talk . this work is partially supported by national natural science foundation of china ( nos . 10721063 , 10575003 , 10528510 ) , by the key grant project of chinese ministry of education ( no . 305001 ) , and by the research fund for the doctoral program of higher education ( china ) . j. r. horandel , j. phys . g * 29 * , 2439 ( 2003 ) . c. a. ayre _ et al . _ , j. phys . a * 5 * , l102 ( 1972 ) . t. hebbeker and c. timmermans , astropart . phys . * 18 * , 107 ( 2002 ) . s. ostapchenko , nucl . suppl . * 151 * , 147 ( 2006 ) . see , e.g. , w. d. apel _ et al . _ [ kascade collaboration ] , arxiv : astro - ph/0510810 . p. hansen , t. k. gaisser , t. stanev and s. j. sciutto , phys . d * 71 * , 083012 ( 2005 ) ; a. cillis and s. j. sciutto , arxiv : astro - ph/9908002 .

the muon charge ratio of ultrahigh energy cosmic rays may provide information to detect the composition of the primary cosmic rays . we propose to extract the charge information of high energy muons in very inclined extensive air showers by analyzing their relative lateral positions in the shower transverse plane . the most high energy particles can be observed by human being are from cosmic rays . the study of them belongs to frontiers of human knowledge in combination of cosmology , astrophysics , and particle physics , and can provide better understanding of the universe from most small to most big , i.e. , connecting quarks to the cosmos . the universe is not empty , but full of background relic particles from the big bang . it has long been anticipated that the highest energy cosmic rays would be protons from outside the galaxy , and there is an upper limit of the highest energy in the observed proton spectrum , commonly referred to as the gzk cutoff @xcite , as the protons traveling from intergalactic distances should experience energy losses owing to pion productions by the photons in the cosmic background radiation . although there have been attentions for the cosmic ray events above the gzk cutoff , it is natural to expect that these ultrahigh energy cosmic rays come from sources within the gzk zone @xcite , i.e. , not far from us in more than tens of mpc . recently there are also reports on the observation of the gzk cut - off by new experiments @xcite . however , questions about the composition of such ultrahigh energy cosmic ray particles , e.g. , whether they are protons , neutrons , or anti - nucleons @xcite , are still open to investigations . muons in the air showers are mainly from decays of pions and kaons produced in the interactions of the primary cosmic rays with the atmosphere . the very high energy secondary pion and kaon cosmic rays can be considered as from the current fragmentation of partons in deep inelastic scattering of the primary cosmic rays with the nucleon targets of the atmosphere in a first approximation @xcite . we also consider only the favored fragmentation processes , i.e. , the @xmath0 , which is composed of valence @xmath1 and @xmath2 quarks , is from the fragmentation of @xmath1 and @xmath2 quarks in the nucleon beam , and the @xmath3 , which is composed of valence @xmath4 and @xmath5 quarks , is from the fragmentation of @xmath4 and @xmath5 quarks @xcite . similarly , the @xmath6 , which is composed of valence @xmath1 and @xmath7 , is from the fragmentation of @xmath1 and @xmath7 quarks , and the @xmath8 , which is composed of valence @xmath4 and @xmath9 , is from the fragmentation of @xmath4 and @xmath9 quarks . the @xmath10 is from the decay of a @xmath0 or a @xmath6 and the @xmath11 is from the decay of a @xmath3 or a @xmath8 . we can roughly estimate the muon charge ratio by @xmath12+\kappa \left[u(x)+\bar{s}(x)\right]\right\}}{\int_0 ^ 1 { \mathrm d } x \left\{\left[d(x)+\bar{u}(x)\right]+\kappa \left[\bar{u}(x)+s(x)\right]\right\ } } , \label{qme}\ ] ] where @xmath13 is the quark distribution with flavor @xmath14 for the incident hadron beam and @xmath15 is a factor reflecting the relative muon flux and fragmentation behavior of @xmath16 . secondary collisions do not influence the above estimation , since the current parton beams still keep their flavor content and act as the current partons after the strong interactions with the partons in the atmosphere targets . adopting a simple model estimation of the parton flavor content in the nucleon without any parameter @xcite , we find that @xmath17 for proton and @xmath18 for neutron . this simple evaluation is in agreement with the empirical expectation of @xmath19 for proton and @xmath20 for neutron @xcite as well as that in an extensive monte carlo calculation @xcite , thus it provides a clear picture to understand the dominant features for the muon charge ratio by the primary hadronic cosmic rays . for the @xmath21 ratio for antiproton , it is equivalent to the @xmath22 ratio for proton by using eq . ( [ qme ] ) , thus we find @xmath23 for antiproton , which is close to that for neutron . the @xmath21 ratio for antineutron is also equivalent to the @xmath22 ratio for neutron , and it is @xmath24 , which is close to that for proton . it is hard to distinguish between the primary neutrons and antiprotons ( or protons and antineutrons ) by the @xmath21 ratio of the air shower , unless very high precision measurement is performed and also our knowledge of the muon charge ratio for each nucleon species is well established . the study of cosmic rays with primary energies above @xmath25gev are typically based on the measurements of extensive air showers ( eas ) that they initiate in the atmosphere . the ground detector array records the secondary particles produced in shower cascades , including photons , electrons ( positrons ) , muons , and some hadrons . then their arrival times and density profiles are used to infer the primary energy and composition of the incident cosmic ray particle , usually through comparison with simulated results . photons , electrons and positrons are the most numerous secondary particles in an eas event . however , for very inclined showers , these electromagnetic components would travel a long slant distance and are almost completely absorbed before they reach the ground . on the other hand , muons are decay products of charged mesons in shower hadronic cascades . most high energy muons survive their propagation through the slant atmospheric depth , during which they lose typically a few tens of gev s energy . these high energy muons carry important information about the nature of the primary cosmic ray hadron , which will be extracted from their energy spectrum and lateral distribution . as discussed by hwang and i @xcite , the ratio of positive versus negative muons @xmath26 is a significant quantity which can help to discern the primary composition , and at high energies this charge ratio also reflects important features of hadronic meson production in cosmic ray collisions . in order to obtain such muon charge information , we would need a way to distinguish between positive and negative high energy muons . unfortunately , existing muon detectors available at shower arrays , usually scintillators and water erenkov detectors , are not commonly equipped with magnetized steel to differentiate the muon charges . even if they were , the limited region of the magnetic field prevents definite determination of high energy muons track curvature . this invites us to think of the geomagnetic field as a huge natural detector for muon charge information . apparently , after being produced high in the atmosphere , a positively charged muon would bend east on its way down while a negatively charged muon would bend west , introducing an asymmetry into the density profile of the shower front . if their separation is large enough as compared with other circularly symmetric `` background '' deviations , it will be possible to distinguish the positive muons from the negative ones . to see such an effect , xue and i @xcite analyzed the possibility of obtaining the charge information of high energy muons in very inclined extensive air showers . we have demonstrated that positive and negative high energy muons in sufficiently inclined air showers can be distinguished from each other through their opposite geomagnetic deviations in the transverse plane . we developed a revised heitler model to calculate this distinct double - lobed distribution , and studied the condition for the two lobes of either positive or negative muons to be separable with confidence . from our criterion of resolvability , we concluded that a zenith angle @xmath27 will be most suitable for our approach . there are already some results from full air shower simulations that take into account the geomagnetic effect on muon propagation @xcite . they illustrated remarkable double - lobed muon lateral density profile in very inclined air showers , which is in agreement with our expectation qualitatively . however , no present study has fully considered the high energy part of muon content , which can be used to compare with our results . thus we would like to propose future simulations of very inclined extensive air showers that focus on the behavior of high energy muons . they also have to keep track of the muon charges and the relation to their lateral positions . for more detailed analysis and discussion , please refer to ref.@xcite . in summary , we propose to extract the charge information of high energy muons in very inclined extensive air showers by analyzing their relative lateral positions in the shower transverse plane . this muon charge information is helpful to detect the composition of cosmic rays , e.g. , the neutron or antiproton content of the ultrahigh energy cosmic rays .

the authors would like to thank professor m.e . grypeos for an informative discussion in atomic clusters 99 i. bialynicki - birula and j. mycielski , commun . meth . phys . * 44 * 129 ( 1975 ) s. r. gadre , phys . rev . a * 30 * 620 ( 1984 ) s. r. gadre , s. b. sears , s. j. chacravorty and r. d. bendale , phys . a bf 32 2602 ( 1985 ) s. r. gadre and r. d. bendale , phys . a * 36 * 1932 ( 1987 ) m. ohya and p.petz , `` quantum entropy and its use '' ( springer- verlag , 1993 ) a. nagy and r. g. parr , int . j. quantum chem . * 58 * 323 ( 1996 ) v. majernic and t. opatrny , j. phys . a : math . gen . * 29 * 2187 ( 1996 ) c. p. panos and s. e. massen , int . j. of mod . e * 6 * 497 ( 1997 ) g. a. lalazissis , s. e. massen , c. p. panos and s. s. dimitrova , los alamos e - print archive nucl - th/9711058 , int . j. of mod . e ( 1998 ) in press i.i hirschman jr . , am . j. math . * 79 * 152 ( 1957 ) w. ekardt , phys . rev . b * 29 * 1558 ( 1984 ) h. nishioka , k. hansen and b. r. mottelson , phys . b * 42 * 9377 ( 1990 ) b.a . kotsos and m.e . grypeos , physica b * 229 * 173 ( 1997 ) c.b . dover and n. van giai , nucl . phys . a * 190 * 373 ( 1972 )

the position and momentum space information entropies of the electron distributions of atomic clusters are calculated using a woods saxon single particle potential . the same entropies are also calculated for nuclear distributions according to the skyrme parametrization of the nuclear mean field . it turns out that a similar functional form @xmath0 for the entropy as function of the number of particles @xmath1 holds approximately for atoms , nuclei and atomic clusters . it is conjectured that this is a universal property of a many - fermion system in a mean field . it is also seen that there is an analogy of our expression for @xmath2 to boltzmann s thermodynamic entropy @xmath3 . pacs : 89.70.+c ; 36.40.+d ; 31.10.+z ; 21.60.-n information theoretical methods have played in recent years an important role in the study of quantum mechanical systems @xcite in two cases : first in the clarification of fundamental concepts of quantum mechanics and second in the synthesis of probability densities in position and momentum spaces . in the first case an important step was the discovery of an entropic uncertainty relation ( eur ) by bialynicki birula and mycielski @xcite which for a three dimensional system has the form : @xmath4 ( see also ref . @xcite for the one dimensional case ) . in ( [ ( 1 ) ] ) @xmath5 is the shannon information entropy in position space : @xmath6 @xmath7 is the corresponding entropy in momentum - space : @xmath8 and @xmath9 , @xmath10 are the position and momentum space density distributions respectively , which are normalized to one . however , for a normalization to the number of particles @xmath1 , the following eur holds @xcite : @xmath11 inequality ( 1 ) , for the information entropy sum in conjugate spaces , is a joint measure of uncertainty of a quantum mechanical distribution , since a highly localized @xmath9 is associated with a diffuse @xmath10 , leading to low @xmath5 and high @xmath7 and vice versa . expression ( [ ( 1 ) ] ) is an information theoretical uncertainty relation stronger than heisenberg s @xcite . we also note that expression ( [ ( 1 ) ] ) does not depend on the unit of length in measuring @xmath9 and @xmath10 i.e. the sum @xmath12 is invariant to uniform scaling of coordinates . gadre @xcite derived the following approximate expression for the information entropies of electron distributions in atoms : @xmath13 using thomas - fermi theory and gadre et al @xcite derived : @xmath14 with hartee - fock calculations . here , @xmath1 is the number of electrons . panos and massen @xcite found the following expression for nuclear distributions , employing the simple harmonic oscillator ( ho ) model of the nucleus : @xmath15 where @xmath1 is the number of nucleons in nuclei . relations of the same functional form hold for @xmath5 and @xmath7 separately but the important quantity is @xmath16 . there is a striking similarity of ( 5 ) , ( 6 ) and ( 7 ) with the eur ( 4 ) , indicating that the functional form @xmath17 is universal for a many - fermion system in a mean field . however , the above relations were derived for a normalization of @xmath9 and @xmath10 to the number of particles @xmath1 . in the following we find it more convenient to normalize to one . there is a simple relationship between the two cases and we can easily transform one case to the other according to the relations : @xmath18=\frac{s_r[norm = n]}{n}+\ln n\ ] ] @xmath19=\frac{s_k[norm = n]}{n}+\ln n\ ] ] hence , we have for normalization to one , the following expressions : @xmath20 @xmath21 @xmath22 in the present letter we extend our calculations for two other cases : the distribution of the valence electrons in atomic clusters using a woods saxon single particle potential and the nuclear distribution in nuclei employing the skyrme parametrization of the nuclear mean field . in atomic ( metallic ) clusters the effective radial electronic potential was derived by ekardt @xcite in his spherical jellium background model study of the self consistent charge density and the self consistent effective one particle potential , using the local density approximations . ekardt s potentials for neutral sodium clusters were parametrized in ref . @xcite by a woods saxon potential of the form : @xmath23 } \label{(11)}\ ] ] with @xmath24 , @xmath25 , @xmath26 and @xmath27 . for a detailed study regarding the parametrization of ekardt s potentials see ref . @xcite . we solved numerically the schrdinger equation for atomic clusters with @xmath28 , @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35 valence electrons in the potential ( [ ( 11 ) ] ) and found the wave functions of the single particle states in configuration space and by fourier transform the corresponding ones in momentum space . using the above wave functions , we calculated the electron density @xmath9 in position space and @xmath10 in momentum space , which were inserted into equations ( [ ( 2 ) ] ) , ( [ ( 3 ) ] ) and gave us the values of the information entropies @xmath5 and @xmath7 . then we fitted the form @xmath0 to these values and obtained the expressions : @xmath36 next the nuclear densities @xmath9 and @xmath10 for several nuclei were obtained with hartee fock calculations using the skyrme parametrization of the nuclear mean field . there are various parametrizations of the skyrme interaction , but they affect slightly the information entropies @xcite . thus we used the skiii interaction @xcite . finally , we fitted the form @xmath37 to the values obtained with skiii interaction and we found the expressions : @xmath38 the fit is in reasonably good agreement with its h.o . counterpart ( comparison of relation ( [ ( 17 ) ] ) to ( [ ( 10 ) ] ) ) , though the individual entropies @xmath5 and @xmath7 do not match with the respective ho ones @xcite that well . it seems that there is a delicate balance between the coordinate and momentum spaces , so that the interesting quantity is the sum @xmath39 ( the net information content of the system ) and not the individual entropies @xmath5 and @xmath7 . in figure 1 we plot our fitted form @xmath40 for atoms ( with hartee - fock , relation ( [ ( 9 ) ] ) , upper curve ) , atomic neutral na clusters ( relation ( [ ( 14 ) ] ) , middle curve ) and nuclei ( with skyrme , relation ( [ ( 17 ) ] ) , lower curve ) . these lines correspond to our fitted expressions , while the corresponding values of our numerical calculations are denoted by solid circles ( clusters ) and open circles ( nuclei with skiii interaction ) . concluding , in the present letter we derive an interesting characteristic of information entropies @xmath5 and @xmath7 for various systems i.e. atoms ( thomas fermi theory , hartee fock ) , nuclei ( harmonic oscillator model , skyrme force ) and atomic clusters(woods saxon potential ) . for all of these systems the entropies can be represented well by a function , which incorporates @xmath41 linearly i.e. @xmath42 where @xmath1 is the number of electrons in atoms or nucleons in nuclei or electrons in atomic clusters . we may conjecture that this is a universal property of a many - fermion system in a mean field . as stated in ref . @xcite , the information entropies seem to be a hidden treasure , as yet remains mostly unexplored . a final comment seems appropriate : there is an analogy of our expression @xmath43 to boltzmann s thermodynamic entropy @xmath3 ( @xmath44 is boltzmann s constant ) . this can be seen as follows : our relation can be written in the form : @xmath45 where @xmath46 . the above entropy is the information entropy @xmath47 , which is related to the physical entropy @xmath48 through jaynes relation : @xmath49 . in our case , we have : @xmath50 here @xmath51 and @xmath52 depend on the system under consideration ( atom , cluster or nucleus ) , but this dependence is not strong . one can take that @xmath53 ( actually equals @xmath54 for atoms , 0.907 for clusters and 0.860 for nuclei ) and @xmath55 ( because @xmath56 for atoms , @xmath57 for nuclei and @xmath58 for clusters ) . thus we obtain the following rough estimate for the entropy of a many fermion system : @xmath59 the number @xmath60 corresponds to the number of equiprobable microstates @xmath61 of boltzmann s relation . hence , starting from shannon s information entropies of quantum mechanical distributions , we arrived at relation ( [ ( 18 ) ] ) , which can be considered as a quantum - mechanical analogue to boltzmann s entropy @xmath3 .

magnetic moment bearing , rare earth containing , quasicrystals , being an example of well ordered solids with sharp diffraction peaks but with conventional requirement of translational symmetry lifted , present a rare example of an `` ideal '' spin glass , in which the spin glass state probably arises from the multiplicity of the r - r distances in the quasicrystalline lattice , @xcite as opposed to a substitutional disorder in crystalline metallic spin glasses . @xcite successful growth of large , single grain , r@xmath1mg@xmath2zn@xmath3 ( r = rare earth ) icosahedral quasicrystals @xcite allowed for detailed studies of the physical properties of the spin glass state in these materials , leading , in particular , to a clear delineation of the experimental differences between heisenberg and non - heisenberg spin glasses . @xcite it was shown that the freezing temperature , @xmath4 , is lower for the gd - based , heisenberg spin glasses , than for r = tb - er , non heisenberg spin glasses for the samples with the same values of the de gennes factor [ @xmath5 , or the weiss temperature . as a consequence , for e.g. ( tb@xmath6gd@xmath7)@xmath1mg@xmath2zn@xmath3 and ( dy@xmath6gd@xmath7)@xmath1mg@xmath2zn@xmath3 pseudo - ternary solid solution the maximum in @xmath4 was observed for @xmath8 when a crossover from from heisenberg to non - heisenberg behavior occurs . @xcite based on the large data sets in refs . @xcite it was suggested that two factors give rise to the spin glass state in the r@xmath1mg@xmath2zn@xmath3 quasicrystals : distribution of r - r distances and distribution of easy axis ( or easy plane ) in the non - heisenberg members of the family . since ( i ) a heisenberg quasicrystal gd@xmath1mg@xmath2zn@xmath3 has a spin glass low temperature state , @xcite and ( ii ) an attempt to design spin glass just by mixing rare earths with different anisotropies in a crystalline structure has failed so far , @xcite the distribution of the r - r distances is apparently a _ necessary _ and _ sufficient _ condition for the formation of a spin glass , and distribution of magnetic anisotropies is neither . the frequency dependence of the freezing temperature ( the position of the peak in ac susceptibility ) has been observed and discussed in a number of spin glass systems . @xcite the fractional relative change in the freezing temperature per decade of frequency , @xmath9 $ ] ( @xmath10 is frequency ) was noticed to vary by more than an order of magnitude for different spin glasses . @xcite it was suggested @xcite that the experimental data could be well described by the empirical vogel - fulcher law , @xmath11\ ] ] where @xmath12 is the boltzmann constant , and @xmath13 , @xmath14 , and @xmath15 are the fitting parameters . from the very beginning , though , it was understood that the usual set of @xmath16 experimental data would not be suitable for obtaining all three parameters , and the value of @xmath17 was either obtained from other measurements or estimated by some independent procedure ( e.g. remnant magnetization measurements @xcite were used to determine @xmath17 in @xcite ) . r@xmath1mg@xmath2zn@xmath3 quasicrystals , with magnetic moment bearing rare earths give us an opportunity to address trends in the frequency dependence of the freezing temperature in the family of spin glasses with heisenberg and non - heisenberg members , a task that is rather difficult to undertake in dilute , substitutional , crystalline spin glasses . to the best of out knowledge frequency dependent measurements in this family were performed and analyzed so far only for tb@xmath1mg@xmath2zn@xmath3 . large single grain r@xmath1mg@xmath2zn@xmath3 quasicrystals were grown from ternary or pseudo - ternary melt as described in detail in refs . @xcite . the actual samples used in this work were taken from the batches extensively studied in the past . @xcite the samples with r = tb , dy , gd , gd@xmath18y@xmath19 , gd@xmath20y@xmath21 , and gd@xmath22tb@xmath22 , were chosen for this work thus covering heisenberg , diluted ( disordered ) heisenberg , and non - heisenberg spin glasses . low temperature , low field ( 25 oe ) zero field cooled - warming and field cooled - warming dc susceptibility measurements were done in a quantum design mpms-7 squid magnetometer so as to ensure that sample chosen indeed have a low temperature spin glass state and are not rhombohedral approximants with a long range magnetic order . @xcite . the low temperature ac susceptibility was measured in 3 - 5 oe ac field at frequencies in the range of 10 hz to 10 khz , in zero dc field using the acms option of quantum design ppms-14 instrument . a criterion @xmath23 ( @xmath24 is the real part of the ac susceptibility ) was used to infer a value for @xmath4 . examples of low temperature ac susceptibility measurements are shown in fig . the maximum in @xmath24 clearly shifts to higher temperatures at higher frequencies for the non - heisenberg spin glasses tb@xmath1mg@xmath2zn@xmath3 and dy@xmath1mg@xmath2zn@xmath3 and is almost unchanged for the heisenberg spin glass gd@xmath1mg@xmath2zn@xmath3 . fig . [ f2 ] summarizes all of such measurements performed in this work : whereas with three orders of magnitude frequency change , the @xmath4 of non - heisenberg spin glasses ( r = tb , dy ) increases by about 20% , the @xmath4 of the heisenberg spin glass ( r = gd ) increases by mere @xmath25% . if substitutional disorder is added to the heisenberg spin glass ( r = gd@xmath18y@xmath19 , gd@xmath20y@xmath21 ) the change is slightly larger , but still very much below those for the non - heisenberg systems . for a mixture of heisenberg and non - heisenberg magnetic moments , r = gd@xmath22tb@xmath22 , the relative change in the @xmath4 is in between the extreme cases but actually quite close to the r = tb data . the fractional relative change in the freezing temperature per decade of frequency , @xmath9 $ ] results are summarized in the table [ t1 ] . the values are within the broad range reported for different spin glasses . @xcite [ t1 ] the volgel - fulcher law can be used to fit the @xmath4 - frequency data . the fits are rather insensitive to the value of @xmath17 . here , for all samples , we have used @xmath26 hz obtained for tb@xmath1mg@xmath2zn@xmath3 @xcite , although the values of @xmath17 as high as @xmath27 hz give a comparable quality fits . fits for r = tb , dy , and gd are shown in fig . [ f3 ] as an example . the parameters of the fits for the ternary and pseudo - ternary quasicrystals in this work are listed in the table [ t1 ] . for the non - heisenberg spin glasses , @xmath28 , as it was reported for a number of spin glasses . @xcite for the heisenberg and disordered heisenberg spin glasses , @xmath29 , and the values are closer to each other . the significance of this difference is not clear at this point . it might just point out to some limitations of the vogel - fulcher fits for a small span of the freezing temperatures and a fixed value of @xmath17 throughout the family . the systematic study of the frequency dependence of the spin glass freezing temperatures in the ternary and pseudo - ternary r@xmath1mg@xmath2zn@xmath3 quasicrystals revealed a distinct difference between non - heisenberg and heisenberg members of the family , the latter showing significantly weaker response to the measurement frequency change ( at least in the studied 10 hz to 10 khz range ) . it appears that the distribution of magnetic anisotropies ( easy axis or plane ) in the non - heisenberg members changes the ( low frequency ) magnetic dynamics of these spin glasses . similar trend was suggested ( based on a very limited experimental data set ) in crystalline rb@xmath30 spin glasses . @xcite it would be of interest to see if such distinct behavior is observed in other families of magnetic rare earth containing spin glasses , and if so , what theoretical models can be used or developed to account for such behavior . help of i.r . fisher , a.f . panchula and k.o . cheon in samples synthesis and decadal room temperature annealing sudies is greatly appreciated . work at the ames laboratory was supported by the department of energy , basic energy sciences , division of materials sciences and engineering under contract no . de - ac02 - 07ch11358 . s.l.b . acknowledges partial support from the state of iowa through iowa state university .

we present ac susceptibility measurements with the frequency spanning three orders of magnitude on single grain , icosahedral r - mg - zn ( r = rare earth ) quasicrystals . the freezing temperature in gd - based , heisenberg spin glasses in this family increases by @xmath0 with a frequency increase from 10 hz to 10 khz , whereas the freezing temperature in the non - heisenberg members of the family is significantly more responsive to the frequency change ( by 16 - 22 % ) , suggesting that an additional magnetic anisotropy distribution in the non - heisenberg spin glasses causes changes in the low frequency magnetic dynamics . spin glass ; quasicrystals ; freezing temperature ; frequency dependence

* figure 1 : * reduction factor @xmath54 for the excitation probability as a function of the characteristic parameter @xmath26 defined in eq . [ zdef ] for the two model wave functions ( i : , ii : - - - ) . + * figure 2 : * reduction @xmath102 of the total cross section for the excitation of the @xmath11 first excited state from the @xmath103 ground state of @xmath0be as a function of the projectile velocity @xmath17 for the two model wave functions ( i : , ii : - - - ) .

we study the corrections of first order electromagnetic excitation due to higher order electromagnetic interactions . an effective operator is introduced which takes these effects into account in the sudden approximation . evaluating the matrix - elements of this operator between the relevant states corrections to the first order result are obtained in a simple way . as an example we discuss the excitation of the first excited state in @xmath0be . it tends to improve the agreement between experiment and theory . 425.70 in 0.80 in 0.20 in electromagnetic excitation in the energy domain of several tens of mev / u up to relativistic energies is a growing field of study . the cross - section can become large and irreducible nuclear effects can be kept under control . with increasing beam energy the equivalent photon spectrum becomes harder , and also particle - unstable states can be reached . the coulomb dissociation @xmath0li @xmath1 @xmath2li + 2n and @xmath3o @xmath1 @xmath4n + p , which is also astrophysically relevant , are examples @xcite . recently , bound states were also excited and their ( doppler shifted ) de - excitation @xmath5-rays were measured . a large deformation of the neutron - rich nucleus @xmath6 mg was recently deduced from a measurement of the @xmath7 885 kev transition to the ground state after medium energy electromagnetic excitation @xcite . the 320 kev @xmath8 @xmath5-transition in @xmath0be was recently observed . the measured cross - section for the @xmath0be ( @xmath9 ) coulomb excitation was found to be noticeably less than expected from the known lifetime and @xmath10 order pure coulomb excitation @xcite . apart from possible nuclear and coulomb - nuclear interference effects , a possible reason for this discrepancy is the influence of higher order electromagnetic interaction . it is the purpose of this letter to describe a framework suitable for fast projectiles . e.g. the rather loosely bound @xmath0be in its @xmath10 excited @xmath11 state could easily be excited electromagnetically into the continuum in a second step @xcite . electromagnetic excitation is mainly characterized by two parameters , the adiabaticity parameter @xmath12 and the strength parameter @xmath13 the excitation energy is given by @xmath14 , the impact parameter in a straight - line approximation is denoted by @xmath15 , and @xmath16 , where @xmath17 is the projectile velocity . the target charge number is denoted by @xmath18 , and @xmath19 the electric multipole operator . in coulomb excitation below the barrier , multiple electromagnetic excitation is usually treated in a coupled channels approach using the relevant states from appropriate nuclear models , like the harmonic vibrator or rigid rotor . for a review see ref . @xcite . the situation for coulomb excitation above the barrier becomes simpler , because the excitations tend to be sudden . while @xmath14 is restricted to a few mev , the adiabaticity parameter @xmath20 is typically less than 1 , for the important range of impact parameters @xmath21 , where @xmath22 and @xmath23 are the nuclear radii of projectile and target . thus fast collisions become the domain of the sudden approximation @xcite , or of a recently developed low-@xmath20 approximation @xcite . in this case it can be advantageous to construct operators which take into account the influence of intermediate states . for simplicity , let us use the straight - line approximation and the dipole approximation . the first order excitation amplitude is given by @xcite @xmath24 with @xmath25 where the projectile moves in the @xmath26-direction and the impact parameter points to the @xmath27-direction . the dipole effective charge is given by @xmath28 using a model of two pointlike inert clusters @xmath15 and @xmath29 with charge numbers @xmath30 , @xmath31 and masses @xmath32 and @xmath33 . @xmath34 and @xmath35 are the modified bessel functions . for @xmath36 we get the classical coulomb push @xmath37 in the limit @xmath38 , the excitation amplitude can be evaluated easily to all orders in the sudden approximation . it is given by @xmath39 this could be generalized to higher multipolarities and trajectories corrected for coulomb deflection . by comparing @xmath40 and @xmath41 the influence of multiple electromagnetic excitation can be assessed . this is a remarkably simple procedure , all intermediate states are included . the reduction of the excitation probability due to higher order effects is given by @xmath42 for loosely bound states , e.g. in @xmath0be = @xmath43be + n , we use simple model wave functions to reveal the characteristic parameters . we choose two models , with the correct asymptotic behaviour . their differences give a feeling about the model dependence . for the wave functions we make the ansatz for the radial part in the initial state ( with orbital angular momentum @xmath44 ) @xmath45 which corresponds to the solution of the schrdinger equation with a @xmath46-like potential . for the final state ( @xmath47 ) we choose @xmath48 and the more extended wave function @xmath49 respectively . the constants @xmath50 ( @xmath51 ) are calculated from the binding energies @xmath52 . with these wave functions the calculated mean lifetimes of the @xmath11 state are 110 fs and 97 fs , respectively . they are smaller than the experimental value of ( @xmath53 ) fs @xcite . despite this difference , the ratio of higher order to first order effects can be given with some confidence , where , e.g. , common spectroscopic factors cancel out . the absolute value depends on more sophisticated details of the nuclear model ( see , e.g. , ref . @xcite ) . the reduction factor @xmath54 can be calculated analytically . we get @xmath55 and @xmath56 resp . , where we have introduced the parameter @xmath57 the parameter @xmath26 is directly related to @xmath58 ( eq . [ chidef ] ) . it describes the ratio of the strength of the coulomb push @xmath59 and the `` looseliness '' of the system , and is a measure of the importance of higher order effects . the quantity @xmath54 is plotted in fig . 1 for the two model wave - functions described above . for large @xmath15 the sudden approximation fails ( @xmath60 ) , on the other hand , higher order effects diminish due to the decrease of the strength parameter @xmath58 . the product @xmath61 is a very small number for low excitation energies @xmath14 and high projectile velocities @xmath17 . the ranges of validity for the first order calculation ( @xmath62 small , @xmath20 arbitrary ) and the sudden approximation ( @xmath20 small , @xmath62 arbitrary ) overlap . in a convenient and accurate interpolation procedure we calculate the total cross section in the following way @xmath63 which should be an accurate expression for all values of b in the integrand . for small impact parameters we have @xmath64 and the first order approximation cancels out in the calculation of @xmath65 . we compare it with the total cross section in the first order calculation @xmath66 both cross sections depend on the value of the minimum impact parameter @xmath67 . the change in the two cross sections will be similar so that their ratio is less affected by a change in @xmath67 . if the sudden approximation is not well enough fulfilled , one could use the low-@xmath20 approximation @xcite which takes second order electromagnetic effects into account . for the @xmath0be coulomb excitation a reduction of the cross section from @xmath68 mb ( expected from the first order calculation ) to the measured @xmath69 mb was recently found in an experiment at ganil @xcite . indeed , the parameter @xmath26 can become substantial in this case , and higher order effects are not negligible . for a collision with @xmath70 fm and an energy of @xmath71 mev ( @xmath72 ) we have @xmath73 and from fig . 1 we see a substantial reduction of the excitation probability . in a recent experiment at riken @xcite , which is currently evaluated , an energy of about @xmath74 mev ( @xmath75 ) for the @xmath0be was used . this leads to a value of @xmath76 for the same impact parameter corresponding to a smaller reduction . the product @xmath77 takes on the small values @xmath78 and @xmath79 , respectively , for the two models and the ganil conditions . at @xmath80 fm we get an excitation probability of 3.4% and 3.9% in the first order calculation , decreasing with @xmath81 . for impact parameters larger than @xmath82 fm the excitation becomes adiabatic and the excitation probability drops off exponentially . the excitation probability is small compared to 1 and the non - conservation of unitarity in the first order approximation will not affect the calculation of the cross section . the apparent reduction of the b(e1)-value ( due to higher order effects ) is given by @xmath83 which is plotted in fig . 2 as a function of the projectile velocity @xmath17 for the two model wave functions described above . we assume a minimum impact parameter @xmath84 fm corresponding to a grazing collision of the projectile and target . this will give an estimate of the largest possible effect to be expected from the higher order contributions . we obtain a reduction , depending on the particular model chosen , of @xmath85 or @xmath86 for the ganil energy and @xmath87 or @xmath88 for the riken energy . the range of the reduction r in the two models gives a feeling of the reliabiliy of the results . the use of more realistic wavefunctions is outside the scope of the present work . the reduction of the excitation probability for the @xmath11 state by higher order effects will be accompanied by an increase of the cross section in the breakup channel . in the dipole approximation , the lowest order correction was of @xmath89 order . e1-e2 excitation contributes already in second order . nevertheless , it is smaller than the third order e1-e1-e1 correction . for low @xmath20 we can estimate the ratio of the two amplitudes as @xmath90 for @xmath91 , @xmath92 , and @xmath93 at the ganil energy . thus the dipole approximation is reasonable , at least for a first exploration . possible higher order effects in the @xmath6 mg intermediate energy coulomb excitation @xcite can also be estimated . assuming a rigid rotor model , high energy coulomb excitation was calculated in the sudden approximation in ref . @xcite . the characteristic strength parameter is @xmath94 using the b(e2)-value found in ref . @xcite we have ( see eq . 6 of ref . @xcite , where a factor @xmath95 is missing on the rhs . ) @xmath96 and @xmath97 with @xmath98 fm for an energy of @xmath99 mev . from fig . 1a of ref . @xcite it can be seen that higher order effects are negligible for the value of the strength parameter @xmath100 . this is in agreement with the result found in the coupled channel calculation of ref . @xcite . in conclusion , we provide a framework to apply corrections to 1@xmath101 order electromagnetic excitation . it is appropriate for fast collisions . we constructed operators which take the influence of intermediate states into account . this can lead to a great simplification as compared , e.g. , to the coupled channels approach . in this approach , a set of states , considered to be relevant , has to be chosen with known electromagnetic matrix - elements . in the present approach , of course , the model dependence can not be altogether avoided ; it enters when the corresponding matrix - elements of the operator has to be calculated , or at least estimated . as an example we studied the excitation of the @xmath11 state in @xmath0be . the importance of higher order effects for this case of an extremely loosely bound nucleus was established . the estimate for the reduction of the cross section can only partly explain the observed reduction of the b(e1)-value in the ganil experiment . however , for a final analysis , more accurate calculations with improved wave functions , including e2 and nuclear effects in the excitation , should be performed . we wish to thank p. g. hansen and m. g. saint - laurent for stimulating discussions . note added in revision : in the meantime we got to know about a coupled channel study of the @xmath0be coulomb excitation by c. a. bertulani , l. f. canto , and m. s. hussein . they get very similar conclusions as compared to our findings . 99 see e.g. g. baur and s. typel , in : proceedings of the 6th international conference on clusters in nuclear structure and dynamics , 6 9 sept . 1994 , ed . by f. haas , ( strasbourg , 1995 ) and further references given there . t. motobayashi et al . , phys . lett . b 346 ( 1995 ) 9 . r. anne et al . , ganil preprint p-94 - 35 ( 1994 ) , z. phys . a in print . p. g. hansen , private communication . k. alder and a. winther , electromagnetic excitation ( north - holland , amsterdam , 1975 ) . s. typel and g. baur , nucl . phys . a 573 ( 1994 ) 486 . s. typel and g. baur , phys . rev . c 50 ( 1994 ) 2104 . d. j. millener , j. w. olness , and e. k. warburton , phys . rev . c 28 ( 1983 ) 497 . t. motobayashi , private communication . g. baur , z. phys . a 332 ( 1989 ) 203 .

after neutrino oscillation experiments have shown that neutrinos possess a non - zero rest mass the question of the absolute mass scale of neutrinos has become important for particle physics and cosmology ( see e.g. @xcite ) . the goal of the karlsruhe tritium neutrino experiment ( katrin , @xcite ) is to search for the mass of the electron antineutrino with a sensitivity of @xmath0{ev / c^2}$ ] . this will probe most of the mass range in which the three neutrino flavours have nearly degenerate masses and where neutrinos are of cosmological importance . to this end a precision measurement of the endpoint region of the @xmath3-decay of tritium will be performed with katrin . the shape of this spectrum depends sensitively on the neutrino mass . this will be done by using a windowless gaseous tritium source for small systematic uncertainties , and an electrostatic energy filter of mac - e filter type ( electrostatic filter with magnetic adiabatic collimation , @xcite ) for the analysis of the electron energy with high luminosity and high resolution . this is the same method as used at the mainz @xcite and troitzk neutrino mass experiments @xcite , which have set the until now best upper limits of @xmath4{ev / c^2 } ( 95\%)$ ] on the neutrino mass . figure [ fig : setup ] gives an overview of the katrin set - up . it consists of a source section with the windowless gaseous tritium source , the wgts ( a ) , a transport section with a differential- and a cryopumping section ( b ) , a pre - spectrometer ( c ) , the main spectrometer ( d ) and a detection section with the focal plane detector ( e ) . the katrin set - up ( explanation see text ) ] the wgts provides a source of electrons from tritium @xmath3-decay with high and uniform intensity . it basically consists of a @xmath5{m}$ ] long beam tube of @xmath6{mm}$ ] diameter through which tritium is circulated in a loop with a flow of @xmath7{ci / s}$ ] and a maximum pressure of @xmath8{mbar}$ ] . this results in a column density of @xmath9{t_2/cm^2}$ ] and @xmath10 @xmath3-particles per second accepted by the spectrometer . in order to keep density fluctuations at @xmath11 or less the wgts is temperature stabilized to @xmath12{mk}$ ] at a temperature of @xmath12{k}$ ] by two - phase neon cooling . the purity of the @xmath13 is maintained at @xmath14 by continous purification of the gas in the tritium loop . these stringent stability requirements result in a highly complex cryostat system @xcite . the technologies used will be tested using a demonstrator set - up , which will be available in spring 2010 . in the final set - up the properties of the source will be checked regularly with an electron source , which is under development @xcite , by laser raman spectroscopy , which already has been deployed successfully for test measurements @xcite , and a penning trap in the beamline to the spectrometers using ft - icr , which has recently been tested successfully @xcite . the transport section serves to guide the electrons from tritium @xmath3-decay to the spectrometers without any losses and to prevent the transport of tritium at the same time , with a reduction factor for tritium of @xmath15 and a final flow of @xmath16mbar - l / s . this is achieved by a differential pumping section , which recently arrived at karlsruhe for testing and commissioning , followed by a cryogenic pumping section . here the remaining tritium gets cryosorbed on a layer of argon frost on the walls of the stainless steel vessel at a temperature of @xmath17{k}$ ] . this method has been tested with the trap experiment successfully @xcite . the pre - spectrometer is a mac - e filter like the main spectrometer . it rejects all electrons with energy @xmath18{ev}$ ] below the endpoint , which are of no interest for the neutrino mass measurement and which even may increase the main spectrometer background . it has been successfully tested and is working at design parameters with an intrinsic background of @xmath19(@xmath20 counts per second ( cps ) ) . for now it is being used as a test case for the technologies and methods used for the main spectrometer , such as the vacuum system ( see e.g. @xcite ) and the electromagnetic design . for these tests it is presently equipped with a 64-pixel pin diode @xcite . the endpoint region of the @xmath3-spectrum is measured with the main spectrometer . this consists of a stainless steel vacuum vessel of @xmath21{m}$ ] length and @xmath5{m}$ ] diameter and will reach a vacuum of @xmath22{mbar}$ ] using turbomolecular pumps and non - evaporating getter material . the magnetic field at the entrance of this mac - e filter is @xmath23{t}$ ] and at its exit @xmath24{t}$ ] while the field in the central analysis plane will be @xmath25{t}$ ] resulting in an energy resolution of @xmath26{ev}$ ] . the retardation voltage is applied directly to the spectrometer hull . for fine shaping of the field and background suppression a modular inner wire electrode system will be used . the main spectrometer has been set - up at karlsruhe and an outgassing rate of @xmath27mbar - l / s has been achieved after bakeout . high demands on the quality of the electric potential and therefore for the precision of the machining of the wire modules required stringent quality control ( see e.g. @xcite ) . the installation of the wire modules is in progress . the high voltage ( hv ) that creates the retardation potential in the analysis plane has to be highly stable . to reach the sensitivity of katrin , fluctuations of the hv of @xmath28{ppm}$ ] , i.e. of @xmath29{mv}$ ] , have to be detected . for this purpose a precision hv - divider has been developed @xcite to measure the applied voltage with this precision . in conjunction with calibration sources based on conversion electrons from the decay of @xmath30 this will ensure the required short and long term stability of the high voltage . electrons with sufficient energy to pass the retardation potential are counted with the focal plane detector . this is a 148-fold segmented pin diode with surroundings made of low - activity materials to reduce the intrinsic background of the detector . simulations show that a background of @xmath31{cps}$ ] can be achieved in the signal region . the detector will be commissioned at karlsruhe in spring 2010 . the katrin background count rate necessary to reach the intended sensitivity is @xmath32{cps}$ ] . by shifting the signal in the detector via a dc - voltage the intrinsic detector background can be reduced to @xmath33{cps}$ ] . however , other sources of background have to be controlled as well . two major sources are background from the tank walls due to muon interactions and radioactive decays , and background from incidential penning traps due to the magnetic and electric fields employed in the mac - e filter . the former is suppressed by the axial magnetic field , which guides most electrons from the wall back to the wall . the remaining wall electrons will be suppressed by the wire electrode system , which is slightly more negative ( o(100v ) ) than the tank wall . the background due to penning traps has been investigated in detail at the pre - spectrometer and can be avoided in large part by proper shaping of the electrodes . however , some unavoidable penning traps still exist , like the trap formed by the pre- and the main spectrometer . investigation of these traps has started and first results are promising @xcite . the katrin experiment searching for the neutrino mass is under construction . the major components are being assembled and tested , and integration of the components will start soon . installation of the inner electrode system of the main spectrometer is ongoing . in 2010 the properties of the main spectrometer will be investigated using calibration sources . data taking using tritium will start in 2012 and will proceed for five years . the work by the author is supported by the german bundesministerium fr bildung und forschung . 9 e. w. otten and c. weinheimer , rep . prog . phys . * 71 * ( 2008 ) 086201 j. lesgourgues and s. pastor , phys . rep . * 429 * ( 2006 ) 307 the katrin collaboration ( j. angrik _ et al . _ ) , _ katrin design report 2004 _ , fzka scientific report 7090 , 2005 , available online at http://bibliothek.fzk.de/zb/berichte/fzka7090.pdf a. picard _ et al . _ , b63 * ( 1992 ) 345 v. m. lobashev and p. e. spivak , nucl . instr . meth . * a240 * ( 1985 ) 305 ch . et al . _ , j. * c 40 * ( 2005 ) 447 v. m. lobashev _ * b 460 * ( 1999 ) 227 s. grohmann , cryogenics * 49 * ( 2009 ) 413 b. bornschein , prog . * 57 * ( 2006 ) 38 k. valerius _ et al . _ , new journal of physics * 11 * ( 2009 ) 063018 m. sturm _ , to be published in las . * 20(2 ) * , 2010 m. ubieto - daz _ et al . _ , int . j. mass spectr . * 288 * ( 2009 ) 1 o. kazachenko _ et al . _ , nucl instr . and meth . * a 587 * ( 2008 ) 136 f. eichelhardt _ et al . _ , fusion science and technology * 54 * ( 2008 ) 615 x. luo _ et al . _ , vacuum * 81 * ( 2008 ) 777 j. wolf , journal of the vacuum society of japan * 52 * ( 2009 ) 278 s. wuestling _ et al . _ , meth * a 568 * ( 2006 ) 382 m. prall _ et al . _ , submitted to ieee transactions on nuclear science , arxiv:0907.5490 th . thmmler , r. marx and ch . weinheimer , new journal of physics * 11 * ( 2009 ) 103007 m. beck , submitted to european physical journal * a * ( 2009 ) , arxiv:0909.3337

the karlsruhe tritium neutrino mass experiment , katrin , aims to search for the mass of the electron neutrino with a sensitivity of @xmath0{ev / c^2}$ ] ( 90% c.l . ) and a detection limit of @xmath1{ev / c^2}$ ] ( @xmath2 ) . both a positive or a negative result will have far reaching implications for cosmology and the standard model of particle physics and will give new input for astroparticle physics and cosmology . the major components of katrin are being set up at the karlsruhe institut of technology in karlsruhe , germany , and test measurements of the individual components have started . data taking with tritium is scheduled to start in 2012 .

monolayer and bilayer graphene are semimetals with good conducting properties @xcite . moreover , in the presence of a microwave field the related optical conductivity is constant over a large regime of frequencies . this has been found in theoretical calculations @xcite and was also observed experimentally @xcite . the reason for this behavior is the existence of at least two bands in both materials , where at fermi energy @xmath0 ( i.e. graphene without a gate potential ) the lower band is occupied and the upper band is unoccupied . as consequence , the absorption of photons of energy @xmath1 from the microwave field creates electron - holes pairs due to the excitation of electrons from the lower band at energy @xmath2 to the unoccupied upper band at energy @xmath3 . this mechanism applies also to gated graphene which has a shifted fermi energy @xmath4 . however , in this case photons can only be absorbed if @xmath5 ( for @xmath6 ) , since all the states in the upper band are occupied up to the energy @xmath7 . correspondingly , a photon can only be absorbed for @xmath8 if @xmath9 . this means that electron - hole creation by a microwave field is only possible if @xmath10 it has been found in a number of recent experiments that the creation of a gap in the semimetallic band structure of monolayer graphene ( mlg ) is possible by absorption of hydrogen @xcite or in bilayer graphene ( blg ) by applying a double gate @xcite . in both cases an electron - holes pair can also be created but this requires a photon energy larger than the band gap @xmath11 ( cf . fig . [ paircreation ] ) . once electron - holes pairs have been created they will contribute to a current in the material , where the latter is related to the strength of the external microwave field by the optical conductivity @xmath12 . this quantity can be measured experimentally and characterizes the electronic properties of the material . in particular , it can be used to determine the band gap @xmath11 , since it vanishes for @xmath13 . blg , in contrast to mlg , has two low- and two high - energy bands . as a result , there are several gaps that lead to electron - hole pair creations on different energy scales with a more complex behavior of the optical conductivity @xcite . in the following the optical conductivity shall be evaluated via the kubo formalism for the low - energy bands in mlg and blg at nonzero temperature @xmath14 . this avoids electron - hole pair creation from higher energy bands and van hove singularities . an important question in this context is the role of the low - energy quasiparticle spectrum on the optical conductivity . in order to focus on simple spectral properties , we consider only non - interacting electrons in a periodic tight - binding model . thus disorder , electron - electron interaction and electron - phonon interaction are not taken into account . . for this process the photon energy must be larger than the band gap @xmath15 . , width=188,height=188 ] the low - energy quasiparticle states in mlg with a gap @xmath15 are described by the massive two - dimensional dirac equation _ [ diracequ00 ] for simplicity , we have set the fermi velocity @xmath16 because this parameter will not appear in the final results for the conductivity . a similar equation exists for the low - energy quasiparticle states of blg @xcite : _ b==0 . [ diracequ01 ] with the plane - wave ansatz @xmath17 we obtain for mlg the following relations _ ( x , y)=_(x , y ) , e^2=m^2+k^2 [ eigen1 ] and for blg _ ( x , y)=_(x , y ) , e^2=m^2+k^4 . [ eigen2 ] these solutions will be used as a basis for evaluating current matrix elements and the optical conductivity . _ kubo formula : _ the optical conductivity can be calculated from the kubo formula . this requires the evaluation of the current operator @xmath18 $ ] , where @xmath19 ( @xmath20 ) is a component of the position of the quasiparticle . the nonzero matrix elements of the current operator with respect to the energy eigenstates of eqs . ( [ eigen1 ] ) , ( [ eigen2 ] ) are either diagonal elements @xmath21|e_k\rangle$ ] or the off - diagonal elements @xmath21|-e_k\rangle$ ] . it turns out that the diagonal elements do not appear in the real part of the optical conductivity @xcite . only the off - diagonal terms contribute because the optical conductivity requires a scattering process between two states whose energy difference is just the photon energy @xmath22 . a convenient representation of the kubo formula then is @xcite @xmath23 with the dirac - fermi distribution @xmath24 at inverse temperature @xmath25 . ( here and in the rest of this paper the spin and valley degeneracy , providing an extra factor 4 , has not been written explicitly . ) integration over @xmath26 gives _ =-_0 ^ 2 radial @xmath27 integration : @xmath28 _ current matrix elements : _ the commutator in the current operator is for dirac fermions the pauli matrix @xmath29 : @xmath30=i\sigma_\mu$ ] ( mlg ) and for blg in fourier representation @xmath31= i\frac{\partial { \bf h}_b}{\partial k_x } = 2i(k_x\sigma_1+k_y\sigma_2 ) \ .\ ] ] then for the current matrix element for mlg we obtain |e|_1|-e|^2 = [ current2 m ] which after angular integration yields _ 0 ^ 2|e|_1|-e|^2 d = = . [ memlg ] for blg ( with @xmath32 , @xmath33 and @xmath34 ) we have |e|k_x_1+k_y_2|-e|^2 = k^2[current2b ] and after the angular integration _ 0 ^ 2|e|k_x_1+k_y_2|-e|^2 d = k^2 . [ meblg ] this is valid only for @xmath35 . as an example , these current matrix elements are plotted for @xmath36 in fig . [ current ] with and without gap . _ conductivity : _ now we insert the results of eq . ( [ memlg ] ) into the kubo formula eq . ( [ kubo0 ] ) and obtain for mlg _ mlg=(^2-^2 ) [ f_(e_f+/2)-f_(e_f-/2 ) ] . [ ocond2 ] inserting eq . ( [ meblg ] ) into the kubo formula gives exactly twice the conductivity of mlg : @xmath37 . thus the conductivities of mlg and blg agree up to a factor 2 . the additive correction due to the gap parameter @xmath38 decays like @xmath39 . as an example , the behavior of the conductivity versus @xmath40 is plotted in fig . [ conductivity ] . the conductivity in eq . ( [ ocond2 ] ) obeys a scaling relation of the conductivity : @xmath41 i.e. the conductivity depends only on three independent parameters . a similar scaling relation exists also for the conductivity in the presence of a scattering rate @xcite . this implies that a reduction of temperature is equivalent to a simultaneous increase of frequency , gap and fermi energy . the optical conductivity vanishes for photon energies less than the gap . it jumps to some finite value when the photon energy exceeds the gap energy , where the size of the jump depends on the fermi energy ( cf . [ conductivity ] ) . the maximal jump appears at @xmath0 . this allows us to measure the gap by measuring the jump of the optical conductivity . such a measurement can be performed as an optical transmission experiment @xcite because the optical conductivity is related to the transmittance @xmath14 through the relation @xmath42 the parameter @xmath43 is the speed of light . then graphene is completely transparent for photonic energies up to the gap energy . this could be used to filter light with frequencies higher than the one given by the gap energy . our model assumption of taking into account only the low - energy bands of blg restricts the photon energies @xmath44 to less than @xmath45ev , which is the gap between the low - energy and the high - energy bands in blg @xcite . this restriction also avoids stronger deviations from the dirac theory of mlg and van hove singularities . taking into account high - energy bands does not change this picture qualitatively , since it would lead to additional jumps of the optical conductivities as soon as the photon energies exceed the gap energies . a van hove singularity would appear as an additional peak . the effect of the gap is a global enhancement by @xmath46 , where for blg the situation is more complex than for mlg . in conclusion , focusing on the low - energy dispersion of gapped monolayer and bilayer graphene , we have found simple expressions for the optical conductivities . they agree for all parameters up to a factor 2 . this is remarkable because the current - matrix elements of both graphene systems are rather different . |-e\rangle|^2 $ ] as a function of the angle @xmath47 between the wave vector @xmath48 and the direction of the current operator . the left panel is the matrix element for @xmath36 without gap ( @xmath49 ) and the right panel is the matrix element with gap ( @xmath50 ) . full ( dashed ) curves are for blg ( mlg ) . , title="fig:",width=264,height=264 ] |-e\rangle|^2 $ ] as a function of the angle @xmath47 between the wave vector @xmath48 and the direction of the current operator . the left panel is the matrix element for @xmath36 without gap ( @xmath49 ) and the right panel is the matrix element with gap ( @xmath50 ) . full ( dashed ) curves are for blg ( mlg ) . ,

we study the optical conductivity in the low - energy regime of gapped mono- and bilayer graphene . a scaling relation is found , in which the four parameters frequency , gap , fermi energy and temperature appear only as combination of three independent parameters . the ratio of the optical conductivity of bilayer and mononlayer graphene is exactly 2 .

cellular automata with complex behavior exhibit dynamical patterns that can be interpreted as the movement of particles through a physical medium . these particles are interpretable as loci for information storage , and their movement through space is interpretable as information transfer . the collisions of these particles in the cellular automaton s lattice are sites of information processing @xcite . cellular automata with complex behavior have immense potential to describe physical systems and their study has had impact in the design of self - assembling structures @xcite and the modelling of biological processes like signaling , division , apoptosis , necrosis and differentiation @xcite . john conway s game of life @xcite is the most renowned complex binary cellular automaton , and the archetype used to guide the search methodology for other complex binary cellular automata that we describe in this work . previously , complex behavior in binary cellular automata has been characterized through measures such as entropy @xcite , lyapunov exponents @xcite , and kolmogorov - chaitin complexity @xcite . we propose the characterization of the behavior of @xmath0-dimensional cellular automata through heuristic measures derived from the evaluation of their minimal boolean forms . this proposed characterization is derived from heuristic criteria validated in elementary cellular automata with simple boolean forms . table [ table : ca - boolean - behavior ] illustrates the rationale for this characterization showing elementary cellular automata whose boolean forms are minimally simple , and whose behavior can be unequivocally identified . cellular behaviors of growth , decrease , and chaoticity are characterized by the boolean operations _ or _ , _ and _ , and _ xor _ , respectively . the cellular behavior of stability can be characterized by the absence of a boolean operator or the use of the _ not _ operator . we define an evaluation criterion to produce metrics that characterize the behavior of cellular automata whose minimal boolean expressions are more complex ( i.e. have more terms and the combination of various operators ) than those appearing in table [ table : ca - boolean - behavior ] . the produced metrics are used to create static and dynamic measures of behavior . the static measure of behavior is calculated from the truth table of the minimal boolean expression of the cellular automaton , and the dynamic measure of behavior is derived from the averaged appearance of the metrics in _ n _ executions of the cellular automaton from _ n _ random initial conditions . we use the euclidean distance of these measures in a given cellular automaton to the measures of the game of life to assess its capacity for complex behavior , and use this distance as a cost function to guide the genetic search of @xmath0-dimensional cellular automata with complex behavior . a cellular automaton is formally represented by a quadruple @xmath1 , where * @xmath2 is the finite or infinite cell lattice , * @xmath3 is a finite set of states or values for the cells , * @xmath4 is the finite cell neighborhood , * @xmath5 is the local transition function , defined by the state transition rule . each cell in the lattice @xmath2 is defined by its discrete position ( an integer number for each dimension ) and by its discrete state value @xmath3 . in a binary cellular automaton , @xmath6 . time is also discrete . the state of the cell is determined by the evaluation of the local transition function on the cell s neighborhood at time @xmath7 ; @xmath8 is the next time step after time @xmath7 . the neighborhood is defined as a finite group of cells surrounding and/or including the observed cell . the global state is the configuration of all the cells that comprise the automaton , @xmath9 . the lattice @xmath2 is the infinite cyclic group of integers @xmath10 . the position of each cell in the lattice is described by the index position @xmath11 . configurations are commonly written as sequences of characters , such as @xmath12 the finite global state is a finite configuration @xmath9 , where @xmath2 is a finite lattice , indexed with @xmath13 integers , @xmath14 the set of neighborhood indices @xmath15 of size @xmath16 is defined by the set of relative positions within the configuration , such that @xmath17 @xmath18 is the neighborhood of the observed cell @xmath19 that includes the set @xmath15 of indices , and is defined as @xmath20 this describes the neighborhood as a character string that includes the cells that are considered neighbors of the observed cell @xmath21 . a compact representation of the neighborhood value @xmath18 is a unique integer , defined as an @xmath22digits , @xmath23based number [ 2 ] @xmath24 the local transition function @xmath5 yields the value of @xmath19 at @xmath25 from the neighborhood of the cell observed at present time @xmath7 is expressed by @xmath26 where @xmath27 specifies the states of the neighboring cells to the cell @xmath21 at time @xmath7 . the transition table defines the local transition function , listing an output value for each input configuration . table [ table : tran - function - truth - table ] is a sample transition table for an elementary cellular automaton with a neighborhood of radius 1 , wherein adjacent neighboring cells of @xmath19 are @xmath28 and @xmath29 , forming a tuple @xmath30 , @xmath31 . .local transition function of @xmath32 as a truth table . [ cols="^,^",options="header " , ] c + averaged spacetime evolution + + + identified glider + we wish to thank jan baetens , hector zenil , alyssa adams , and nima dehghani for their helpful comments . we appreciate the support of the physics and mathematics in biomedicine consortium . we also wish to thank todd rowland for his encouragement and continued interest in the project h. abelson , d. allen , d. coore , c. hanson , e. rauch , g. j. sussman , g. homsy , j. thomas f. knight and r. w. radhika nagpal , `` amorphous computing , '' _ communications of the acm _ , * 43*(5 ) , 2000 , pp . 74 - 82 . m. hirabayashi , s. kinoshita , s. tanaka , h. honda , h. kojima and k. oiwa , `` cellular automata analysis on self - assembly properties in dna tile computing , '' _ lecture notes in computer science _ , * 7495 * , 2012 , pp . 544 - 553 . m. hwang , m. garbey , s. a. berceli and r. tran - son - tay , `` rule - based simulation of multi - cellular biological systems a review of modeling techniques , '' _ cellular and molecular bioengineering _ , * 2*(3 ) , 2009 , pp . 285 - 294 .

we propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal boolean form of a cellular automaton s transition function . these behavioral metrics are formulated to satisfy heuristic criteria derived from elementary cellular automata . behaviors characterized through these metrics are growth , decrease , chaoticity , and stability . from these metrics , two measures of global behavior are calculated : 1 ) a static measure that considers all possible input patterns and counts the occurrence of the proposed metrics in the truth table of the minimal boolean form of the automaton ; 2 ) a dynamic measure , corresponding to the mean of the behavioral metrics in _ n _ executions of the automaton , starting from _ n _ random initial states . we use these measures to characterize a cellular automaton and guide a genetic search algorithm , which selects cellular automata similar to the game of life . using this method , we found an extensive set of complex binary cellular automata with interesting properties , including self - replication .

1 . temperature dependence of the magnetization , measured with @xmath2 = 1 t with zero - field - cooling ( zfc ) , field - cooled - cooling ( fcc ) , and field - cooled - warming ( fcw ) procedures . the inset shows the time evolution of the normalized magnetization after zfc to @xmath15 = 8 , 40 , 60 and 100k . field dependence of the sample s temperature showing an abrupt warming from 2.5 to @xmath20 30 k at @xmath21 @xmath19 2.2 t. the inset shows a spontaneous magnetization jump , measured with a fixed magnetic field . time dependence of the magnetization during a magnetic field sweep , for different waiting times between consecutive field increments : @xmath62 = 7.5 ( squares ) , 15 ( circles ) , 30 ( up triangles ) and 60 min . ( down triangles ) , at @xmath15 = 2.5 k. the inset shows an enlarged portion of the region just before the magnetization jump .

the occurrence at low temperatures of an ultrasharp field - induced transition in phase separated manganites is analyzed . experimental results show that magnetization and specific heat step - like transitions below 5 k are correlated with an abrupt change of the sample temperature , which happens at a certain critical field . this temperature rise , a magnetocaloric effect , is interpreted as produced by the released energy at the transition point , and is the key to understand the existence of the abrupt field - induced transition . a qualitative analysis of the results suggests the existence of a critical growing rate of the ferromagnetic phase , beyond which an avalanche effect is triggered . mixed valent manganites show a great deal of fascinating properties , arising from the strong interplay between spin , charge , orbital , and lattice degrees of freedom @xcite . the most intriguing one is the existence of a phase separated state , the simultaneous coexistence of submicrometer ferromagnetic ( fm ) metallic and charge ordered ( co ) insulating regions dagotto . the phase separation scenario has its origin in the unusual proximity of the free energies of these very distinct fm and co states , and in the fact that the competition between both phases is resolved in mesoscopic length scales , giving rise to real space inhomogeneities in the material . yet another surprising result more recently found in manganites is the appearance of ultrasharp magnetization steps at low temperatures ( below @xmath0 5 k ) in the isothermal magnetization @xmath1(@xmath2 ) curves @xcite . this effect , the field induced transition of the entire compound from one phase to the other of the coexisting states , is included in the category of metamagnetic transitions @xcite . however , unlike the broad continuous transitions expected for inhomogeneous granular systems , in this case it occurs in an extremely narrow window of magnetic fields . these ultrasharp steps were observed in both single crystals and polycrystalline samples , indicating that it is not related to a particular micro - structure of the material . the actual existence of a phase separated state was recognized as a key parameter for the observation of these magnetization jumps @xcite . the effect was first reported in manganites doped at the mn site , and the disorder in the spin lattice was thought to play a relevant role hebert1 . however , a similar behavior was also found in pr@xmath3ca@xmath4mno@xmath5 , and the qualitative interpretation of the phenomenon shifted to the martensitic character of the phase separated state @xcite . accommodation strains were shown to be relevant in the stabilization of phase separation @xcite , but their role in the magnetization steps is not clear , since it is expected that grain boundaries would act as a sort of firewall for the movement of the domain walls , stopping the avalanche process . additionally , despite its intrinsic first - order character , the martensitic transformation is spread over a large range of the external parameter driving the transition , the magnetic field in the present case , in strong disagreement with the abrupt character of the transition . the aim of this investigations is to address a basic question concerning this abrupt field - induced transition : why is this metamagnetic transition so sharp , and what is actually causing it ? we report the occurrence of ultrasharp magnetization steps at low temperatures in a prototype phase separated manganite , which are accompanied by discontinuities in the magnetic field dependence of the specific heat . concomitantly with these facts , we found that the field - induced transition is accompanied by a large increase in the temperature of the sample , by dozens of degrees . this feature suggests a mechanism in which the abrupt first order transition in the whole sample is triggered by the released heat in a microscopic phase transformation . a low temperature heat controlled magnetization avalanche was previously found in bulk disordered magnets @xcite due to the heat released by the fm domain wall motion during the reversal of the remnant magnetization . also , local heating induced by non - uniform current flow was proposed as the origin of the mesoscopic fluctuations between coexisting phases observed in la@xmath6pr@xmath7ca@xmath8mno@xmath5@xcite . we propose that in phase separated manganites the interplay between the growth of the fm phase induced by the magnetic field and the heat generated by this growth is the key to explain the avalanche process leading to an ultrasharp field - induced transition in these inhomogeneous strongly correlated systems . the particular compound under study is a high quality polycrystalline sample of la@xmath6pr@xmath7ca@xmath8mno@xmath5 , synthesized by the sol - gel technique . it belongs to the well known family of compounds la@xmath9pr@xmath10ca@xmath11mno@xmath12 whose tendency to form inhomogeneous structures in the range 0.3@xmath130.4 is extensively documented . uehara , uehararate , kim , balagurov , kiryukhin , nonvolatile scanning electron micrographs revealed a homogeneous distribution of grain sizes , of the order of 2 @xmath14 m . an identification of the magnetic phases of the material can be made through the temperature dependence of the magnetization , @xmath1(@xmath15 ) . the results were obtained on an extraction magnetometer with a field @xmath2 = 1 t , and are shown in fig . 1 . as the temperature is lowered the sample changes from a paramagnetic to a charge - ordered antiferromagnetic state at @xmath16 = 220 k. just below , a small kink at 190 k is a signature of the onset of the formation of ferromagnetic clusters @xcite . a more robust ferromagnetic phase appears at @xmath17 = 70 k ( 90 k on warming ) , which coexists with the majority co state in an inhomogeneous phase separated state @xcite . in a temperature window extending from @xmath17 down to a temperature @xmath18 @xmath19 20 k the magnetization shows considerable relaxation effects , as shown in the inset of fig . 1 , signaling the growth of the fm phase against the co background . the temperature @xmath18 ( which depends on the applied field ) can be identified as a blocking temperature ; relaxation below @xmath18 is strongly reduced . additionally , the magnetic state below @xmath18 is highly dependent on the sample magnetic field and cooling history . if the sample is cooled without an applied field ( zfc ) the magnetization at 2 k shows a significant low value , that remains unchanged while warming until @xmath18 , above with it shows a continuous increase and merges with the field cooling warming curve . = 1 t with zero - field - cooling ( zfc ) , field - cooled - cooling ( fcc ) , and field - cooled - warming ( fcw ) procedures . the inset shows the time evolution of the normalized magnetization after zfc to @xmath15 = 8 , 40 , 60 and 100k.,width=264 ] with the application of a large enough magnetic field the low temperature ( below @xmath20 5 k ) zero - field - cooled state is transformed into a fm phase in an abrupt step - like metamagnetic transition . figure 2(a ) shows magnetization measurements as a function of applied field , @xmath1(@xmath2 ) , measured at @xmath15 = 2.5 k. at a certain critical field @xmath21 the entire system changes to a nearly homogenous fm state , which remains stable even after the field is removed . the width of the transition , determined by repeating the measurements with lower field increments , is below 10 oe . figure 2(b ) shows specific heat data as a function of applied field , @xmath22(@xmath2 ) , measured by the relaxation method at the same base temperature , @xmath15 = 2.5 k. as can be readily noticed , a discontinuous transition occurs at approximately the same magnetic field , indicating that a true thermodynamic transition is taking place . = 2.5 k. both measurements show an abrupt change at the same critical field @xmath21 @xmath19 2.2 t.,width=226 ] since the observed transition is first order , it is expected that the latent heat involved should affect the thermodynamic state of the sample , for instance , its temperature . in order to gain some insights on the magnitude of the effect the following experiment was performed : with the sample placed in a vacuum calorimeter with a weak thermal link to the temperature controlled surroundings ( kept at 2.5 k ) , the sample s temperature was measured while the magnetic field was increased , with field increments identical to the data of fig.2 . the obtained result , plotted in fig . 3 , shows the occurrence of a sudden and huge increase of the sample s temperature , greater than 25 k , at the same critical field of the magnetization jump . since the relaxation time for temperature stabilization between the sample and the temperature controlled surroundings ( of the order of several seconds ) is much larger than the internal time constant between the sample and the sample holder ( of the order of milliseconds ) , the temperature rise measured is intrinsic to the sample . the abrupt increase of the sample s temperature can be then doubtless ascribed to the heat generated when the non - fm fraction of the material is converted to the fm phase . the same experiment was repeated with samples of la@xmath23pr@xmath24ca@xmath11mno@xmath5 with different pr content , as well as in samples of the series landcamno . whenever a magnetization jump occurs a sizable increase of the sample s temperature was observed . it is also worth mentioned that in the @xmath1(@xmath2 ) and @xmath22(@xmath2 ) data of figure 2 the sample s temperature is in fact not strictly constant ; there is also a sudden temperature rise at the field of the step transition , followed by a quick relaxation to the base temperature of system . the process which starts with nearly the whole material in the non - fm phase at @xmath25 = 2.5 k and ends with a nearly homogeneous fm state at @xmath26 @xmath27 30 k , is conceptually related with the magnetocaloric ( mc ) effect @xcite . 30 k at @xmath21 @xmath19 2.2 t. the inset shows a spontaneous magnetization jump , measured with a fixed magnetic field.,width=226 ] the mc effect consists basically in a temperature change @xmath28 induced by the application of a magnetic field , which , within the approximation of reversible process , is related with the entropy change @xmath29 generated by ordering the spin lattice . in our case , however , the approximation of reversible adiabatic process is not valid , due to the strong irreversible character of the field - induced transformation . also , as the phase transition from de co to the fm phases involves large changes in the magnetic , structural and electronic properties , which are strongly correlated , the magnetic field affects all the degrees of freedom of the system . this fact makes inapplicable some of the usual basic equations employed in the description of the mc effect . a more realistic approach is to use the conservation of the internal energy during the fast conversion process ( hypothesis of adiabaticity ) . neglecting small changes of the sample volume , we can make the identity @xmath30 , where @xmath31 is the internal energy per volume unit . replacing the whole ( irreversible ) process by an isothermal plus an isobaric one , we can write : @xmath32 where @xmath33 is the specific heat of the fm phase at constant pressure . this yields an estimate for the released heat at the field induced transition given by @xmath34 . this estimated value was obtained from specific heat measurements as a function of temperature performed at zero magnetic field after the sample was transformed to the fm phase by application of a field of 9 @xmath15 . the magnetization and specific heat results , shown in fig . 2 , are macroscopic signatures of a phenomenon which must be understood at a microscopic level . below the temperature @xmath18 the sample gets into a strongly blocked regime , in which the fm clusters can not grow against the co background ( see inset of fig 1 ) . after zero- field - cooling , the sample reaches the blocked state with a small , time independent , fraction @xmath35 of fm phase , which can be thought as distributed in isolated regions or clusters surrounded by a co matrix . the application of an external magnetic field @xmath2 weakens this frozen - in state , inducing the increase of each cluster of volume @xmath36 in an amount @xmath37 , which can depend on @xmath38 , @xmath15 , @xmath2 and time . the released heat yielded by this particular process is @xmath39 . part of this energy is used to locally increase the temperature of the fm volume @xmath36 , a process that can be considered as instantaneous , taking into account that the thermal conductivity of the fm phase is much greater than that of the co phase . the remaining energy @xmath40 is evacuated through the surrounding co region . this balance yields @xmath41 once a process involving a change of the local fm fraction happens , the further evolution of the system is determined by the interplay between the rates at which the system is generating heat , and the rate at which the co phase is releasing it . when the former is greater than the latter , a local temperature rise within the fm region is obtained . if this temperature reaches values beyond the blocking temperature corresponding to the applied field @xmath2 the system becomes critical , in the sense that the adjacent co regions , which in turn will increase their local temperature too , become highly unstable . these unstable co regions are now easily transformed to the fm state , releasing heat , and so on , inducing an avalanche - like chain reaction . at the end , all regions which have ferromagnetism as its equilibrium state at @xmath15=@xmath26 and field @xmath2 had been converted from co to fm . the equilibrium fractions of the coexisting phases at that @xmath15 and @xmath2 values then determine the size of the avalanche process . following equation ( 2 ) , we can make an estimation of the critical value of the volume change @xmath42 which is needed to _ turn - on _ the avalanche process . the first condition to be accomplished is that the temperature of the local fm region increases beyond the blocking temperature @xmath18(@xmath2 ) . assuming that it occurs in a time scale @xmath43 , and that in this scale the heat transferred to the co region is negligible , we obtain @xmath44 where @xmath45 8 k at @xmath46 = 2.2 t was estimated from zfc magnetization measurements . this calculation yields @xmath47 , i.e. , almost one per cent increase of the local fm volume is needed to initiate the abrupt transition . this condition must be accompanied by another one , related with the time @xmath43 in which the volume enlargement occurs . as mentioned above , this time has to be short enough to avoid the heat be released through the surrounding co region , i.e. , the condition @xmath48 must hold , where @xmath49 is the area of the cluster surface , @xmath50 is the thermal conductivity of the co phase and @xmath51 is a local spatial coordinate . a crude estimation of @xmath43 can be done assuming that , within the adjacent co region , the temperature decays from @xmath52 to @xmath25 in a length @xmath53 , and taking into account that typical low temperature values for @xmath50 could range between 0.1 - 1 w/(mk ) . these assumptions give , for instance , @xmath5410@xmath55 - 10@xmath56 s for clusters of volume @xmath36 = ( 50 nm)@xmath57 , and predicts a critical rate @xmath58 . therefore , we estimate that thermal processes that happen within a narrow time window , involving a one percent increase of the local fm regions are needed to initiate the abrupt field - induced transition , the critical rate scaling as the linear size of the fm cluster . the occurrence of the step transition is then governed by the probability of such an event , once the magnetic field has yielded the crossover between the free energies of the coexisting phases . one way to modify the avalanche probability is allowing the system to relax before reaching the critical state . allowing relaxation an increase of the fm fraction as a function of the elapsed time occurs , and consequently the value of the @xmath59 needed to _ turn - on _ the process should also increases this would be reflected on the dependence with the elapsed time of the critical field @xmath21 at which the jump occurs . to verify this hypothesis we have measured the time dependence of the magnetization during a field sweep , @xmath1(@xmath2,@xmath60 ) at 2.5 k , starting with @xmath2 = 1.9 t , and waiting a time @xmath61 at fixed @xmath2 before changing to the next field value . in fig . 4 we show the @xmath1 vs @xmath60 curves obtained for different values of @xmath62 , confirming the above presumption : for larger @xmath62 the magnetization jump occurs at higher critical fields . as a remarkable result , we observed that in most cases the step transition occurs spontaneously within the time interval where the field was unchanged . this fact signs unambiguously that the width of the step transition , beyond any experimental resolution , is strictly zero . the inset of fig . 3 shows a spontaneous ( as opposed to field - induced ) magnetization jump , which happens at a fixed field and temperature values . the occurrence of spontaneous magnetization jumps in phase separated manganites was also reported by another group.spontaneous = 7.5 ( squares ) , 15 ( circles ) , 30 ( up triangles ) and 60 min . ( down triangles ) , at @xmath15 = 2.5 k. the inset shows an enlarged portion of the region just before the magnetization jump.,width=321 ] the fact that the step transition can be reached spontaneously while the external parameters ( @xmath2 and @xmath15 ) are kept constant indicates that the abrupt transition is truly connected with the probability of occurrence of certain microscopic process , which within the above described scenario is a particular enlargement of the fm phase . however , this process will initiate the avalanche only when the local increment of the fm phase is large and fast enough to yield the appropriate increase of the local temperature through a magnetocaloric effect . figure 4 and its inset clearly show that not any enlargement process is able to trigger the step transition . the relaxation effects displayed by the system before the occurrence of the magnetization jump indicate that the system can in fact increase its fm phase fraction without initiating the avalanche , i.e. , there are fm regions that starts to become unblocked for field values just below the critical field , increasing their local volume by overcoming energy barriers . for instance , the curve for @xmath62 = 60 min . ( with @xmath21 = 2.56 t ) shows a sizable increase of the fm fraction before the occurrence of the magnetization jump . from inspection of fig . 4 , it is likely that for larger values of @xmath62 larger values of the fm fraction before the jump would be obtained . the waiting time @xmath62 is a key parameter to determine the energy barriers values for which the system is blocked . eventually , for an extremely large value of @xmath62 the whole system would behave as unblocked and the @xmath1(@xmath2 ) curve obtained in this hypothetical situation would display a continuous metamagnetic transition behavior , without jumps . therefore , once the value of the minimal @xmath21 corresponding to the fastest experiment is established , the limit temperature above which the step transition no longer occurs is determined by the blocking temperature corresponding to this field , @xmath18(@xmath21 ) . this suggests why the magnetization jump occurs only below a very specific temperature , mahendiran above which the system overcomes the energy barriers without turning on the avalanche process . in conclusion , we have presented evidence that the low temperature abrupt field - induced transition occurring in phase separated manganites is intimately related with the sudden increase of the sample temperature at the first order transition point , a feature which is crucial for the understanding of the phenomenon . we proposed a simple model in which the close interplay between the local increase of the fm phase and the heat released in this microscopic transformation can turn - on the avalanche leading to the observed step - like transition . within this framework , the entity which is propagated is heat , not magnetic domain walls , so the roles of grain boundaries in ceramic samples or strains which exist between the coexisting phases are less relevant . the observation of spontaneous transitions gives additional support to that view , demonstrating that the step transition is not only the result of a crossover between macroscopic free energies induced by the magnetic field , but must be triggered by a microscopic mechanism which initiates the avalanche process . additionally , we have established that a critical relative increment of a fm region or cluster is needed for the system to reach the `` chain reaction '' state , i.e. , larger initial fm factions require larger critical fields to _ turn - on _ the process , a feature previously observed . @xcite finally , it must be emphasized that the basic condition for the occurrence of the abrupt transition is that the system must reach the low temperature regime in a strongly blocked state . at temperatures just a few degrees higher the abrupt step - like transition no longer occurs , and it is replaced by a standard continuous metamagnetic transition @xcite . in summary , we propose that some microscopic mechanism promotes locally a fm volume increase , which yield a local temperature rise , and triggers the observed avalanche process . this work was partially supported by capes , cnpq , fapesp , conicet , and fundacin antorchas .

d.f . acknowledges financial support from the european research council under the european unions seventh framework programme ( fp/20072013)/erc ga 306559 and epsrc ( uk , grant ep / j00443x/1 ) . i. c. acknowledges financial support by the erc through the qgbe grant , by the eu - fet proactive grant aqus , project no . 640800 , and by the autonomous province of trento , partly through the siquro project ( `` on silicon chip quantum optics for quantum computing and secure communications '' ) here we provide further details on the effect of nonlocal interactions on the landau critical velocity . the starting point of this discussion is the bogoliubov dispersion of collective excitations in such a _ nonlocal fluid _ when this is at rest . after simple manipulation of eq.(4 ) of the main text , this can be written in the more usual form @xcite : @xmath150 that allows for transparent analytical manipulations and easier connection to the many - body literature . with respect to the usual case of a local fluid @xcite , the nonlocality enters via the denominator of the interaction term that suppresses interactions at large @xmath151 . for a propagating fluid of light , the frequency @xmath25 corresponds to the wavevector @xmath152 in the propagation direction expressed in temporal units , @xmath153 , and @xmath151 is the transverse wavevector ( note the different convention from @xcite ) . in terms of the optical parameters of the optical medium , @xmath154 is the effective mass of the photons , @xmath155 is the fluid density , @xmath156 is the interaction constant , and the nonlocality is again modeled with a lorentzian function of size @xmath157 . here , @xmath7 is the background refractive index and @xmath158 the free wavevector in the medium , and @xmath159 is the optical nonlinearity . the units of this latter are such that @xmath160 is the nonlinear refractive index shift . , the right ( b , d ) panels are for a nonlocal fluid with a value of @xmath161 inspired by the experiment . the dotted curve in the right panels repeats the local fluid dispersion for comparison . the red dashed line is the straight line @xmath162 corresponding to the critical speed @xmath106 . the panels in the bottom row show the same curves in log - log scale . ] examples of such a bogoliubov dispersion are shown in fig.[fig : bogo ] both in linear - linear and in log - log scales . the landau critical velocity is defined as the minimum of the phase velocity @xmath163 where in our case @xmath164^{1/2}.\ ] ] on the nonlocal length @xmath157 [ upper panel ( a ) ] and on the density @xmath165 [ lower panel ( b ) ] . in this latter , the density is normalized to @xmath166 and the velocity to @xmath167 . the vertical dot - dashed lines indicate the transition points between the two @xmath168 regimes . the vertical dashed line in the upper panel indicate the experimental conditions . the dotted line in the lower panel shows how @xmath169 behaviour would extend to the whole domain . ] * for weak nonlocalities @xmath171 [ fig.[fig : bogo](a , b ) ] , the phase velocity @xmath172 is a monotonically growing function of @xmath151 , so the minimum is attained at @xmath173 . the critical landau speed is then the speed of sound , @xmath174 * for strong nonlocalities @xmath175 [ fig.[fig : bogo](c , d ) ] , the phase velocity @xmath172 has a local minimum at @xmath176 where it attains the smaller value @xmath177}\ ] ] plots of the critical velocity @xmath178 as a function of the nonlocality length and of the fluid density are shown in the two panels of fig.[fig : vc ] . the former clearly shows that the critical velocity is equal to the sound velocity upto @xmath179 , then it quickly decays to zero according to the formulas : @xmath180 the latter shows the usual @xmath169 dependence at low @xmath165 , which then transforms into a slower @xmath181 law at high @xmath165 according to the formulas : @xmath182 note that the two regimes continuously connect at the transition point @xmath179 . for the parameters of the experiment @xmath183 with a background refractive index estimated around @xmath184 , one has @xmath185 which gives a factor @xmath186 reduction of the critical velocity @xmath106 below the speed of sound @xmath187 . 40ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/revmodphys.85.299 [ * * , ( ) ] link:\doibase 10.1098/rspa.2014.0320 [ * * , ( ) ] link:\doibase 10.1103/physreva.92.043802 [ * * , ( ) ] link:\doibase 10.1103/physreva.60.4114 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevlett.69.1644 [ * * , ( ) ] @noop _ _ ( , ) @noop _ _ ( , ) link:\doibase 10.1038/nphys1364 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1038/nphoton.2011.211 [ * * , ( ) ] link:\doibase 10.1038/nphys1959 [ * * , ( ) ] link:\doibase 10.1364/optica.2.000484 [ * * , ( ) ] http://prl.aps.org/abstract/prl/v69/i17/p2503_1 [ * * ( ) ] @noop * * , ( ) link:\doibase 10.1364/ol.37.002325 [ * * , ( ) ] link:\doibase 10.1038/nphys486 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.99.043903 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physreva.87.013802 [ * * , ( ) ] @noop _ _ ( , ) link:\doibase 10.1103/physreva.78.063804 [ * * , ( ) ] http://www.ncbi.nlm.nih.gov/pubmed/17572718 [ * * , ( ) ] link:\doibase 10.1007/bf02780991 [ * * , ( ) ] link:\doibase 10.1016/s0079 - 6417(08)60077 - 3 [ * * , ( ) ] link:\doibase 10.1098/rspa.1957.0071 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1073/pnas.1400033111 [ * * , ( ) ] link:\doibase 10.1073/pnas.1312737110 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physreva.91.023621 [ * * , ( ) ] link:\doibase 10.1364/ao.27.005082 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1209/0295 - 5075/92/14002 [ * * , ( ) ] link:\doibase 10.1103/physreva.85.045602 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) http://stacks.iop.org/0034-4885/72/i=12/a=126401 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) y. pomeau and s. rica , _ model of superflow with rotons _ , phys 71 * , 247 ( 1993 ) .

recent work has unveiled a new class of optical systems that can exhibit the characteristic features of superfluidity . one such system relies on the repulsive photon - photon interaction that is mediated by a thermal optical nonlinearity and is therefore inherently nonlocal due to thermal diffusion . here we investigate how such a nonlocal interaction , which at a first inspection would not be expected to lead to superfluid behavior , may be tailored by acting upon the geometry of the photon fluid itself . our models and measurements show that restricting the laser profile and hence the photon fluid to a strongly elliptical geometry modifies thermal diffusion along the major beam axis and reduces the effective nonlocal interaction length by two orders of magnitude . this in turn enables the system to display a characteristic trait of superfluid flow : the nucleation of quantized vortices in the flow past an extended physical obstacle . these results are general and apply to other nonlocal fluids , such as dipolar bose - einstein condensates , and show that `` thermal '' photon superfluids provide an exciting and novel experimental environment for probing the nature of superfluidity , with applications to the study of quantum turbulence and analogue gravity . over the past decade , theoretical and experimental studies of photon fluids have opened new routes to realizing quantum many - body systems . in the most general case , a photon fluid is created by propagating a laser beam through a defocusing nonlinear medium such that the photons in the beam act as a gas of weakly interacting particles @xcite . as in atomic many - body systems , the collective photon behavior can be described by a gross - pitaevskii equation @xcite , where the electric field plays the role of the order parameter , a macroscopic wave function with a clear resemblance to dilute - gas bose - einstein condensates ( becs ) and superfluid helium . much research with photon fluids has therefore centered on exploring characteristics of superfluidity , such as the nucleation of vortices of quantized circulation in the flow past an obstacle for sufficiently high flow speeds @xcite . + significant progress on this front has been made in the field of _ polariton _ fluids , strongly coupled exciton - polaritons in semiconductor microcavities , that have shown superfluid characteristics , such as the frictionless flow around an obstacle @xcite , and shedding of solitons @xcite and quantized vortices @xcite . differently from these driven - dissipative systems with a _ local _ nonlinearity , signatures of superfluid behavior in the dispersion relation have also been observed for room - temperature , _ nonlocal _ photon fluids in a propagating geometry @xcite . in such a system , heating induced by a laser beam leads to a decrease in the refractive index of the propagation medium and a consequent defocusing effect for the laser beam , resulting in an effective repulsive photon - photon interaction established by the medium . for a monochromatic beam , the transverse beam profile acts to define the geometry of the two - dimensional ( 2d ) fluid and is fully described by hydrodynamic equations , where the propagation direction maps on to an effective time coordinate @xcite . due to heat diffusion , this interaction is inherently nonlocal , i.e. , the photon density at one point in space influences the interactions at a distant point . photon - photon interactions are therefore effectively spread out over distances of the order of the characteristic thermal diffusion ( or nonlocal ) length . while solitons and vortex solitons have previously been reported in these systems @xcite , the nonlocal aspect of the interaction has only recently attracted attention @xcite , enabling studies of novel shock front and turbulence dynamics @xcite . the main effect of the fluid nonlocality in the context of superfluidity is a reduction and even cancellation of the effect of interactions on intermediate length scales and a restoration of the standard single - particle dispersion relation for excitations in the medium at much lower wavevectors than the inverse healing length . while one can expect that this effect may result in the inhibition of superfluid behavior in generic nonlocal superfluids such as dipolar atomic becs , the interplay of nonlocality and superfluidity has not yet been completely explored in the literature . + here we analyze in detail the nature of a propagating laser beam s thermal photon - photon interactions mediated by a dilute dispersion of graphene nanoflakes in methanol . our primary result is that with a suitable configuration of the photon fluid s geometry , as determined by the laser beam s transverse profile , nonlocal interactions can exist simultaneously with characteristics of superfluidity , as evidenced by the nucleation of quantized vortices in the photon fluid s flow past an obstacle . analytically , we start with a model that accounts for the boundary conditions of the system . by introducing a distributed loss term in the heat diffusion equation , we recover and thus justify the lorentzian response function that has been used in many previous works @xcite . we then show that , for fixed boundary conditions , changing the geometry of the photon fluid , e.g. by using a highly elliptical rather than circular beam , enables us to control and reduce the effective nonlocal interaction length by two orders of magnitude . this choice of beam geometry has the primary effect of restoring locality to a sufficient extent so as to restore superfluid behavior . with such an elliptical beam , we experimentally demonstrate evidence of superfluidity in nonlocal photon fluids revealed by the nucleation of quantized vortices in the wake of an extended obstacle . + _ photon fluids : _ although the findings of this work are general and apply to any nonlocal superfluid , we derive the main conclusions by focusing our attention on the specific case of a thermal photon fluid where the photon - photon interaction is mediated by heating induced by the local intensity of a propagating laser beam . details of the system we are analyzing can be found in ref . @xcite and are summarized in fig . [ fig : fig1 ] , which shows the experimental layout used in the experiments described below . the essential component in the system is the actual nonlinear medium , a cylindrical cell with a radius @xmath0 cm and length @xmath1 cm , filled with methanol ( whose negative thermo - optic coefficient provides the repulsive photon - photon interaction ) and a low concentration of graphene nanoflakes ( on the order of @xmath2 ) , providing a weak absorption of the input beam needed to enhance the nonlinearity . + we briefly recall the main features and equations describing photon fluids . the nonlinear propagation of a laser beam of electric field amplitude @xmath3 in a defocusing medium can be described within the paraxial approximation @xcite in terms of a nonlinear schrdinger equation , @xmath4 here , @xmath5 is the optical wavenumber , @xmath6 is the vacuum wavelength of the light , and @xmath7 is the linear refractive index . in the limit of negligible absorption @xmath8 , and a local interaction such that @xmath9 , with @xmath10 the negative nonlinear refractive index , eq . is formally identical to the gross - pitaevskii equation for dilute boson gases with a repulsive interatomic interaction @xcite . by considering the propagation direction @xmath11 as time coordinate @xmath12 , where @xmath13 is the speed of light in vacuum , and the electric field @xmath14 as a function of photon fluid density @xmath15 ( with units of @xmath16 ) and phase @xmath17 , one arrives at a set of hydrodynamic equations over transverse spatial coordinate @xmath18 that describes the laser beam as a 2 + 1-dimensional quantum fluid of light @xcite , @xmath19 the transverse gradient of the phase of the beam determines the transverse fluid flow velocity @xmath20 and the speed of long - wavelength sonic waves is given by @xmath21 . here @xmath22 is proportional to the phase of the wave function , and by taking the transverse gradient , eq . may be recast as the equation of motion for @xmath23 in direct analogy to the hydrodynamic euler equation for dilute - gas becs @xcite . transverse wave perturbations propagating on an intense plane - wave beam obey the well known bogoliubov dispersion relation @xcite . @xmath24 relating frequency @xmath25 and wavenumber @xmath26 of phonon excitations . here @xmath27 is the fourier transform of the medium response function . in the local case , @xmath28 but in the nonlocal case @xmath29 will take on a more complicated functional form that will ultimately determine the extent of superfluid behavior observable in the photon fluid . it is precisely the nature of this response function that we investigate in more detail in the following . + _ thermal , nonlocal nonlinearity : _ we now consider in detail the case of _ nonlocal _ photon - photon interactions . the cell used in our experiments is sufficiently long and the characteristic frequency of the propagation evolution ( eq . ( [ eq : nlse ] ) ) is sufficiently slow that we may neglect any variations of the heat diffusion profile along @xmath11 . under these assumptions , the nonlocal change in the refractive index @xmath30 , at a given propagation plane along @xmath11 , can then be found by convolving the material response function @xmath31 with the source beam intensity profile @xmath32 on that plane . we assume a beam that occupies the central region of the fluid , far from the system s physical boundaries , so that the system is approximately shift - invariant with @xmath33 with the constant @xmath34 accounting for the properties of the material , and @xmath35 . for a thermal nonlinearity such as that provided by the methanol - graphene system , the temperature dependent change in the index of refraction is @xmath36 where @xmath37 . the spatial profile of @xmath38 is then determined by the 2d steady - state heat equation , @xmath39 where @xmath40 is the thermal conductivity . + thus the response function is , to within a constant , the green s function for heat diffusion in the medium , and obeys @xmath41 we can find a numerical solution for @xmath31 by using a narrow gaussian source beam @xmath42 to approximate the delta function , and then numerically solving eq . with the condition @xmath43 for @xmath44 . our choice of boundary condition assumes that , due to efficient heat transport to the surrounding environment at the boundaries , there is no change in temperature at the boundary itself . + that determines the flow of the photon fluid [ inset ( a ) ] . inset ( b ) shows the measured nonlocal dispersion relation of the photon fluid from ref . @xcite . solid red line - bogoliubov dispersion relation , eq . ( [ eq : bogodr_nl ] ) with a local nonlinearity @xmath45 . solid blue line - nonlocal dispersion relation with @xmath46^{-1}$ ] , and @xmath47 @xmath48 and @xmath49 determined from the best fit to the experimental data ( black circles ) . , scaledwidth=48.0% ] alternatively , we can approximate the effect of the boundary by incorporating a distributed loss term @xmath50 into the steady - state heat equation , @xmath51 with the addition of this distributed loss term we obtain a lorentzian @xmath52-space response function , @xmath53 where the nonlocal length @xmath54 is fixed by the system boundary and determines the spatial - frequency cutoff of the response function . in @xmath52-space the nonlocal change in the index of refraction is @xmath55 , with @xmath56 the effective nonlinear coefficient . the response function defined in eq . , which we derive from the distributed loss model ( dlm ) , has been taken as an a priori assumption in previous works @xcite . the dlm solution proves to be a valid analytical approximation to the exact numerical solution of eq . . indeed , the corresponding dlm real - space response function @xmath57 where @xmath18 and @xmath58 is the zeroth - order modified bessel function of the second kind , is shown in fig . to provide quantitative agreement with the numerical solution to the heat equation assuming a narrow gaussian source beam . in the same figure we also show the measured @xmath59 ( red curve ) , obtained using an interferometric method similar to that used by minovich _ et al . _ @xcite . summarizing this first result , the experimental measurement of the response function indicates that the dlm provides a good approximation to both the measured @xmath60 and to the exact numerical solution to eq . . + we next turn to the analytical dlm solution to describe how the beam or fluid geometry may be used to control the nonlocal interaction length . we first point out that for a medium with physical boundaries , as in the experiments described below and in ref . @xcite , a cylindrically symmetric beam with @xmath61 beam radii @xmath62 implies superfluid behavior only for very low wavevectors such that @xmath63 where the response function approaches a local response @xmath64 . however , accessing these wavevectors is experimentally unrealistic as it requires observation and measurement of waves in the transverse plane of the beam that have a wavelength that is of the order of the size of the medium itself . + however , the situation is more interesting in the case of an elliptical beam geometry with @xmath65 . the focused beam radius @xmath66 leads to a temperature distribution whose width scales with @xmath67 along the @xmath68-axis . this focusing along the @xmath68-axis also leads to enhanced thermal diffusion away from the major axis of the beam aligned with the @xmath69-axis , as may be seen by applying the approximation @xmath70 in eq . . within this approximation we may use an effective one - dimensional heat equation , resulting in an effective 1d response function @xmath71 with the introduction of an effective nonlocal length , @xmath72 . the key point here is that focusing along the @xmath68-axis decreases the length scale for thermal diffusion to @xmath73 along both major and minor beam axes . thus our elliptical geometry can lead to superfluid behavior for the range @xmath74 , which is now experimentally accessible . a circular beam with @xmath75 may seem an option , but is impractical from an experimental standpoint since the spatial extent of the fluid would then be too small to observe superfluid behavior such as vortex nucleation in the flow past an obstacle . + . red curve : experimental measurement using a methanol - graphene medium with @xmath76 cm , @xmath77 cm , @xmath78 , similar to that used in the experiments in fig . [ fig : flowobstacle ] . dashed blue curve : the numerical solution to eq . with a physical circular boundary at @xmath77 cm . black curve : the analytical solution from the dlm model with @xmath79 cm . all curves are normalized to one.,width=264 ] we arrive at an alternative view of the effective geometry - induced tailoring of the medium response by considering the spatial extent of the focused spot size @xmath67 and the associated @xmath68-component of the wavevector @xmath80 , where @xmath81 is largest wavelength oscillation supported by the spatial extent of the minor axis of the elliptical photon fluid , such that @xmath82 . we may then determine the @xmath52-space response function by first numerically solving the full 2d heat equation and taking the fourier transform to obtain @xmath83 . we found that either integrating the response function over all @xmath84 or simply taking @xmath85 gives similar functions . in the latter case , the dlm response function may again be rewritten as @xmath71 , and together with eq . provides good agreement with the dispersion relation reported in ref . @xcite ( see fig . [ fig : fig1 ] ) . therefore , the dlm approach explicitly indicates that the highly elliptical geometry of the beam leads to an effective 1d response function with a nonlocal length , which in the limit @xmath86 loses all trace of the physical boundary conditions and is essentially determined solely by the beam or fluid geometry , @xmath73 . this provides a clear route to re - establishing and controlling the onset of superfluid behavior in an otherwise highly nonlocal and non - superfluid medium . + _ superfluidity and vortices : _ in order to verify our findings we performed a series of experiments and numerical simulations with both round and highly elliptical pump beams , aimed at observing a characteristic trait of superfluid flow , namely quantized vortex nucleation in supercritical flows around an obstacle . we first briefly describe the characteristics of quantized vortices in superfluids . the physics of quantized vortices has been of great interest ever since their discovery in @xmath87he @xcite and later in becs @xcite , and their inherent dynamics are intensively studied in quantum turbulence @xcite . unfortunately , due to the relatively short coherence length in @xmath87he , the vortex core diameter is of the order of a few ngstrms and is hard to visualize by optical means , although progress has been made using hydrogen tracer particles @xcite . in contrast , in becs and photon fluids , the diluteness of the fluid leads to larger healing lengths , with vortex core diameters on the order of half a micron and tens of microns respectively , allowing for direct observation @xcite . furthermore , in photon fluids straightforward optical interferometry provides easy access to phase information and thus photon fluids provide an accessible platform to study quantized vortex dynamics , where core position , circulation and winding number can be easily identified . + _ experiments : _ the experimental setup is shown in fig . [ fig : fig1 ] . we launch a highly elliptical continuous - wave laser beam with wavelength @xmath88 nm through a cylindrical cell with length @xmath89 cm and radius @xmath77 cm , filled with a methanol - graphene solution as a thermal nonlinear medium . as shown in inset ( a ) of fig . [ fig : fig1 ] , the beam propagates along @xmath11 , with its minor axis oriented along @xmath68 . methanol has a negative thermo - optic coefficient of @xmath90 1/k ( providing the repulsive photon - photon interaction ) and thermal conductivity @xmath91 w/(m@xmath92k ) , while nanometric graphene flakes ( on the order of 1.6 mg of graphene in the 60 @xmath93 volume of methanol ) are added in order to increase the absorption coefficient to @xmath94 @xmath95 and ensure sufficient thermo - optic nonlinearity at the input intensities ( of the order 4 - 7 w/@xmath96 ) used in the experiments . the beam is loosely focused onto the sample by a set of cylindrical lenses with a minor axis @xmath61 beam radius of @xmath97 m ( the major axis radius is @xmath98 cm ) . the sample is placed in one arm of a mach - zehnder interferometer . the other arm is used to probe the spatial phase profile of the sample output plane with a reference beam . to this end , a piezo - controlled delay stage is introduced in order to retrieve the full phase information by a phase - shifting interferometry technique @xcite . finally , the intensity profile of the beam at the cell output is imaged with 4x magnification onto a ccd camera . as an obstacle , a knife blade is immersed in the sample along the beam path [ see inset ( a ) , fig . [ fig : fig1 ] ] so that the beam propagation axis is at a slight angle @xmath99 with respect to the knife axis , thus introducing a relative transverse flow @xmath100 along the @xmath69-axis , determined by the respective angle @xmath99 . + for excitations with wavenumbers smaller than the inverse of the effective nonlocal length @xmath101 the dispersion is a linear function in @xmath52 ( @xmath102 . using the parameters and the technique described in ref . @xcite , we measured the @xmath103 spectrum of elementary excitations and indeed show that these follow the bogoliubov dispersion with an effective 1d nonlocal length , @xmath104 m and @xmath105 determined from the best fit to the experimental data [ see fig . [ fig : fig1](b ) ] . hence there exists a critical velocity @xmath106 for which a fluid with flow speed @xmath107 behaves as a superfluid and is not perturbed by small defects inserted in the flow . for local fluids , the critical velocity is determined by the speed of sound . however , as discussed in the appendix , the nonlocality can significantly reduce the critical velocity . for our experimental parameters , this reduction amounts to approximately a factor of two . furthermore , in this work we consider an extended impenetrable obstacle such that the local flow speed can become supercritical in its vicinity , even if the asymptotic speed @xmath108 far from the obstacle remains subcritical . + the breakdown of superfluidity leads to dissipation and drag forces on the obstacle and consequently , the nucleation of quantized vortices is expected to appear in the local interaction case @xcite . figure [ fig : flowobstacle ] shows experimental evidence in our _ nonlocal _ superfluid of the breakdown of the viscousless flow and subsequent nucleation of quantized vortices , which are considered to be hallmark evidence of superfluid behavior . in detail , figs . [ fig : flowobstacle](a ) and ( b ) show the normalized near - field intensity profile at the sample output @xmath109 for two different input intensities @xmath110 w/@xmath96 and @xmath111 w/@xmath96 , respectively ( corresponding to two different sound speeds , @xmath112 and @xmath113 ) and with @xmath99 chosen to create a flow speed @xmath114 m / s along the positive @xmath69-axis . , normalized by input beam intensity @xmath115 . ( a ) and ( b ) @xmath109 showing superfluid instability at high flow speed , @xmath116 m / s : ( a ) @xmath110 w/@xmath96 , i.e. , @xmath117 and @xmath118 , and ( b ) @xmath111 w/@xmath96 , i.e. , @xmath119 and @xmath120 . white circles indicate the position of the vortex singularities obtained from the corresponding phase diagrams shown in ( c ) and ( d ) , respectively . , scaledwidth=48.0% ] the intensity profiles show how the rigid obstacle creates a wake in the downstream region , but just as in an ordinary fluid , the light intensity is able to flow around the tip of the obstacle and fill in the shadowed region . a series of vortices ( dark regions in the intensity profile , marked with white dots ) are seen to nucleate from close to the tip . one vortex is observed for @xmath112 and a second vortex is formed for higher excitation ( i.e. sound ) speeds , @xmath113 . this interpretation finds confirmation in the phase profiles shown in figs . [ fig : flowobstacle](c ) and ( d ) where the drag on the obstacle is visualized by the bending of the phase pattern around the tip of the obstacle . the nucleation of vortices in the wake of the obstacle is evidenced by the clockwise - circulating phase singularities . we note that increasing the light intensity , and therefore the magnitude of @xmath121 , both increases the speed of sound of the fluid ( decreasing @xmath122 ) , and also speeds up the effective temporal " evolution of the fluid , such that within certain limits increasing @xmath123 will have the same effect as increasing the propagation length . the observation of two vortices in fig . [ fig : flowobstacle](d ) is therefore due to the faster sound speed , i.e. faster overall evolution ( rather than to an increase in flow speed ) . + beam radius : ( a ) intensity profile at the output of the nonlinear medium , zoomed in around the obstacle tip . the inset shows the full beam profile . ( b ) phase profile for the circular beam ( wrapped between @xmath124 and @xmath125 . the smoothness and absence of singularities indicate a complete absence of vortex nucleation around the obstacle . elliptical input pump beam ( @xmath126 mm , @xmath127 mm ) : ( c ) intensity profile with a white circle indicating the position of a vortex nucleated from the obstacle , and ( d ) the phase profile . a clear phase singularity can be observed confirming the presence of the vortex . simulations in ( a)-(b ) and ( c)-(d ) are performed under identical conditions , aside from the input beam profile , with input intensity @xmath128 w/@xmath96 , propagation length @xmath1 cm , fluid flow speed @xmath129 m / s , and nonlocal interaction length @xmath130 cm.,scaledwidth=48.0% ] _ numerical simulations : _ in order to investigate these observations of vortex nucleation in more depth , we performed numerical simulations that were based on split - step propagation of eq . , with @xmath131 chosen to match the experiment . nonlocality is described by the dlm 2d lorentzian response function @xmath83 with @xmath130 cm . the dimensions and shape of the obstacle were chosen so as to match the experiments . as can be seen in figs . [ numerics](a)-(b ) ( normalized intensity and phase , respectively ) , when using a round beam no particular features are observed in the flow around the obstacle . however , figs . [ numerics](c)-(d ) show the results for the exact same simulation parameters ( in particular , for the same intensity @xmath128 w/@xmath96 ) for an elliptical beam with minor axis @xmath132 @xmath133 m , and vortex nucleation is clearly observed close to the tip of the obstacle . these numerical results are in good agreement with our experiments and show how by simply controlling the geometry of the beam , or more generally the geometry of the fluid , one may tune the effective nonlocal interaction length @xmath134 and hence re - establish and control superfluid behavior in nonlocal fluids . + radii , @xmath135 and @xmath136 , normalized to the local healing length @xmath137 , versus @xmath138 . the inset , corresponding to the white region in ( e ) , shows a vortex core with labeled major axis @xmath135 and minor axis @xmath136 . ( b ) normalized beam intensity , @xmath109 , ( c ) phase @xmath139 and ( d ) nonlinear potential , @xmath140 , for a purely local superfluid after 20 cm of propagation , with @xmath141 , @xmath142 , and @xmath61 beam radii @xmath143 = 1 mm . ( e ) , ( f ) and ( g ) show the corresponding profiles for a nonlocal superfluid with @xmath144 @xmath133 m , and @xmath145 . , scaledwidth=48.0% ] as a side note , the vortices nucleated in the presence of nonlocality have an elliptical shape that is observed both in the experiments and numerical simulations described above . in fig . [ fig : sims2](a ) we plot the vortex core @xmath61 radii @xmath135 , @xmath136 ( normalized to a local healing length @xmath146 so as to account for any local variation in the fluid density associated with the output beam intensity ) as a function of increasing nonlocality , @xmath138 . for each value of the 2d nonlocal interaction length @xmath138 , the input power is chosen such that we observe one clearly defined vortex core , and flow speed is adjusted to maintain a constant @xmath141 . at @xmath147 m ( purely local response ) the vortex cores are circular . however , as we increase @xmath138 , we observe a continuous increase in the core aspect ratio , @xmath148 . figures [ fig : sims2](b)-(d ) show the normalized intensity @xmath109 , phase @xmath139 and effective nonlinear potential energy @xmath140 profiles , respectively , for a purely local superfluid after 20 cm of propagation . as can be seen in fig . [ fig : sims2](b ) , the nucleated vortices have the expected circular central core region , which is reflected in the effective nonlinear potential energy profile shown in fig . [ fig : sims2](d ) . figures [ fig : sims2](e)-(g ) show the corresponding profiles for @xmath149 m , taken as a representative example from the points shown in fig . [ fig : sims2](a ) . the vortices are now clearly elliptical : in particular , fig . [ fig : sims2](g ) shows a marked deformation of the effective nonlinear potential energy term so that the spatial extent of the knife blade felt by any point in the fluid is much larger when compared to the local case . we may thus interpret the vortex deformation in terms of a nonlocal smearing of the nonlinear potential along the obstacle edge . + large nonlocal interaction lengths will strongly suppress superfluid behavior , effectively removing the photon - photon ( or particle - particle ) interactions that are at the origin of the linear superfluid dispersion relation . however , by controlling the geometry of the beam or fluid , it is possible to limit the effective nonlocal interaction length and thus re - establish superfluid behavior . a distributed loss model for heat flow can quantitatively justify this effect and explain how we reduced the effective nonlocal length by two orders of magnitude in our experiments . both experiments and numerical simulations with elliptical beams demonstrate the nucleation of quantized vortices from an extended hard obstacle in a flowing photon fluid , which is considered to be the hallmark trait of superfluid behavior . + although it was necessary to consider the full details of our specific system in order to unveil the role of the fluid geometry , the general conclusions reach beyond thermal photon fluids and apply to any nonlocal superfluid , or , for that matter , to any form of nonlocal interaction . the photon superfluids specifically described here are of relevance in relation to recent proposals for studying horizon and hawking - like emission in artificial spacetime geometries that mimic lorentz - invariance based on the superfluid dispersion relation @xcite , or for cases in which it is the nonlocality itself that is used to mimic long - range gravitational effects @xcite . thermal photon fluids may also provide an alternative testbed for nonlocal effects observed in dipolar becs @xcite .

through the @xmath14 transition at quark level , the @xmath15 decays are able to produce the @xmath16 bound states like @xmath17 ; particularly , the hidden charm tetraquarks to consist of @xmath18 , such as @xmath19 , @xmath20 , and @xmath21 , known as the @xmath22 states @xcite . for example , we have @xcite @xmath23 where @xmath3 is composed of @xmath24 , measured to have the quantum numbers @xmath25 . on the other hand , the @xmath26 decays from the @xmath27 transition can also be the relevant production mechanism for the @xmath16 and @xmath18 bound states . however , the current measurements have been done only for the ratios , given by @xcite @xmath28 where @xmath29 are the fragmentation fractions defined by @xmath30 . in addition , none of the @xmath22 states has been observed in the @xmath31 decays yet . from figs . [ fig1]a and [ fig1]d , the @xmath32 decays proceed with the @xmath33 transition , which is followed by the recoiled @xmath2 with @xmath34 , respectively , presented as the matrix elements of @xmath35 . unlike @xmath17 as the genuine @xmath16 bound state , while the matrix element for the tetraquark production is in fact not computable , @xmath36 is often taken as the charmonium state in the qcd models @xcite . in this study , we will extract @xmath37 from the data of @xmath38 in eq . ( [ data1 ] ) to examine the decays of @xmath39 , @xmath40 , and @xmath41 , of which the extraction allows @xmath36 to be the tetraquark state . on the other hand , to calculate the @xmath42 decays in figs . [ fig1]b and [ fig1]e and the semileptonic @xmath43 decays in figs . [ fig1]c and [ fig1]f , we use the @xmath44 transition matrix elements from the qcd calculations . and @xmath31 decays with the formations of the @xmath16 pair , where @xmath45 , @xmath46 and @xmath47 correspond to the @xmath48 , @xmath49 , and @xmath50 decays , while @xmath51 , @xmath52 and @xmath53 the @xmath54 , @xmath55 , and @xmath56 decays , respectively.,title="fig:",width=192 ] and @xmath31 decays with the formations of the @xmath16 pair , where @xmath45 , @xmath46 and @xmath47 correspond to the @xmath48 , @xmath49 , and @xmath50 decays , while @xmath51 , @xmath52 and @xmath53 the @xmath54 , @xmath55 , and @xmath56 decays , respectively.,title="fig:",width=192 ] and @xmath31 decays with the formations of the @xmath16 pair , where @xmath45 , @xmath46 and @xmath47 correspond to the @xmath48 , @xmath49 , and @xmath50 decays , while @xmath51 , @xmath52 and @xmath53 the @xmath54 , @xmath55 , and @xmath56 decays , respectively.,title="fig:",width=192 ] and @xmath31 decays with the formations of the @xmath16 pair , where @xmath45 , @xmath46 and @xmath47 correspond to the @xmath48 , @xmath49 , and @xmath50 decays , while @xmath51 , @xmath52 and @xmath53 the @xmath54 , @xmath55 , and @xmath56 decays , respectively.,title="fig:",width=192 ] and @xmath31 decays with the formations of the @xmath16 pair , where @xmath45 , @xmath46 and @xmath47 correspond to the @xmath48 , @xmath49 , and @xmath50 decays , while @xmath51 , @xmath52 and @xmath53 the @xmath54 , @xmath55 , and @xmath56 decays , respectively.,title="fig:",width=192 ] and @xmath31 decays with the formations of the @xmath16 pair , where @xmath45 , @xmath46 and @xmath47 correspond to the @xmath48 , @xmath49 , and @xmath50 decays , while @xmath51 , @xmath52 and @xmath53 the @xmath54 , @xmath55 , and @xmath56 decays , respectively.,title="fig:",width=192 ] in terms of the effective hamiltonians at quark level for the @xmath57 , @xmath58 , and @xmath59 transitions in fig . [ fig1 ] , the amplitudes of the @xmath60 , @xmath32 , and @xmath61 decays can be factorized as @xcite @xmath62 respectively , where @xmath63 , @xmath64 , @xmath65 for @xmath66 , @xmath67 , @xmath68 , @xmath69 is the fermi constant , @xmath70 are the ckm matrix elements , and @xmath71 are the parameters to be determined . in eq . ( [ amp1 ] ) , the decay constant , four momentum vector , and four polarization @xmath72 are defined by @xmath73 while the matrix elements of the @xmath74 transitions can be parametrized as @xcite @xmath75 f_1^{bm}(t)+\frac{m^2_b - m^2_m}{t}q^\mu f_0^{bm}(t)\,,\nonumber\\ \langle j/\psi|\bar c\gamma_\mu b|b_c^-\rangle&=&\epsilon_{\mu\nu\alpha\beta } \varepsilon^{\ast\nu}p_{b_c}^{\alpha}p_{j/\psi}^{\beta}\frac{2v(t)}{m_{b_c}+m_{j/\psi}}\;,\nonumber\\ \langle j/\psi|\bar c\gamma_\mu \gamma_5 b|b_c^-\rangle & = & i\bigg[\varepsilon^\ast_\mu-\frac{\varepsilon^\ast\cdot q}{t}q_\mu\bigg](m_{b_c}+m_{j/\psi})a_1(t ) + i\frac{\varepsilon^\ast\cdot q}{t}q_\mu(2m_{j/\psi})a_0(t)\nonumber\\ & -&i\bigg[(p_{b_c}+p_{j/\psi})_\mu-\frac{m^2_{b_c } -m^2_{j/\psi}}{t}q_\mu \bigg](\varepsilon^\ast\cdot q)\frac{a_2(t)}{m_b+m_{j/\psi}}\;,\nonumber\\ % \langle x_c^0|\bar c\gamma_\mu \gamma_5 b|b_c^-\rangle&=&-\epsilon_{\mu\nu\alpha\beta } \varepsilon^{\ast\nu}p_{b_c}^{\alpha}p_{x_c^0}^{\beta}\frac{2ia(t)}{m_{b_c}-m_{x_c^0}}\;,\nonumber\\ \langle x_c^0|\bar c\gamma_\mu b|b_c^-\rangle & = & -\bigg[\varepsilon^\ast_\mu-\frac{\varepsilon^\ast\cdot q}{t}q_\mu\bigg](m_{b_c}-m_{x_c^0})v_1(t ) - \frac{\varepsilon^\ast\cdot q}{t}q_\mu(2m_{x_c^0})v_0(t)\nonumber\\ & + & \bigg[(p_{b_c}+p_{x_c^0})_\mu-\frac{m^2_{b_c } -m^2_{x_c^0}}{t}q_\mu \bigg](\varepsilon^\ast\cdot q)\frac{v_2(t)}{m_b - m_{x_c^0}}\;,\end{aligned}\ ] ] respectively , where @xmath76 , @xmath77 , and @xmath78 with @xmath79 are the form factors . in our numerical analysis , we use the wolfenstein parameterization for the ckm matrix elements in eq . ( [ amp1 ] ) , given by @xmath80 , @xmath81 , and @xmath82 , with @xcite @xmath83 the parameters @xmath71 , decay constants and form factors , adopted from refs . @xcite , @xcite , and @xcite are as follows : @xmath84 where the form factors correspond to the reduced matrix elements derived from eqs . ( [ amp1 ] ) and ( [ ff1 ] ) , given by @xmath85 the momentum dependence for @xmath86 from ref . @xcite is taken as @xmath87 with @xmath88 , @xmath89 and @xmath90 gev for @xmath91 , @xmath92 and @xmath93 , respectively . with @xmath94 from eq . ( [ data1 ] ) , we obtain @xmath5 mev , which is lower than @xmath95 mev @xcite from perturbative and light - front qcd models , respectively . the momentum dependences for the @xmath44 transition form factors are given by @xcite @xmath96 where the values of @xmath97 and @xmath98 in table [ ff0 ] are from refs . @xcite and @xcite , respectively . .the @xmath99 form factors at @xmath100 and @xmath98 for the momentum dependences in eq . ( [ f_mc ] ) . [ cols="^,^,^,^,^",options="header " , ] for the @xmath101 decays , the results are given in table [ tab1 ] . while @xmath5 mev leads to @xmath102 in accordance with the data , we predict that @xmath6 , @xmath7 , and @xmath8 , which are accessible to the experiments at the lhcb . besides , our results of @xmath103 and @xmath104 in table [ tab1 ] are also supported by the @xmath105 and isospin symmetries , respectively . with the form factors adopted from ref . @xcite , we calculate that @xmath106 and @xmath107 , which are 2 - 3 times smaller than the results from the same reference . the differences are again reconciled after keeping the next - leading order contributions in the @xmath108 expansion . for the semileptonic @xmath109 decays , @xmath110 is due to the both negligible electron and muon masses , of which the numerical value is close to those from refs . note that by taking @xmath111 as the theoretical input in eq . ( [ data2 ] ) , we derive that @xmath112 which agrees with the above theoretical prediction . for the @xmath113 mode , which suppresses the phase space due to the heavy @xmath114 , we obtain @xmath115 . the ratio of @xmath116 is close to that in ref . @xcite , but @xmath117 is apparently 4 - 5 times smaller than that in ref . @xcite , though with uncertainties the two results overlap with each other . with the spectra of @xmath118 in fig . [ spec ] , our results can be compared to the recent studies on the semileptonic @xmath31 cases in refs . @xcite for the @xmath22 states . and ( b ) @xmath119 decays , where the solid and dotted lines correspond to @xmath120 and @xmath121 , respectively.,title="fig:",width=288 ] and ( b ) @xmath119 decays , where the solid and dotted lines correspond to @xmath120 and @xmath121 , respectively.,title="fig:",width=288 ] in sum , we have studied the @xmath0 and @xmath1 decays with @xmath122 and @xmath3 . we have presented that @xmath123 and @xmath124 , and @xmath9 and @xmath10 . with @xmath125 as the theoretical input , the extractions from the data have shown that @xmath13 and @xmath126 . we have estimated @xmath127 with @xmath68 to be @xmath12 , @xmath12 , and @xmath128 , respectively . the work was supported in part by national center for theoretical sciences , national science council ( nsc-101 - 2112-m-007 - 006-my3 ) , and most ( most-104 - 2112-m-007 - 003-my3 ) . 99 for a review on the tetraquark states , see h.x . chen , w. chen , x. liu and s.l . zhu , phys . rept . * 639 * , 1 ( 2016 ) . olive _ et al . _ [ particle data group collaboration ] , chin . c * 38 * , 090001 ( 2014 ) .

we study two - body @xmath0 and semileptonic @xmath1 decays with @xmath2 , where @xmath3 is regarded as the tetraquark state of @xmath4 . with the decay constant @xmath5 mev determined from the data , we predict that @xmath6 , @xmath7 , and @xmath8 . with the form factors in qcd models , we calculate that @xmath9 and @xmath10 , and @xmath11 and @xmath12 , respectively , and extract the ratio of the fragmentation fractions to be @xmath13 .

the fully dressed fermionic propagator @xmath105 is calculated from the bare propagator @xmath106^{-1}$ ] via the dyson equation @xmath107 where @xmath108 are fermionic matsubara frequencies , and @xmath109 is the self - energy which captures the interaction effects . dilute fermi gases are well described in the ladder , or t - matrix , approximation . the bosonic vertex function is then given by @xmath110^{-1}\end{aligned}\ ] ] in terms of the bare coupling @xmath111 , which depends on the uv momentum cutoff @xmath112 ( see below ) , and the pair propagator @xmath113 for bosonic matsubara frequencies @xmath114 . in the ladder approximation the bosonic vertex function is equivalent to the t matrix , which describes the propagation of bound fermion pairs , or dimers , via dressed fermion - fermion excitations . finally , the fermionic self - energy describes how fermions scatter off ( virtual ) dimers , @xmath115 the pair propagator @xmath116 has a logarithmic ultraviolet divergence @xcite ; this is regularised by expressing the bare coupling @xmath111 in eq . in terms of the physical binding energy @xmath22 of the two - body bound state which is always present in an attractive 2d fermi gas , @xmath117 note that the existence of a bound state is both necessary and sufficient for pairing in 2d @xcite . equations constitute a set of coupled integral equations . the convolution integrals and are computed in fourier space @xmath118 on a logarithmic grid of @xmath119 grid points @xcite to account for the logarithmically slow decay of the t matrix in 2d . the integral equations are solved by iteration , and once convergence is reached one obtains the self - consistent fermion green s function @xmath120 and the t matrix @xmath121 , respectively . @xmath120 is analytically continued to real frequencies @xmath122 using pad approximants to determine the spectral function @xmath123 . in the luttinger - ward approach , the density is most conveniently obtained from the green s function in fourier space as @xmath124 without the need for analytical continuation . similarly , in the normal state , the contact density corresponds to the total density of dimers @xcite and can be expressed in terms of the self - consistent t matrix as @xmath125 . the interaction strength in a purely 2d system is characterized by the physical binding energy @xmath22 , see eq . , but different definitions of the scattering length @xmath104 are used in the literature . we follow the convention that @xmath126 , and hence @xmath23 @xcite . alternatively , one may use @xmath127 , and consequently @xmath128 , see e.g. @xcite . in a quasi-2d system realized by a harmonic confinement in the third direction , as is common for ultracold atomic gases , @xmath22 is related to the confinement length @xmath129 and the 3d scattering length @xmath130 , which can be tuned by a magnetic feshbach resonance @xcite . @xcite argues that the correct quasi-2d scattering length in the bose limit is obtained by matching the scattering amplitudes of the pure and quasi-2d systems . the interaction parameter @xmath131 used in that work is related to our definition by @xmath132 for a single - spin density @xmath133 . the transition temperature @xmath0 is characterised by the thouless criterion , @xmath134 @xcite . the t matrix is proportional to the green s function @xmath135 of a dilute bose gas as @xmath136 in the bkt limit @xcite , and the bose green s function for an @xmath81-particle system with coherence length @xmath137 approaches @xmath138 @xcite . in our analysis we therefore consider the thouless criterion @xmath139 for @xmath80 particles typical of current experiments @xcite .

we determine the thermodynamic properties and the spectral function for a homogeneous two - dimensional fermi gas in the normal state using the luttinger - ward , or self - consistent t - matrix , approach . the density equation of state deviates strongly from that of the ideal fermi gas even for moderate interactions , and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling , consistent with recent experiments . we also compute the superfluid transition temperature for a finite system in the crossover region . there is a pronounced pseudogap regime above the transition temperature : the spectral function shows a bogoliubov - like dispersion with back - bending , and the density of states is significantly suppressed near the chemical potential . the contact density at low temperatures increases with interaction and compares well with both experiment and zero - temperature monte carlo results . the formation of fermion pairs and superfluidity of such pairs are distinct but related phenomena : in weak - coupling bcs theory , both are predicted to occur at the same temperature @xmath0 . however , a basic question of many - body physics is how they are related at stronger coupling and in low dimensions , where quantum fluctuations play a large role . while preformed pairs in the normal phase trivially exist in the strong - coupling bose limit where one has tightly bound dimers , it has been argued that pairing above @xmath0 can also occur in the bcs regime . in this case , one expects a significant suppression of spectral weight at the fermi surface even above @xmath0 . this so - called pseudogap regime extends up to a crossover temperature @xmath1 , and its spectral and thermodynamic properties deviate strongly from the predictions of fermi - liquid theory @xcite . recently , pairing and superfluidity have been studied in ultracold atomic gases , which afford accurate control of both the interaction strength and dimensionality , and allow access to the crossover between the bcs and bose regimes @xcite . in these systems , a pseudogap can be detected through the suppression of the spin susceptibility or directly via the spectral function , which is experimentally accessible by arpes or momentum - resolved rf spectroscopy @xcite . the possibility of a pseudogap regime has already been investigated both experimentally and theoretically in three dimensions ( 3d ) @xcite . in two - dimensional ( 2d ) fermi gases , the pseudogap regime is expected to be much more pronounced than in 3d , and a pairing gap has recently been observed experimentally @xcite . here , we compute the spectral function for the homogeneous 2d fermi gas in the normal phase of the bcs - bose crossover . we indeed find a strong suppression of the density of states at the fermi surface above @xmath0 , as shown in fig . [ fig : dos ] . this allows us to map the extent of the pseudogap regime in the temperature - vs - coupling phase diagram ( fig . [ fig : tc ] ) , and we find that it extends further than in 3d @xcite . as the binding between fermions increases , the cooper pairs evolve into a bose gas of tightly bound molecules . long - range fluctuations in 2d are so strong that they inhibit superfluid long - range order at nonzero temperature . thus , the 2d bose gas exhibits a berezinskii - kosterlitz - thouless ( bkt ) transition at @xmath2 into a quasi - ordered phase with algebraically decaying correlations @xcite . it is a challenging many - body problem to precisely characterise the crossover between the bosonic bkt and fermionic bcs limits , where the composite nature of the molecules becomes apparent . , normalised by @xmath3 for the free fermi gas , at interaction @xmath4 for different temperatures : @xmath5 ( top curve at @xmath6 ) to @xmath7 ( bottom ) . * inset : * spectral function @xmath8 for @xmath9 . the grey dashed line marks the maximum in the spectral weight of the bottom band . [ fig : dos ] ] in this work , we present the first computation of the finite - temperature density and pressure equation of state in the crossover regime and find a strong renormalisation already for moderate interactions see fig . [ fig : density ] . the pressure at low temperatures has very recently been measured in experiment @xcite . we find that the pressure computed at @xmath10 is closer to the experimental data than zero - temperature monte carlo calculations @xcite , offering a resolution of previous discrepancies ( fig . [ fig : p ] ) . furthermore , we determine @xmath0 for finite systems ( fig . [ fig : tc ] ) , which is relevant for experiments on quasi-2d atomic gases , in the crossover regime between the known limiting cases @xcite . finally , the contact density agrees well with experiment @xcite and shows surprisingly little variation with temperature ( fig . [ fig : contact ] ) . the dilute , two - component ( @xmath11 , @xmath12 ) fermi gas with short - range interactions is described by the hamiltonian @xmath13 where @xmath14 creates a fermion with spin @xmath15 , momentum @xmath16 , and kinetic energy @xmath17 . the chemical potential @xmath18 is taken to be the same for both species in a spin - balanced gas . the energy scale is set by the fermi energy @xmath19 for a total density @xmath20 . the bare attractive contact interaction @xmath21 has to be regularised and is expressed in terms of the physical binding energy @xmath22 of the two - body bound state which is always present in an attractive 2d fermi gas . we define the 2d scattering length as @xmath23 and parametrise the interaction strength by @xmath24 . in the following we set @xmath25 , @xmath26 , and write @xmath27 . we investigate the behavior of the strongly interacting fermi gas in the normal state using the luttinger - ward , or _ self - consistent _ t - matrix , approach @xcite , which goes beyond earlier works @xcite by including approximately the interaction between dimers as well as dressed green s functions . thermodynamic precision measurements for the unitary fermi gas in 3d @xcite have confirmed the accuracy of this method , both for the value of @xmath28 and the bertsch parameter @xmath29 @xcite . recently , the luttinger - ward approach has been extended to study transport properties @xcite . the success of this method in three dimensions encourages its application to the homogeneous 2d fermi gas , which is particularly challenging due to the logarithmic energy dependence of the scattering amplitude . within the luttinger - ward approach , pairs of dressed fermions with green s function @xmath30^{-1}$ ] can form virtual molecules whose dynamics are described by the t matrix @xmath31 . the fermions can scatter from these molecules , which determines their lifetime and self - energy @xmath32 ( see supplemental material @xcite ) . from the self - consistent solution @xmath33 one obtains the spectral function @xmath34 . of the 2d fermi gas vs chemical potential @xmath35 , for different interaction strengths @xmath36 ( see legend ) . since the density is normalised by @xmath37 for the non - interacting gas , the non - monotonic behavior of @xmath38 reflects the impact of interactions , while the compressibility @xmath39 is always positive . the inset shows a typical trajectory in @xmath40 vs @xmath41 corresponding to the dotted line of fixed @xmath42 . along this line , @xmath43 increases with decreasing @xmath40 . [ fig : density ] ] _ density of states._the density of states @xmath44 describes at which energies fermionic quasiparticles can be excited , and is computed as the momentum average of the spectral function , @xmath45 . figure [ fig : dos ] shows the density of states for an interaction strength of @xmath46 , which is weak enough that there should be a fermi surface at low temperatures @xcite . for decreasing temperature , we see that the density of states is strongly suppressed at the chemical potential , while it increases on either side of the fermi surface . this marks the pseudogap regime which is part of the normal phase , but with anomalous properties due to the lack of low - energy fermionic excitations . there is no uniquely defined temperature associated with this crossover , so for concreteness we define the pseudogap temperature @xmath47 as the temperature where the density of states at the chemical potential drops by @xmath48 of the value at the left fringe . the full spectral function @xmath49 , shown in the inset of fig . [ fig : dos ] for a temperature of @xmath50 slightly above @xmath0 , shows a bcs - like dispersion with a clear reduction of spectral weight near the fermi energy . while the upper branch has a minimum at a finite wavevector @xmath51 , the lower branch exhibits `` back - bending '' towards lower energy for large momenta ( cf.ref . @xcite ) . we note that back - bending alone is not sufficient to define the pseudogap regime and can arise also for other reasons in the occupied spectral function @xcite . the two - peak structure of the @xmath52 spectral function qualitatively agrees with the momentum - resolved rf spectrum measured at @xmath53 @xcite , which is the only measurement that may lie within the pseudogap regime @xcite . for stronger attraction , the pseudogap regime eventually crosses over into preformed fermion pairs , where the fermi surface is lost ( @xmath54 ) and the spectral function resembles the one predicted using the virial expansion @xcite . _ density equation of state._the total density of both spin components follows from the density of states as @xmath55 , where @xmath56 is the fermi distribution . in fig . [ fig : density ] , we plot the density equation of state @xmath57 as a function of @xmath58 for different values of the interaction parameter @xmath36 . this manner of plotting the equation of state allows one to make a direct connection with experiments in trapped gases , since the density versus chemical potential at fixed @xmath36 can be easily extracted from the measured density profile in a trap @xcite . to expose the effects of interactions , we normalise the density @xmath59 by that of the ideal fermi gas , @xmath60 , where @xmath61 is the thermal wavelength . in the high - temperature limit where @xmath62 , all properties approach those of an ideal boltzmann gas however , with decreasing temperature , we find that @xmath38 eventually exhibits a maximum around @xmath63 , implying that interactions are strongest at intermediate temperatures . this is easily understood from the fact that decreasing @xmath40 at fixed @xmath64 results in an increasing @xmath41 , as shown in the inset of fig . [ fig : density ] . thus , we likewise expect the system to approach a weakly interacting gas in the low temperature regime . this behavior is qualitatively different from that observed in 3d @xcite , and is a direct consequence of the fact that one can have a _ density_-driven bcs - bose crossover in 2d . the curves for large @xmath64 are shown up to the critical value @xmath65 where the system is expected to enter the bkt phase . vs interaction strength , normalised by the pressure @xmath66 of an ideal fermi gas of the same density at @xmath67 . luttinger - ward data at temperature @xmath68 ( top , dotted ) to @xmath69 ( solid ) in comparison with experimental data @xcite ( symbols ) and @xmath67 monte carlo results @xcite ( dashed ) . [ fig : p ] ] _ pressure._the pressure is obtained by integrating the density according to the gibbs - duhem relation , @xmath70 . figure [ fig : p ] shows the luttinger - ward data for finite temperatures @xmath68 ( top ) to @xmath71 ( bottom ) : the pressure decreases from the free fermi pressure in the bcs limit to the much lower pressure of a dilute bose gas in the bkt limit . this is a strong coupling effect beyond the mean - field bcs prediction @xmath72 at @xmath67 @xcite . as the temperature is lowered , our data approach the @xmath67 monte carlo results @xcite ( dashed ) . a recent measurement at low temperatures @xmath73 @xcite ( symbols ) found a deviation from the @xmath67 pressure in the bcs limit , attributed to mesoscopic effects . we , however , find that the @xmath74 pressure from the luttinger - ward calculation agrees well with experiment in this regime , thus suggesting that the discrepancy is in large part due to the effect of temperature . vs interaction strength @xmath41 . the luttinger - ward result for a finite system ( blue solid line ) in the crossover region @xmath75 is compared with analytical limits @xcite . the red dots marks the crossover temperature @xmath47 to the pseudogap regime for @xmath76 . [ fig : tc ] ] _ phase diagram of the 2d fermi gas._the berezinskii - kosterlitz - thouless ( bkt ) transition at a finite temperature @xmath0 marks the onset of a nonzero superfluid density @xmath77 and algebraically decaying correlations @xcite . the jump in @xmath78 at @xmath0 is universal for a bose superfluid and becomes exponentially small of order @xmath79 on the weak - coupling bcs side @xcite . the transition temperature is characterised by the thouless criterion , where the coefficient of the quadratic term in a ginzburg - landau action for the pairing field changes sign . in practice , the relevant question is when this transition occurs for a finite system , for instance inside a trapping potential ( see supplemental material @xcite ) . in our analysis we therefore compute @xmath0 for @xmath80 particles typical of current experiments @xcite , as depicted in fig . [ fig : tc ] . we have checked that different values for @xmath81 lead to small quantitative but not qualitative changes in the @xmath0 curve . in the weak - coupling bcs limit @xmath82 [ @xmath83 , the mean - field transition temperature is given by @xmath84 $ ] ( dashed line in fig . [ fig : tc ] ) , where @xmath85 is euler s constant @xcite . petrov et al . @xcite have included gorkov melik - barkhudarov corrections and obtained a lower value @xmath86 $ ] ( dash - dotted line ) . on the bkt side for strong binding @xmath87 , the thouless criterion fixes @xmath88 and the number equation determines @xmath0 @xcite . a more elaborate analysis using monte carlo data for the weakly interacting bose gas in 2d @xcite yields a bkt temperature of @xmath89 for @xmath90 @xcite , which decreases for even stronger binding ( left dashed curve in fig . [ fig : tc ] ) . this limiting behaviour implies the existence of a maximum @xmath0 in the crossover region ( cf.ref . @xcite ) , but does not determine its value or the precise crossover behaviour . the luttinger - ward result for @xmath0 grows monotonically from the bcs limit towards strong coupling @xmath91 : it suggests a maximum @xmath0 at negative @xmath92 , which is unlikely to exceed @xmath93 . this is consistent with experiments which did not observe signatures of superfluidity down to @xmath94 @xcite , but is considerably lower than a recent calculation for a harmonically trapped gas @xcite . the red dots in the phase diagram in fig . [ fig : tc ] mark the crossover temperature to the pseudogap regime @xmath47 , where the density of states @xmath44 at the chemical potential drops by @xmath48 of the value at the left fringe . in the weak coupling bcs limit , @xmath47 approaches @xmath0 since pairing and condensation occur simultaneously , and both @xmath0 and @xmath47 tend towards the dashed weak - coupling result . the large pseudogap regime at strong binding leads to clear signatures in the spin susceptibility and spectral properties well within reach of current experiments . vs interaction strength @xmath95 at temperature @xmath96 . we compare our result ( blue solid line ) with the experimental data at @xmath96 @xcite ( red symbols ) , the weak - coupling result ( green dash - dotted line ) , and monte carlo at @xmath67 @xcite ( cyan dashed line ) . [ fig : contact ] ] _ contact density._the contact density @xmath97 @xcite characterises the probability of finding particles of opposite spin close to each other @xcite . it determines the _ universal _ high - energy properties of a quantum gas with contact interactions , e.g. , the momentum distribution function @xmath98 at large momenta . the contact density is related to the variation of the pressure with scattering length by the adiabatic theorem @xcite , @xmath99 using the weak - coupling expansion of the ground state energy in @xmath100 @xcite one obtains at @xmath67 : @xmath101/4 $ ] . in the normal state the contact density corresponds to the total density of dimers @xcite . in fig . [ fig : contact ] we show our result for the contact ( solid line ) at @xmath102 and compare with the experimental data at the same temperature from frhlich et al . @xcite , as well as with the weak - coupling estimate above . remarkably , our calculation in this low - temperature region is very close to the @xmath67 monte carlo result @xcite ( dashed line ) , showing that the contact has only a weak temperature dependence . note , further , that while one generally expects the contact to decrease with increasing temperature , our result for larger @xmath41 is higher than the contact at @xmath67 from monte carlo , thus suggesting that @xmath97 is a non - monotonic function of @xmath103 , similarly to 3d @xcite . in conclusion , we have presented results for the density and pressure equation of state which shed light on a recent pressure measurement @xcite . the values for the transition temperature @xmath0 and the pseudogap crossover temperature @xmath47 in the phase diagram reveal a large pseudogap regime ; its effect on the spectral function and low - energy density of states are accessible and relevant for current experiments using momentum - resolved rf spectroscopy @xcite . we find that the contact depends only weakly on temperature , providing a robust interaction gauge . it will be worthwhile to extend the luttinger - ward technique into the low - temperature bkt phase , which is characterised by binding of vortex - antivortex pairs , and study the signatures of the superfluid phase for a trapped 2d fermi gas . the bkt transition itself is revealed by a jump in the sound velocities @xcite . we thank wilhelm zwerger for suggesting the problem , valuable discussions and careful reading of the manuscript . we acknowledge discussions with marcus barth , stefan baur , gianluca bertaina , rudolf haussmann , selim jochim , michael khl , jesper levinsen , vudtiwat ngampruetikorn , richard schmidt and andrey turlapov . mb thanks the gates cambridge trust for financial support . mmp acknowledges support from the epsrc under grant no . ep / h00369x/2 . 49 m. randeria , proceedings of the international school of physics `` enrico fermi '' course cxxxvi on high temperature superconductors , pp . 5375 ( ios press , amsterdam , 1998 ) ; v. m. loktev , r. m. quick , and s. g. sharapov , phys . rep . * 349 * , 1 ( 2001 ) . i. bloch , j. dalibard , and w. zwerger , rev . mod . phys . * 80 * , 885 ( 2008 ) ; w. zwerger , ed . , _ the bcs bec crossover and the unitary fermi gas _ , lecture notes in physics , vol . 836 ( springer , berlin , 2012 ) . j. t. stewart , j. p. gaebler , and d. s. jin , nature * 454 * , 744 ( 2008 ) ; j. p. gaebler , j. t. stewart , t. e. drake , d. s. jin , a. perali , p. pieri , and g. c. strinati , nature physics * 6 * , 569 ( 2010 ) . m. feld , b. frhlich , e. vogt , m. koschorreck , and m. khl , nature * 480 * , 75 ( 2011 ) . q. chen , j. stajic , s. n. tan , and k. levin , phys . rep . * 412 * , 1 ( 2005 ) ; y. he , q. chen , and k. levin , phys . rev . a * 72 * , 011602 ( 2005 ) ; q. chen , c. a. regal , m. greiner , d. s. jin , and k. levin , phys . rev . a * 73 * , 041601 ( 2006 ) ; a. perali , f. palestini , p. pieri , g. c. strinati , j. t. stewart , j. p. gaebler , t. e. drake , and d. s. jin , phys . rev . lett . * 106 * , 060402 ( 2011 ) . r. watanabe , s. tsuchiya , and y. ohashi , phys . rev . a * 88 * , 013637 ( 2013 ) . d. s. fisher and p. c. hohenberg , phys . rev . b * 37 * , 4936 ( 1988 ) ; z. hadzibabic , p. krger , m. cheneau , b. battelier , and j. dalibard , nature * 441 * , 1118 ( 2006 ) . n. prokofev and b. svistunov , phys . rev . a * 66 * , 043608 ( 2002 ) . m. holzmann , g. baym , j .- p . blaizot , and f. lalo , proc . natl acad . sci . usa * 104 * , 1476 ( 2007 ) . v. makhalov , k. martiyanov , and a. turlapov , phys . rev . lett . * 112 * , 045301 ( 2014 ) . g. bertaina and s. giorgini , phys . rev . lett . * 106 * , 110403 ( 2011 ) . d. s. petrov , m. a. baranov , and g. v. shlyapnikov , phys . rev . a * 67 * , 031601 ( 2003 ) . b. frhlich , m. feld , e. vogt , m. koschorreck , m. khl , c. berthod , and t. giamarchi , phys . rev . lett . * 109 * , 130403 ( 2012 ) . r. haussmann , z. phys . b * 91 * , 291 ( 1993 ) ; r. haussmann , phys . rev . b * 49 * , 12975 ( 1994 ) . r. haussmann , w. rantner , s. cerrito , and w. zwerger , phys . rev . a * 75 * , 023610 ( 2007 ) . p. nozires and s. schmitt - rink , j. low temp . phys . * 59 * , 195 ( 1985 ) ; s. schmitt - rink , c. m. varma , and a. e. ruckenstein , phys . rev . lett . * 63 * , 445 ( 1989 ) . m. j. h. ku , a. t. sommer , l. w. cheuk , and m. w. zwierlein , science * 335 * , 563 ( 2012 ) . t. enss , r. haussmann , and w. zwerger , ann . phys . 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this work was supported by the canada excellence research chairs ( cerc ) program , the natural sciences and engineering research council of canada ( nserc ) and the uk epsrc . o.s.m.l . acknowledges support from conacyt and the mexican secretaria de educacion publica ( sep ) . dklo , jj , and vp acknowledge quisco . v.p . , f.m.m . , d.k.l.o . and j.j . developed the theory . f.m.m . , a.c.l . and r.w.b . conceived the experiment . m.m . o.s.m.l . and a.c.l . carried out the experiment . f.m.m . performed the data analysis . all authors contributed to writing the paper . the authors declare no competing financial interests .

in 1924 david hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of `` infinity '' . in continuous - variable quantum mechanics we routinely make use of infinite state spaces : here we show that such a theoretical apparatus can accommodate an analog of hilbert s hotel paradox . we devise a protocol that , mimicking what happens to the guests of the hotel , maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner , producing infinitely many unoccupied levels in the process . we demonstrate the feasibility of the protocol by experimentally realising it on the orbital angular momentum of a paraxial field . this new non - gaussian operation may be exploited for example for enhancing the sensitivity of n00n states , for increasing the capacity of a channel or for multiplexing multiple channels into a single one . the `` hilbert hotel paradox '' demonstrates the counterintuitive nature of infinity @xcite . the hilbert hotel has infinitely many rooms numbered @xmath0 , all of which are currently occupied . each new visitor that arrives can be accommodated if every current guest in the hotel is asked to move up one room ( @xmath1 ) . even if a countably infinite number of new guests arrives at once , they can still be accommodated if each of the existing occupants moves to twice their current room number ( @xmath2 ) leaving the odd - numbered rooms free . we may ask whether such phenomena can exist physically . one possibility is in continuous - variables systems where in principle we have infinite ladders of energy eigenstates . previously @xcite , the first of the hilbert hotel paradoxes ( with a single new guest ) was proposed in cavity qed using the sudarshan - glogower bare raising operator @xmath3 that shifts all the amplitudes up one level leaving the vacuum state unoccupied . here , we show how we can implement the extended case where every second level of an infinite set of states is vacated . this can be performed coherently and deterministically , preserving all the initial state amplitudes by remapping them to twice their original levels using a short and simple sequence of instantaneous , dynamic , and adiabatic processes . we first show how to map the eigenstate amplitudes of a infinite square potential well to twice their original level , and then we report results of a physical implementation of an analogous protocol on the orbital angular momentum ( oam ) eigenstates of light , where we coherently multiply any linear superposition by a fixed integer ( in our case , by three ) . in the supplementary material we describe further details of the experiment and we show that the square well protocol can be generalised to implement a multiplication of the eigenstate numbers by any positive integer , not only by two . consider a quantum system with an infinite ladder of energy eigenstates bounded from below , @xmath4 . an arbitrary state can be then represented as @xmath5 . our earlier work @xcite has introduced the hilbert hotel operator @xmath6 , transforming @xmath7 to @xmath8 our new aim is to extend the toolbox by an operator @xmath9 , @xmath10 representing the second hilbert hotel paradox by leaving every second energy level vacant . both operators are non - unitary isometries , as @xmath11 . we show that we can deterministically implement @xmath9 on a infinite square potential well with initial width @xmath12 with the following operations ( fig . [ fig : protocol ] ) : _ i _ ) we instantaneously expand the well from @xmath12 to @xmath13 , _ ii _ ) we let it evolve for the original fundamental period , _ iii _ ) we divide the well into two sub - wells of width @xmath12 with a barrier , _ iv _ ) we let each half - well evolve with a relative potential offset , to correct the relative phase , _ v _ ) we merge the half - wells together into one well of width @xmath13 , _ vi _ ) we adiabatically shrink the well back to width @xmath12 . in general , the amplitudes of an initial state can be mapped to any integer multiple ( @xmath14 ) using a slightly modified procedure ( see supplementary material for details ) . within an infinite square potential well . * b * , we instantaneously expand the well to twice its original width . the original wavefunction is not immediately changed but the eigenbasis is different . * c * , we allow free evolution for a period corresponding to the original fundamental period . the wavefunction is reflected around the centre of the expanded well , with an undesired phase shift . * d * , we insert an infinite barrier in the centre ( where the wavefunction is zero ) to split it into two independent wells that evolve separately , an energy shift on one well corrects the relative phase . * e * , after the phase correction we align the potentials and merge the two halves back together . * f * , an adiabatic compression of the well maps the eigenstates of the expanded well to those of the original well . the original wavefunction has now been halved and reflected , corresponding to the hilbert hotel operation @xmath9 being applied to the eigenstates @xmath15.[fig : protocol],width=288 ] ideally steps _ i _ , _ iii _ and _ v _ should be instantaneous while step _ vi _ should be adiabatic . the fidelity of a physical implementation will depend on the accuracy of the timing and the quality of the approximations , especially the maximum effective excitation number @xmath16 of the initial state in comparison to the validity regime of the schrdinger equation approximation in any realistic system under consideration . the hilbert space of a particle in a well of width @xmath12 consists of the set of square - integrable functions , @xmath17 and the free particle hamiltonian is @xmath18 with boundary conditions @xmath19 . this describes a one - dimensional particle in an infinite square potential well , but it can also describe other situations , e.g. an ideal two - dimensional optical waveguide within the paraxial wave approximation . the hamiltonian yields an infinite ladder of nondegenerate energy eigenfunctions of the form @xmath20 with eigenvalues @xmath21 where @xmath22 . the desired operation @xmath9 transforms an initial state @xmath23 into @xmath24 interleaving the amplitudes of the initial state in the energy eigenbasis with zeros . the first step of the hilbert hotel protocol is to double the width of the well so the original wave function @xmath25 extends from @xmath26 to @xmath27 , filling the new interval by constant zero . we denote this extended wave function by @xmath28 and the free hamiltonian with the new boundary conditions @xmath29 by @xmath30 . this hamiltonian has a new set of eigenfunctions @xmath31 which we use to express @xmath32 . we allow @xmath28 to evolve over a time @xmath33 into @xmath34 where @xmath35 is @xmath36 for even @xmath16 and @xmath37 for odd @xmath16 , thus @xmath38 where @xmath39 is the identity operator and @xmath40 the mirror reflection ( or parity ) operator . therefore , after step _ ii _ we have ( up to a global phase factor ) the state @xmath41 this resembles the point symmetry extension of @xmath25 to @xmath27 but the phase factor in @xmath42 needs to be corrected . steps _ iii _ , _ iv _ and _ v _ remove the undesired @xmath43 factor while preventing cross - talk between the two sub - wells . after splitting the interval @xmath27 in two , each part will evolve separately under the hamiltonian @xmath44 with appropriate boundary conditions . the two halves can be phase - matched by applying potentials @xmath45 in @xmath26 and @xmath46 in @xmath42 for a time @xmath47 . after removing the barrier ( step _ v _ ) , the wave function of the system becomes @xmath48 substituting for @xmath49 from , we find that both branches allow for a common analytic expression , as the domain of @xmath31 is twice that of @xmath49 : @xmath50 the final step is an adiabatic compression of the well back to its original width @xmath12 . up to a relative phase due to free evolution , which can be corrected by matching the total time of the evolution to an integer number of full revolutions of the running eigenbasis , this adiabatically transforms the basis states @xmath31 into @xmath49 of the same @xmath16 , keeping coherent superpositions intact . this shows the resulting state is indeed . the crucial step in the hilbert hotel operation is the coherent mapping @xmath51 ( for @xmath52 ) on a countably infinite set of basis states @xmath53 , as described above . instead of a particle in an infinite square potential well , we can use systems that share important characteristics in order to perform analogous operations . in our experimental realisation ( fig . [ hhsetup ] ) we choose the set of oam eigenstates of a beam of light , denoted by @xmath54 , and the coherent multiplication makes use of two well - known optical devices in a novel configuration : an oam sorter and a `` fan - out '' refractive coherent beam copier @xcite . the oam multiplier has four steps : _ i _ ) unwrapping the initial azimuthal phase ring into a linear phase ramp with a polar - to - cartesian mapping , _ ii _ ) branching out new copies of the linearised field and correcting their relative phase with a suitable grating , _ iii _ ) demagnifying the juxtaposed copies with a cylindrical lens , and _ iv _ ) wrapping the resulting field back to polar coordinates . the combination of these four steps amounts to the transformation : @xmath55 where @xmath56 is the number of copies produced in step _ ii_. the first step is achieved by way of an oam sorter @xcite , which unwraps any oam mode into a linear gradient ( and therefore it turns a combination of oam modes into a combination of linear gradients ) by way of an extremely astigmatic lens @xmath57 followed by a phase - correcting element @xmath58 , which effectively stops the unwrapping after the transformation is complete . these two elements can be described by the phase delay that they impose on the incoming field as a function of position : @xmath59 where @xmath60 is the focal length of the fourier lens connecting near - field and far - field , @xmath61 is the wavelength of the light beam , and the free parameters @xmath62 and @xmath63 determine the scaling and position of the transformation in the fourier plane of coordinates @xmath64 and @xmath65 . at this point we produce equal - weighted copies of the unwrapped phase ramp using a fan - out element by way of a suitable 1d phase grating on the far field . it is crucial that the copies have the same intensity in order to obtain the desired oam modes at the end of the process . in our experiment , the fan - out grating produces three copies and the equation describing the phase delay of the grating as a function of position in the far field is @xmath66,\end{aligned}\ ] ] where @xmath67 . such a phase mask does not depend on the @xmath68 coordinate , as we are copying a linear field . this grating is displayed on a spatial light modulator ( slm ) , so the output of the sorter needs to be fourier transformed onto the fan - out slm with a @xmath69 system , followed by another @xmath69 system which images it through a second sorter operated _ in reverse_. in order to wrap the field back correctly without leaving wide gaps or without wrapping more than necessary , we use a cylindrical lens to demagnify the horizontal cartesian coordinate before the beam enters the reverse - sorter . exploiting the flexibility of slms , we achieve this by adding the phase of a cylindrical lens directly on top of the fan - out grating . in the first part of our experiment we test the coherence of the protocol , i.e. its ability to preserve superpositions . to do this , we generate balanced superpositions of @xmath70 and @xmath71 , with @xmath72 ranging from 1 to 3 . such initial modes display @xmath73 maxima , or `` petals '' . we feed them to the multiplier ( here set to multiply by @xmath74 ) and a successful protocol results in @xmath75 petals with high visibility at the output , as can be seen in fig . [ petals ] . * coherent oam multiplication . * top row : near field of input coherent superpositions . bottom row : tripled output states . the number of petals is @xmath75 , as expected from a coherent operation.,width=288 ] * oam multiplication performance . * for each input eigenmode we measure the composition of the multiplied output . circle size is linearly proportional to the overlap with the output modes . as can be seen , the small leakage onto the neighbouring output modes is contained within a few adjacent modes . a sufficiently distant input superposition such as @xmath76 would maintain an effective orthogonality.,width=288 ] in the second part of our experiment we assess the accuracy of the protocol by measuring the leakage onto neighbouring oam eigenmodes . to do this , we multiply single oam eigenmodes by @xmath74 and projectively measure the oam spectrum of the output . the results show that the overlap decays quickly enough for suitably distant superpositions to maintain their orthogonality ( fig . [ dataanalysis ] ) . for instance , the superposition @xmath76 which ideally maps to @xmath77 , was mapped to a superposition of modes , peaked on @xmath78 , but nevertheless with negligible cross - talk ( details in supplementary material ) . in summary , we showed how to implement the hilbert hotel `` paradox '' , where the rooms of the hotel are the excitation modes of an infinite square potential well . we then reported the successful implementation of the core step of the operation ( the coherent multiplication of the basis states of a countably infinite basis ) on the oam eigenmodes of a paraxial beam of light . we show that the operation is coherent and that even in our proof - of - principle experiment , the multiplication of sufficiently distant modes can be performed with negligible overlap . mode multiplication could be implemented also in other quantum systems , such as becs in a box potential with predicted talbot carpet features , though nonlinear interactions may spoil the ideal free particle expansion required for perfect wavefunction mirroring @xcite . nonetheless , we note that this idea could be used to enhance several state production schemes without the need to modify the existing apparatuses , because it can act as an extension . for instance , it could prove useful in quantum and classical information processing as a means of multiplexing an arbitrary number of input channels into a single output channel , or to enhance the sensitivity of systems that use n00n states , or to distribute ordered gaps in the spectral profile of a state . 99 kragh , h. the true ( ? ) story of hilbert s infinite hotel . arxiv:1403.0059v2 ( 2014 ) . oi , d. k. l. , potoek , v. , and jeffers , j. nondemolition measurement of the vacuum state or its complement . _ phys . rev . lett . _ * 110 , * 210504 ( 2013 ) . gaunt , a. l. , schmidutz , t. f. , gotlibovych , i. , smith , r. p. , and hadzibabic , z. bose - einstein condensation of atoms in a uniform potential . _ phys . rev . lett . _ * 110 , * 200406 ( 2013 ) . jenkins , r. m. , devereux , r. w. j. , and heaton , j. m. a novel waveguide mach - zehnder interferometer based on multimode interference phenomena . _ opt . comm . _ * 110 , * 410424 ( 1994 ) . prongu , d. , herzig , h. p. , dndliker , r. , and gale , m. t. optimized kinoform structures for highly efficient fan - out elements . _ appl . opt . _ * 31 , * 5706 ( 1992 ) . romero , l. a. , and dickey , f. m. theory of optimal be a splitting by phase gratings . i. one - dimensional gratings . _ j. opt . soc . am . a _ * 24 , * 2280 ( 2007 ) . berkhout , g. c. g. , lavery , m. p. j. , courtial , j. , beijersbergen , m. w. , and padgett , m. j. efficient sorting of orbital angular momentum states of light . _ phys . rev . lett . _ * 105 , * 153601 ( 2010 ) . mirhosseini , m. , malik , m. , shi z. , and boyd , r. w. efficient separation of the orbital angular momentum eigenstates of light . _ nat . comm . _ * 4 , * 2781 ( 2013 ) . ruostekoski , j. , kneer , b. , schleich , w. p. , and rempe , g. interference of a bose - einstein condensate in a hard - wall trap : from the nonlinear talbot effect to the formation of vorticity . _ phys . rev . a _ * 63 , * 043613 ( 2001 ) .

we first calculate the electronic spin driven by the effective su(2 ) yang - mills field due to the spin - orbit interaction . to confirm rigorously the su(2 ) gauge covariance , we consider up to the third - order contribution of the non - abelian spin - orbit gauge potential . therefore , we will obtain the gauge invariant result after the strict calculation . the diagrammatic representation of the spin density induced by the first order in @xmath7 is shown in fig . 1(a ) , and this contribution is written down @xmath104,\end{aligned}\ ] ] where @xmath105 is the system size , @xmath106 denotes the fermi distribution function , @xmath107 ( @xmath108 ) is the impurity - averaged retarded ( advanced ) green s function of free electrons defined as ( @xmath109 ) @xmath110 and @xmath111 represents contribution of the diffusion ladder @xmath112 considering the slowly varying spin - orbit coupling , @xmath113 and @xmath114 , we carry out the gradient expansion and the leading contribution reads @xmath115 \pi_{\omega}({{\bm q}},{\omega } ) \notag \\ & -{{\mathcal a}_t}^a({{\bm q}},{\omega } ) { g^{\rm r}}_{{{\bm k}},{\omega } } { g^{\rm a}}_{{{\bm k}},{\omega } } \bigg [ \frac{i}{\tau } + { \omega}\pi_{\omega}({{\bm q}},{\omega } ) \bigg ] \bigg\}.\end{aligned}\ ] ] after integrating the green s function with respect to @xmath38 and @xmath39 , we finally obtain @xmath116 \notag \\ & = \frac{{\sigma_{\rm c}}}{l^d } \int{d^d r ' } \int{d t ' } \sum_{{\bm q}}\sum_{\omega}\frac{e^{i { { \bm q}}\cdot ( { { \bm r}}-{{\bm r } } ' ) -i { \omega}(t - t')}}{d { { \bm q}}^2 -i { \omega } } { { \bm \nabla}}_{{{\bm r } } ' } \cdot \big [ { \partial}_{t ' } { { \bm{\mathcal a}}}^a({{\bm r}}',t ' ) + { { \bm \nabla}}_{{{\bm r } } ' } { { \mathcal a}_t}({{\bm r}}',t ' ) \big ] \notag \\ & \equiv { \sigma_{\rm c}}{{\bm \nabla } \cdot}\langle{{\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a}\rangle.\end{aligned}\ ] ] the spin current is similarly calculated , @xmath117 { { \rm im}}\big [ k_j ' k_l ' { g^{\rm r}}_{{{\bm k}}',{\omega } } ( { g^{\rm a}}_{{{\bm k}}',{\omega}})^2 \big ] \pi_{\omega}({{\bm q}},{\omega } ) \notag \\ & -i 2 \hbar q_j { \omega}{{\mathcal a}_t}^a({{\bm q}},{\omega } ) { { \rm im}}\big [ k_i k_j { g^{\rm r}}_{{{\bm k}},{\omega } } ( { g^{\rm a}}_{{{\bm k}},{\omega}})^2 \big ] \pi_{\omega}({{\bm q}},{\omega } ) \bigg\},\end{aligned}\ ] ] and results in @xmath118 here we consider the higher - order contribution for the su(2 ) gauge covariance . we show the feynman diagrams of the second- and third - order contributions in fig . the same manner to the first - order case is applicable to this higher - order case , and each spin polarization is obtained as @xmath119 -{{\mathcal a}_t}^b s^{(1 ) c } + { { \bm{\mathcal a}}}^b \cdot { { \bm j}}^{(1 ) c } } \big\rangle,\ ] ] and @xmath120 + { { \mathcal a}_t}^b s^{(2 ) c } -{{\bm{\mathcal a}}}^b \cdot { { \bm j}}^{(2 ) c } } \bigg\rangle,\ ] ] respectively . correspondingly the spin current is also calculated , @xmath121 -d { { \bm \nabla}}s^{(2 ) a } , \\ { { \bm j}}^{(3 ) a } & = \frac{2 e}{\hbar } \epsilon^{abc } \bigg [ \frac{e { \chi_{\rm l}}}{\hbar } \epsilon^{cde } { { \bm{\mathcal a}}}^b \times ( { { \bm{\mathcal a}}}^d \times { { \bm{\mathcal a}}}^e ) + { { \bm{\mathcal a}}}^b s^{(2 ) c } \bigg ] -d { { \bm \nabla}}s^{(3 ) a}.\end{aligned}\ ] ] from all the results , the spin and its current densities are represented in a su(2 ) gauge invariant form @xmath122 } \bigg\rangle \notag \\ & -\frac{2 e}{\hbar } \epsilon^{abc } \big\langle{{{\mathcal a}_t}^b ( s^{(1 ) c } + s^{(2 ) c } ) -{{\bm{\mathcal a}}}^b \cdot ( { { \bm j}}^{(1 ) c } + { { \bm j}}^{(2 ) c})}\big\rangle,\end{aligned}\ ] ] and @xmath123 -d { { \bm \nabla}}s^a,\end{aligned}\ ] ] respectively . this results are rewritten by the effective yang - mills field , @xmath49 and @xmath55 , @xmath124 we here introduce the covariant derivative as @xmath125 where @xmath126 is an arbitrary function in spin space . the spin current is simplified using this covariant derivative , @xmath127 and the spin polarization is given by the covariant conservation law of spin , @xmath128 next , we calculate the spin arising from a combination between the effective su(2 ) yang - mills field and the usual u(1 ) maxwell electromagnetic field . the diagrams of this contribution is shown in fig . although the calculation becomes more and more complicated , spin and spin current densities are straightforwardly derived , @xmath129 \notag \\ & + ( { { \bm \nabla } \times}{{\bm{\mathcal a}}}^a ) \times \big [ { \partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi}+d { { \bm \nabla}}\big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi})}\big\rangle \big ] \notag \\ & -({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi } ) \big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a)}\big\rangle -({\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a ) \big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi})}\big\rangle \notag \\ & + \frac{1}{d } { \phi}{{\mathcal a}_t}^a + { { \bm \nabla}}\big [ { \phi}\big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a)}\big\rangle \big ] + { { \bm \nabla}}\big [ { { \mathcal a}_t}^a \big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi})}\big\rangle \big ] \bigg\rangle , \\ { { \bm j}}^a = & -\frac{e \tau { \sigma_{\rm c}}}{m } \bigg\ { ( { { \bm \nabla } \times}{{\bm a}^{\rm em } } ) \times \big [ { \partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a + d { { \bm \nabla}}\big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a)}\big\rangle \big ] \notag \\ & + ( { { \bm \nabla } \times}{{\bm{\mathcal a}}}^a ) \times \big [ { \partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi}+d { { \bm \nabla}}\big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi})}\big\rangle \big ] \notag \\ & -({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi } ) \big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a)}\big\rangle -({\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a ) \big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi})}\big\rangle \notag \\ & + \frac{1}{d } { \phi}{{\mathcal a}_t}^a + { { \bm \nabla}}\big [ { \phi}\big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm{\mathcal a}}}^a + { { \bm \nabla}}{{\mathcal a}_t}^a)}\big\rangle \big ] + { { \bm \nabla}}\big [ { { \mathcal a}_t}^a \big\langle{{{\bm \nabla } \cdot}({\partial_t}{{\bm a}^{\rm em}}+{{\bm \nabla}}{\phi})}\big\rangle \big ] \bigg\ } -d { { \bm \nabla}}s^a.\end{aligned}\ ] ] this result expressed by the su(2 ) and u(1 ) gauge potentials has a lot of contribution and it is obscure to explain phenomena . to replace each gauge potential with the effective yang - mills field and the electromagnetic field , the equation is simplified as @xmath130 -d { { \bm \nabla}}s^a.\end{aligned}\ ] ] in this calculation , we considered the linear response of the non - abelian spin - orbit gauge potential . the effective yang - mills field does not contain non - commutative parts proportional to @xmath131 and @xmath88 , and therefore the field turns to @xmath132 and @xmath133 . however , the non - commutative contribution should exist at the viewpoint of the su(2 ) gauge covariance . since the result depends on the first - order spin - orbit coupling , spin polarization and spin current given by eqs . ( s.26 ) and ( s.27 ) are exactly conserved , @xmath134 considering the non - commutative parts in the yang - mills field , the derivative of this identity is surely replaced by the covariant derivative .

by associating a spin - orbit interaction with a non - abelian gauge potential , we theoretically present a spin polarization in a quite general form using an effective yang - mills field and a usual electromagnetic field . in this gauge invariant result , we focus on a purely electrically - induced spin contribution . we find that both the inverse spin galvanic effect and the spin hall effect arise from the same origin , i.e. , the su(2)@xmath0u(1 ) hall effect . we also discover that a large effective magnetic field of the order of @xmath1 t is induced in the rashba system . generation of spin by applying an electric current in the presence of spin - orbit interaction has been investigated with much theoretical and experimental attention in spintronics @xcite . one of the most successful phenomena of electronic spin - and - charge coupled transport is the spin hall effect @xcite . in a system with spin - orbit interaction , a spin current appears in the transverse direction to an applied electric current . as a result , electronic spin accumulates at the edges of the sample . as a similar effect , in the inverse of the spin galvanic effect @xcite a spin polarization is also induced by applying an electric current . these two phenomena are different in a direction of an emergent spin polarization . in a case of a two - dimensional electron system without inversion symmetry , the induced spin polarization is out - of - plane in the spin hall effect , while the in - plane spin arises in the inverse spin galvanic effect . although the electronic spin is the well - defined quantity , the theoretical definition of spin current is not uniquely given under the spin - orbit interaction . in the presence of spin - orbit interaction , electronic spin dynamics always accompanies the relaxation compared with the equation of motion for electric charge . to resolve this ambiguity in the definition , the non - abelian gauge theory is one of the possible solutions . to connect the spin - orbit coupling with the non - abelian gauge theory in condensed matters has been the well - known idea for many years @xcite , and a proper definition of spin current is given on the basis of the su(2 ) gauge invariance by treating the spin - orbit interaction as the non - abelian vector potential @xcite . in this context , despite the conservation law for spin is still broken , the electronic spin is covariantly conserved , @xmath2 where @xmath3 is the electronic spin , @xmath4 is the spin current flowing in the @xmath5-direction and spin - polarized in the @xmath6-direction , and @xmath7 represents the non - abelian spin - orbit gauge potential . in recent years , several spin - dependent phenomena based on this non - abelian gauge theory have been actively reported @xcite . following the non - abelian gauge theory , time and space derivatives of the spin - orbit coupling are corresponding to effective yang - mills electric and magnetic fields , respectively , which drive spin current and spin polarization . in experiment , a spatial and temporal variation of the spin - orbit coupling is feasible . for example , since the rashba effect emerges when the gate voltage breaks the structural inversion symmetry in two - dimensional semiconductor heterostructures @xcite , the alternating gate voltage could change the rashba coupling , and in the specific sample configuration the spatially - varying rashba coupling is realized @xcite . this space - time dependent spin - orbit coupling is expected to open up the possibilities of electrical spin manipulation . in this paper , we derive analytically a general expression of spin polarization in terms of an effective non - abelian su(2 ) yang - mills field corresponding to the spin - orbit interaction and zeeman effect , and the usual u(1 ) maxwell electromagnetic field . in particular , we focus on the generation of spins by electric field alone without any magnetic contributions . a related work has been done by gorini _ et al . _ who demonstrated theoretically a su(2)@xmath0u(1 ) covariant boltzmann equation in a space - time dependent two - dimensional rashba system , and derived explicitly electronic spin and charge transport @xcite . the focus of their work , however , is the spin and charge currents in contrast to the spin polarization in the present paper . we consider a general disordered electron system coupled to an external electromagnetic field and a spin - orbit interaction in condensed matters whose hamiltonian is represented by @xmath8 \psi({{\bm r}},t ) \big|^2 \notag \\ & -e \int{d^d r } \psi^\dagger({{\bm r}},t ) \big [ { \phi}({{\bm r}},t ) + { { \mathcal a}_t}^a({{\bm r}},t ) { \hat{\sigma}}^a \big ] \psi({{\bm r}},t ) \notag \\ & -{\varepsilon_{\rm f}}\int{d^d r } \psi^\dagger({{\bm r}},t ) \psi({{\bm r}},t ) + h_{\rm i } , \label{eq : hamiltonian}\end{aligned}\ ] ] where @xmath9 is the annihilation operator of conduction electron , @xmath10 denotes the number of dimensions , @xmath11 and @xmath12 are mass and charge of electron , respectively , @xmath13 is the planck constant , @xmath14 is the fermi energy , @xmath15 is the vector of the pauli matrices ( @xmath16 and the caret means a matrix ) , and @xmath17 denotes the spin - independent random impurity scattering which gives rise to the relaxation time of electron , @xmath18 . here , the external electric and magnetic fields are defined using the potential @xmath19 and @xmath20 as @xmath21 and @xmath22 , respectively . the non - abelian spin - orbit gauge potential @xmath23 ( @xmath24 ) is the first - order relativistic correction of electromagnetic field derived from the dirac equation , and its time and space components are consistent with the zeeman splitting and the spin - orbit coupling , respectively , @xmath25 where @xmath26 is the speed of light and @xmath27 is the antisymmetric tensor . according to the non - abelian gauge theory , the effective yang - mills electric field is defined as @xmath28 , and its magnetic counterpart is @xmath29 . , the wavy line describes the interaction with general u(1 ) electromagnetic potential , @xmath30 . the double dotted line is the diffusion ladder due to the impurity scattering described by the single dotted line . ] from the covariant spin conservation law [ eq . ] , we can introduce a covariantly conserved spin current , @xmath31 where @xmath32 denotes trace over spin indices and @xmath33 is the quantum expectation value . using the keldysh green s function @xcite , we carry out the analytic calculation of the spin and its current densities induced by the effective yang - mills field and electromagnetic field . the electronic spin density is generally defined as @xmath34 $ ] , where @xmath35 is the lesser component of the keldysh green s function . for calculation , we show feynman diagrams of the spin density in fig . [ fig : spin ] . we consider slowly - varying electric and magnetic fields , subject to @xmath36 and @xmath37 ( @xmath38 and @xmath39 are wavenumber and frequency of electromagnetic field , and @xmath40 denotes a mean free path of electrons ) , and we do the gradient expansion . the calculation on the basis of the quantum many - body theory ( see supplemental material in detail ) yields the following result up to the second order in @xmath30 and @xmath7 ( including the third - order terms which guarantees the gauge covariance ) , @xmath41 this spin polarization is clearly formed in terms of the effective su(2 ) yang - mills field due to spin - orbit coupling and the u(1 ) maxwell electromagnetic field . this simple equation is one of the main conclusions in the present paper . in eq . , the angle bracket denotes the average of a diffusive electron motion satisfying the relation @xmath42 ( @xmath43 is the arbitrary function with respect to space and time ) , @xmath44 is the conductivity , @xmath45 is the density of states per volume involving spin degree of freedom , @xmath46 is the diffusion constant , @xmath47 is the landau diamagnetic susceptibility , and @xmath48 is the bohr magneton . the spin polarization and the spin current driven by the yang - mills electric field @xmath49 are defined as @xmath50 and @xmath51 , respectively , and as their u(1 ) counterparts the electric charge and electric current are given by @xmath52 and @xmath53 . in a similar manner , the spin current is also obtained , @xmath54 this result of spin current is consistent with the previous theoretical works @xcite . the spin polarization and the spin current given by eqs . and , of course , satisfy the spin continuity equation [ eq . ] . we note that the electronic spin is exactly conserved at the linear - order su(2 ) gauge potential . in other words , spin is conserved in a weak spin - orbit coupling system . equation is a really compact equation of spin polarization ; however , the effective yang - mills field , @xmath49 and @xmath55 , is inappropriate to explain the real spin - related phenomena . here we replace the non - abelian spin - orbit gauge potential by the real electromagnetic field using eq . , and therefore the spin polarization in eq . is rewritten as @xmath56 \notag \\ & + \frac{{\mu_{\rm b}}\tau}{2 m c^2 } \bigg\ { { \sigma_{\rm c}}\big\langle{({{\bm \nabla } \times}{{\bm b}}-{{\bm b}}\times { { \bm \nabla } } ) \times { \partial_t}{{\bm e}}}\big\rangle -\nabla_i \langle{\nabla_i { { \bm e}}\times { { \bm i}}}\rangle \notag \\ & -{\partial_t}\big\langle{\big ( { { \bm \nabla } \times}{{\bm e}}-{{\bm e}}\times { { \bm \nabla}}\big ) \rho}\big\rangle -\nabla_i \big\langle{\big ( { { \bm \nabla } \times}{{\bm e}}-{{\bm e}}\times { { \bm \nabla}}\big ) i_i}\big\rangle \notag \\ & + \frac{2 c^2}{d } \nabla_i \langle{i_i { { \bm b}}}\rangle -2 e^2 \nu c^2 \nabla_i \big [ \big\langle{\big ( { { \bm e}}+d { { \bm \nabla } \times}{{\bm b}}\big)_i \langle{{\partial_t}{\tilde{\bm b}}}\rangle}\big\rangle \notag \\ & + \nabla_i \big\langle{{\phi}\langle{{\partial_t}{\tilde{\bm b}}}\rangle}\big\rangle \big ] \bigg\ } , \label{eq : spin_elemag}\end{aligned}\ ] ] where @xmath57 is the magnetic field including the spin - orbit correction . this is a general form of spin polarization induced by electric and magnetic fields in the presence of spin - orbit interaction . the first term is due to the zeeman field . the next five terms represent the generalized spin pumping effect . in the usual spin pumping effect @xcite , dynamic magnetization or magnetic field induces a flow of spin angular momentum and it is a purely magnetic effect . we here revealed that the electrical counterpart of the spin pumping effect also occurs thanks to the spin - orbit coupling which converts orbital energy into spin . the origin of the spin pumping effect is the spin torque . the usual spin pumping effect comes from a precession of electronic spin around a magnetic field , @xmath58 . in contrast , the origin of the electrical spin pumping effect is a torque owing to the spin - orbit coupling proportional to @xmath59 . since electrical control of spin is quite important for developing spintronics , we focus on the purely electrical manipulation of electronic spin . we pick out the electrically induced spin polarization in eq . and it reads @xmath60 here we ignored the rotation of electric field because the alternating magnetic field must be necessarily applied to generate a rotational electric field based on the faraday s law . equation expresses a generation of spin by space - time dependent electric field and this is the second main result in this paper . the first term represents the electrical spin pumping effect and the other contributions originate from the lorentz force of the effective yang - mills electric and magnetic fields , @xmath61 . assuming a case of uniform or stationary electric field , eq . is useful to demonstrate various spintronic phenomena shown in the following . let us first consider the spatially uniform case . in this situation , the induced spin is due to the electrical spin pumping effect shown in the first term of eq . . since this is due to the second order of spin - orbit coupling , it is usually very weak and hard to detect this phenomenon . as a material effect , the rashba spin - orbit interaction is a candidate for realizing experimental observation of the electrical spin pumping effect because the really huge rashba coupling emerges at a boundary or surface of metals @xcite and bulk rashba semiconductors @xcite . the rashba effect is given by ( @xmath62 is the rashba coupling ) @xmath63 if we consider two kinds of rashba effect : the bulk rashba effect along the @xmath64-axis , @xmath65 , and the time - evolving rashba effect by the gate voltage in the @xmath66-direction , @xmath67 , the induced spin polarization is lying in the @xmath68-direction , @xmath69 we set a weak rashba coupling in a metallic sample , where @xmath70 , @xmath71 ( @xmath72ev and @xmath73@xmath74 being the fermi wavenumber ) , and @xmath75 . then the emergent spin polarization is roughly estimated at @xmath76 t as an effective magnetic field , where @xmath77 is the magnetic permeability in vacuum and @xmath78 is the gyromagnetic ratio . this effective magnetic field is quite large enough to control magnetization . as a related study , it was theoretically proposed that a spin is driven by applying two orthogonal gate electric fields on the different sections of a one - dimensional wire @xcite . next , we investigates the case of steady state in eq . . here we consider two - dimensional rashba and dresselhaus systems given by @xmath79 ( @xmath80 ) and @xmath81 where @xmath82 represents the dresselhaus coupling @xcite . to assume the injection of electric current along the @xmath66-direction in the present system , the in - plane spin polarization emerges @xmath83 i({{\bm q } } ' ) , \\ s^y({{\bm q}}+{{\bm q } } ' ) & = \frac{m}{\hbar { \varepsilon_{\rm f } } } \frac{q_x + q_x'}{|{{\bm q}}+{{\bm q}}'|^2 } \big [ q_x \beta({{\bm q } } ) -q_y \alpha({{\bm q } } ) \big ] i({{\bm q } } ' ) . \end{split}\ ] ] the effect is very sensitive to the spatial dependence of the rashba and dresselhaus spin - orbit couplings and the external electric current . the result becomes changed by whether we take first the limit to the constant spin - orbit coupling , @xmath84 , or the uniform electric current , @xmath85 . ( i ) when we inject the uniform electric current in the spatially - varying rashba and dresselhaus systems , the spin polarization turns to ( @xmath86 ) @xmath87 this effect is well - known as the inverse of the spin galvanic effect @xcite . in the previous theoretical prediction of the inverse spin galvanic effect in the rashba system @xcite , the constant rashba coupling was treated non - perturbatively , whereas our calculation is carried out by the perturbation expansion and we take account of the spatial dependence of the rashba coupling . nevertheless these quite distinct calculations are exactly consistent in a condition of the uniform electric current . ( ii ) when the limit to the constant spin - orbit coupling is taken first , the spin is not induced identically . according to the previous work , the inverse spin galvanic effect should occur even in the spatially uniform rashba system . it indicates that the inverse spin galvanic effect in the uniform rashba system is a non - perturbative effect , and thus our result can not be applicable to the constant rashba case . in the above discussion , we omitted the higher - order contribution of electromagnetic field such as the non - commutative contribution of the yang - mills magnetic field , @xmath88 , in the su(2)@xmath0u(1 ) hall effect , @xmath89 . in fact , this component is related to the spin hall effect @xcite , @xmath90 interestingly the origin of the spin hall effect is exactly same as the inverse spin galvanic effect , and they are connected with the su(2)@xmath0u(1 ) hall effect , @xmath91 . these effects are classified by whether the non - commutative contribution of the yang - mills magnetic field , @xmath88 , or the other , @xmath92 . in conclusion , we have analytically derived the general expression of spin polarization arising from electric and magnetic fields in the presence of spin - orbit interaction . as a result , we obtained the purely electrical spin manipulation , and we have shown that this formula connects different spintronic phenomena which have ever been independently discussed : the inverse spin galvanic effect and the spin hall effect . we found also that two different time - dependent rashba fields yield a large effective magnetic field . to handle freely the rashba effect would be a key to the future spintronics . this work was supported by grant - in - aid for scientific research ( s ) ( grant no . 24224009 ) from the ministry of education , culture , sports , science and technology of japan ; 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first principles calculations are used to investigate the effects of epitaxial strain on the structure of the perovskite oxide catio@xmath0 , with particular focus on the stabilization of a ferroelectric phase related to a polar instability hidden in the orthorhombic equilibrium bulk @xmath1 structure but found in previous first - principles studies of the ideal cubic perovskite high - symmetry reference structure . at 1.5% strain , we find an epitaxial orientation transition between the @xmath2-@xmath3 phase , favored for compressive strains , and the @xmath4-@xmath3 phase . for larger tensile strains , a polar instability develops in the @xmath4-@xmath3 phase and an epitaxial - strain - induced ferroelectric phase is obtained with polarization along a @xmath5110@xmath6 direction with respect to the primitive perovskite lattice vectors of the square substrate . with the recent dramatic advances in the synthesis of coherent epitaxial films of complex oxides @xcite , it is possible to maintain extremely high strains in thin film materials , often as much as 23% . in some materials , such high strains can drive the system through a structural phase boundary to a novel phase with structure and properties distinct from those of the bulk equilibrium phase . first principles calculations can provide quantitative predictions about these novel phases and phase boundaries ; in particular , such phases can be identified from examination of the lattice instabilities of the high - symmetry reference structure of the bulk phase @xcite , and their structure and properties predicted . a prototypical example is strain - induced ferroelectricity in srtio@xmath0 . starting from the bulk equilibrium paraelectric phase , strain - polarization coupling results in a polar instability beyond critical values of both tensile and compressive ( 001 ) epitaxial strain . this behavior was predicted by landau theory @xcite and further analyzed in first principles investigations @xcite . experimental observation of epitaxial - strain induced ferroelectricity in srtio@xmath0 @xcite demonstrates this strain - induced ferroelectricity both for compressive and tensile strain . catio@xmath0 presents a greater challenge for the observation of strain - induced ferroelectricity . a relatively large temperature - dependent dielectric response has led to the characterization of catio@xmath0 , like srtio@xmath0 , as an incipient ferroelectric @xcite . however , unlike srtio@xmath0 , catio@xmath0 has a strong tendency to oxygen - octahedron rotations , which tend to suppress polar lattice instabilities @xcite . indeed , the bulk @xmath1 structure @xcite , a structure type that includes a large number of other perovskite oxides , is obtained as a distortion of the high - symmetry cubic perovskite reference structure by freezing in components of the m@xmath7 and r@xmath8 oxygen octahedron modes ( notation from ref . ) involving rotation around [ 001 ] and tilting around [ 110 ] , respectively , with additional changes in the lattice constants @xmath9 , @xmath10 and @xmath4 and ca displacements preserving the space group symmetry . all other known phases are also nonpolar : these include a paraelectric cubic structure at high temperatures and two intermediate phases ( one tetragonal and one orthorhombic ) @xcite . less is known about high - pressure phases , though a transition to a nonpolar orthorhombic @xmath11 structure and , at higher pressures , to a nonpolar post - perovskite structure like that of mgsio@xmath0 have been proposed based on first - principles results @xcite . first - principles calculations of the full phonon dispersion relation of the cubic perovskite structure of catio@xmath0 show that in addition to the expected instability of m@xmath7 and r@xmath8 , the cubic perovskite structure does have a strongly unstable polar @xmath12 mode @xcite . freezing in of this polar mode , which involves displacements of the ca and ti ions relative to the oxygen octahedron network , would yield a ferroelectric phase with nonzero spontaneous polarization . the fact that it does not contribute to the observed bulk phases suggests that it is inhibited by the oxygen octahedron rotations . if the rotations are artificially suppressed , as is possible in a first - principles calculation , the @xmath12 mode dominates and the resulting ferroelectric @xmath13 phase is found to have a very large polarization @xcite . to stabilize a ferroelectric phase of catio@xmath0 under conditions realizable in the laboratory , it is necessary to change the balance of the competition between the octahedral rotations and the polar instability in favor of the latter . as in srtio@xmath0 , the polar instability in catio@xmath0 could be strengthened through the well - established sensitivity of the polar mode to strain in the titanates @xcite , specifically by tuning epitaxial strain @xcite . however , the oxygen - octahedron distortions inevitable in catio@xmath0 will couple to the epitaxial strain and polar instability , leading to a richer set of possibilities than in srtio@xmath0 . in this paper , we study the use of epitaxial strain to stabilize a ferroelectric phase of catio@xmath0 . we focus on the orthorhombic bulk ground state , and investigate whether epitaxial strain can induce a polar instability , analogous to the behavior of srtio@xmath0 . the relatively low symmetry of the @xmath1 structure requires careful attention in imposing the epitaxial constraints , and introduces new features into the strain - induced ferroelectric state . we performed density functional theory total - energy calculations within the lda approximation using the vasp code @xcite with its supplied paw potentials @xcite . the plane - wave energy cutoff was 680 ev and the k - point grid was @xmath14 . for the study of the effects of epitaxial strain , we carried out strained bulk " calculations , in which total - energy calculations are performed for the periodic crystal with appropriate epitaxial constraints imposed on the lattice parameters . in some cases , these are constraints which can not be automatically imposed within the available vasp relaxation algorithms . in such cases , we developed an elastic energy expansion around the lowest energy @xmath1 structure that satisfies the epitaxial constraint by fitting to the energies of structures with small changes in strain ( the latter structures not necessarily satisfying the epitaxial constraints ) . this elastic energy is then minimized with respect to strain subject to the epitaxial strain constraint ; the resulting lattice parameters are then fixed in a total - energy calculation in which the internal structural parameters are relaxed . all structures were relaxed until the forces on the atoms were less than @xmath15 mev / . for selected structures , we compute the stability against zone - center modes by performing frozen phonon calculations in which single atoms are displaced by approximately @xmath16 . from finite differences of the resulting forces , the force constant matrices are determined and subsequently diagonalized to obtain eigenfrequencies and eigenvectors . our results for the structure of the bulk orthorhombic ground state are given in table [ wyckoff ] . the structure has an energy 410 mev / f.u . lower than the ideal cubic perovskite structure . consistent with previous first - principles calculations @xcite , we find good agreement between the computed structure and experiment , taking into account that in the local density approximation lattice constants typically tend to be underestimated by about one percent . .[wyckoff ] the wyckoff parameters of the @xmath1 ground state and the @xmath4-@xmath3 structure at 3% tensile strain . [ cols=">,^,^,^",options="header " , ] next , we investigate the effects of epitaxial strain on the @xmath1 phase . as in ref . , we designate the strained phases as @xmath3 , where the prefix @xmath17 denotes `` epitaxial . '' we consider epitaxial strain on a square lattice substrate , corresponding to a ( 001 ) perovskite surface . to allow direct comparison with experiment despite the lattice constant underestimate discussed above , we define epitaxial strain relative to @xmath18 = 3.77 , which is the cube root of the computed volume per formula unit of the relaxed @xmath1 structure . in the @xmath1 structure , there are two symmetry - inequivalent primitive perovskite ( 001 ) planes , as shown in fig . [ epbnm ] . thus , there are two distinct orientations for an epitaxial film : the first , with @xmath19 in the matching plane and @xmath20 and @xmath21 out of the plane ( @xmath2-@xmath3 , figure [ epbnm ] ( a ) ) , and the second , with @xmath19 normal to the matching plane ( @xmath4-@xmath3 , fig . [ epbnm](b ) ) . we compute the total energies for these two orientations for epitaxial strains ranging from @xmath221.5% to 4% @xcite . for @xmath4-@xmath3 , the @xmath4 lattice parameter and internal structural parameters are relaxed at each strain , maintaining the @xmath1 symmetry ; the @xmath9 and @xmath10 lattice parameters are fixed by the constraint . the epitaxial constraint allows for @xmath19 not to be normal to the matching @xmath2-plane and tilting @xmath19 could lower the energy . however , an elastic analysis for the @xmath221.5% and 4% cases showed that tilting @xmath19 does not lower the energy and we assumed this to be true for the intermediate strains as well . @xmath2-@xmath3 has lower symmetry than @xmath4-@xmath3 ; that is , distinguishing one of the two ( 110 ) planes removes space group symmetries , resulting in a space group @xmath23 ; the constraint fixes @xmath24 and @xmath25 , as well as the condition @xmath26 = 0 . to optimize the lattice parameters for this case , we use the elastic energy expansion method described in the previous section . the results are shown in fig . [ totalenergy ] . @xmath2-@xmath3 is favorable for compressive strains and @xmath4-@xmath3 is favored with increasing tensile strains . within this subspace of nonpolar structures , there is an epitaxial orientation transition at 1.5% . the two distinct relative orientations of the lattice vectors and the primitive perovskite substrate matching planes in the @xmath1 structure are shown for ( a ) the @xmath2-@xmath3 phase and ( b ) the @xmath4-@xmath3 phase . ] total energy per five - atom formula unit for various epitaxially constrained structures as a function of misfit strain . at each strain , the energy of the @xmath4-@xmath3 structure is taken as the zero of energy . the connecting lines are a guide to the eye . ] next , we turn to the stability of the @xmath3 phases against symmetry - breaking distortions , with special attention to polar phonons . previous computation of the phonon frequencies for the bulk equilibrium structure showed three low - frequency polar phonons at 94 @xmath27 , 88 @xmath27 and 89 @xmath27 , with induced polarizations along @xmath9 , @xmath10 and @xmath4 , respectively @xcite . these phonons are expected to be sensitive to changes in strain , based on known polarization - strain coupling in calcium titanate @xcite . we first consider @xmath4-@xmath1 with 4% tensile strain , with computed structural parameters reported in table 1 . a zone - center frozen phonon computation for this structure showed four unstable phonons , the lowest two , at 213i @xmath27 and 209i @xmath27 , being polar and generating structures with space groups @xmath28 ( polarization along @xmath9 ) and @xmath29 ( polarization along @xmath10 ) , respectively . in both cases , the orientation of polarization with respect to the primitive perovskite axes is along the @xmath5110@xmath6 directions . the energies of the structures for these two space groups , optimized under the epitaxial strain constraint , are 35 mev / f.u . and 28 mev / f.u . below @xmath4-@xmath1 , respectively , with polarizations 0.46 c / m@xmath30 and 0.45 c / m@xmath30 computed using born effective charges and atomic displacements @xcite . thus , at 4% tensile strain , we predict strain - induced ferroelectricity in catio@xmath0 . for the full range of strains , the unconstrained internal structural parameters were optimized within these two polar space groups . only in the 4% case was @xmath24 re - optimized for the polar structures ; this only had a marginal effect on the energy and the polarization compared to when the relaxed value for the @xmath4-@xmath3 structure was used , presumably because the polarizations are in the @xmath2-plane . at compressive strain , the nonpolar @xmath4-@xmath3 structure is stable against polar distortions , and no ferroelectricity is observed . for tensile strain , the ferroelectric instabilities first appear at 2% strain , and the energy gain and polarization of the optimized ferroelectric phases grow with increasing strain . let us now consider @xmath2-@xmath3 with 4% tensile strain . we looked for polar instabilities in this structure by displacing atoms in such a way that the resulting , lowered symmetry allowed for nonzero polarization , and then relaxing the internal structural parameters while keeping the lattice parameters fixed at their @xmath2-@xmath3 values . this procedure revealed two structures with polarizations in the matching plane of 0.33 c / m@xmath30 along @xmath4 ( space group @xmath31 ) and 0.40 c / m@xmath30 along the @xmath2 diagonal ( space group @xmath32 ) , respectively . ( the polarizations were obtained using born effective charges and atomic positions @xcite . ) the former is the lowest in energy but still above @xmath28 and @xmath29 , see fig . [ totalenergy ] . this procedure was also carried out for epitaxial strains of 3% and @xmath221.5% . no polar phase was found in the latter case . the mechanism of strain - induced ferroelectricity in the @xmath1 phase is closely related to that for srtio@xmath0 , which similarly has a high strain sensitivity of the low - frequency polar mode . however , the effect in srtio@xmath0 is equally strong for compressive as for tensile strain , as elongation of the unit cell produced by compressive strain destabilizes the polar mode as effectively as elongation in the in - plane direction for tensile strain . this is a direct consequence of the fact that srtio@xmath0 is cubic in the paraelectric phase ; the cubic - tetragonal transition being at low temperatures and the rotational distortion not being strong enough to inhibit the strain - enhanced polar instability . in catio@xmath0 , in contrast , the rotational instabilities are much stronger and the resulting distortions are much larger . no ferroelectric @xmath3 phase was found for compressive strain , despite elongation of the unit cell along the direction normal to the surface ; this presumably is due to inhibition by the pattern of octahedral rotations . this highlights the idea that in a nonpolar low - symmetry phase , unlike in a cubic phase , the relationship between the crystal axes and the epitaxial constraints is very important , different choices yielding quite distinct structures and coupling to potential instabilities . to investigate the relative importance of enhancing the polar instability compared to suppressing the rotational instabilities , we analyzed the structural parameters of the @xmath4-@xmath3 phase as a function of epitaxial strain . the amplitudes of the m@xmath7 and r@xmath8 modes change surprisingly little in the range of strains reported here , suggesting that the dominant mechanism of the strain - induced ferroelectricity is the strain enhancement of the polar instability . epitaxial strain in the @xmath1 is not the only possible avenue to a ferroelectric phase . another promising approach is to replace the rotational pattern in the @xmath1 structure with a different pattern which allows the gain associated with the octahedral rotation instability but which is less inhibitory to the polar modes ; this will be discussed in a separate publication @xcite . in comparing these predictions with experiments on epitaxial strained catio@xmath0 , it is important to keep in mind that our approach considers only the effect of strain on the ground state structure and properties . in a real thin film , especially the ultrathin films needed to sustain very high strains , other factors can affect the observed phase , including temperature , the atomic arrangements at the substrate and the film - substrate interface , relaxation , reconstruction , and adsorption at the free surface , and defects and impurities in the film itself . however , the tendency to ferroelectricity with increasing tensile strain is clear in our results , and to the extent that these other factors do not act dominantly against it , we expect ferroelectricity in catio@xmath0 to be observed at experimentally accessible strains . investigations are currently in progress @xcite . in summary , we have performed first - principles calculations for epitaxially strained structures of catio@xmath0 . at 1.5% strain , we find an epitaxial orientation transition between the @xmath2-@xmath3 phase , favored for compressive strains , and the @xmath4-@xmath3 phase , favored for tensile strains . for sufficiently large tensile strains , a polar instability , which was hidden in the equilibrium bulk structure , develops in both phases . the epitaxial - strain - induced ferroelectric phase lowest in energy originates in the @xmath4-@xmath3 phase and has the polarization along a @xmath5110@xmath6 direction with respect to the primitive perovskite lattice vectors of the square substrate .

numerical studies of accretion discs have been mostly restricted to 2d cases , due to computing time limitations . among many things , these 2d simulations have shown that spiral shocks appear in inviscid discs ( e.g. sawada et al . recently some 3d simulations have been carried out ( see yukawa , boffin & matsuda , 1997 for an uncomplete list ) , mostly using particles methods . these simulations were apparently unable to generate spiral shocks in the accretion disc , but this could be related to the fact that they used either an isothermal or pseudo - isothermal equation of state , either neglected pressure effects or used too low resolution . we have run three - dimensional smoothed particle hydrodynamics ( sph ; see e.g. monaghan 1992 for a review ) simulations with a polytropic equation of state . this method includes self - consistently the effect of pressure forces and we checked that we could always resolve the disc in the vertical dimension . concerning this last point , we therefore used a variable smoothing length ( which , in sph , decides the resolution ) and checked that at each point in space , the smoothing length , @xmath0 , was smaller than the disc scale height , @xmath1 . details of the method and of some of the results can be found in yukawa et al . in figure [ bhm : slice2 ] , we show the flow at the end ( i.e. two orbital periods ) of our simulation with mass inflow when we use a polytropic index , @xmath2=1.2 . as can be seen , a spiral structure is clearly present , confirming the fact that sph is able to tracks these structures but , more importantly , that these structures are present in 3d accretion flows . this result also confirms that a disc does form in 3d , even for such a large value of the polytropic index . moreover , the disc is in hydrostatic balance , as its disc height is precisely equal to the value expected : @xmath3 , where @xmath4 is the sound speed and @xmath5 is the angular velocity . because , we use a rather large sound speed as initial condition ( 0.1 , where the orbital velocity corresponds to 1.0 ) and a large polytropic index , the disc we obtain is rather hot , hence rather thick ( @xmath6 ) . for the smaller value of @xmath2 used , 1.1 and 1.01 , we obtain smaller disc heights : 0.12 to 0.2 and 0.09 , respectively . in both cases , the hydrostatic balance in the vertical direction holds true . and in all cases , the ratio between the local vertical disc height ( i.e. the disc semi - thickness ) and the local smoothing length lies between about 2 and 6 . thus , we have certainly resolved the disc vertically . just a note in passing concerning the viscosity present in our code . we use the standard artificial viscosity of sph which , as shown e.g. by murray ( 1996 ) , has an equivalent shear viscosity , @xmath7 . in term of the shakura - sunyaev @xmath8-viscosity , @xmath9 , this can be rewritten , @xmath10 with the value of @xmath11 used , we therefore have an equivalent @xmath9 of 0.02 to 0.05 . + it has to be noted that we can not claim to have obtained a true steady state as the mass in the disc is still increasing at the end of the simulations . two - dimensional simulations ( boffin et al . , in preparation ) show us that several tens of orbital periods are necesary to reach a steady state . however , in our 3d simulations , we can see that the structure of the flow does not change after , say , one orbital period . we therefore believe that we have reached a `` quasi - steady state '' and can study the final structure of the flow . we can not , however , make any definite claims about the mass accretion rate . from figure [ bhm : slice2 ] , we also observe that we do not have a true `` hot spot '' but more a kind of `` hot line '' . this is , we believe , again due to the large initial sound speed , resulting in a very wide inner lagrangian stream . in figure [ bhm : slice ] , we show the same as in figure [ bhm : slice2 ] , except that we have divided the particles following their height above the orbital plane . this can be used to study the possible variation of the disc height with the orbital phase as obtained by hirose et al . we do not seem to find any conclusive variations , however . also , we can not observe any stream overflow in the z - direction as obtained by armitage & livio ( 1996 ) . the reason for this discrepancy is unclear and we are presently working on this . possible reasons are : their use of a large viscosity , their initial conditions , our large initial sound speed , ... we have also performed several simulations without any mass inflow . in this case , a disc is initially set - up around the primary , so that it is resolved vertically and in hydrostatic balance . it is then evolved with the full potential of the binary system taken into account . here again , as shown in figure [ bhm : comp ] , which is a greyscale map of the asymmetric component of the density , spiral shocks can clearly be seen , both in the @xmath2=1.2 and @xmath2=1.01 cases . thus , these spiral shocks are not the result of the inner lagrangian flow . this is not a surprise if , as believed , the spiral structures are due to the tidal force of the companion ( _ e.g. _ savonije et al . 1994 ) . figure [ bhm : comp ] also shows the importance of resolution : although with 9,000 particles we can not find any severe difference between @xmath2=1.2 and 1.01 , this is no more true with 30,000 particles . for @xmath2=1.01 indeed , in the inner part of the disc , the spirals become more tightly wound , a result well known in 2d ( _ e.g. _ sawada et al . the reason for this difference may lie in the fact that for the @xmath2=1.2 case , the mach number of the flow always remains smaller than 10 , while for the @xmath2=1.01 case , it starts at a little below 10 in the outer part of the disc to reach above 30 in the inner part . it was already shown by , _ e.g. _ , savonije et al . ( 1994 ) that the higher the mach number , the more tightly wound the spiral . what is noticeable in our 3d simulations , is the fact that we can not make any clear distinction between a cooler disc ( @xmath2=1.01 ) and a hotter disc ( @xmath2=1.2 ) when we restrict ourselves to the outer parts of the disc . if confirmed , this result may be useful to reproduce the observations of spiral shocks in ip peg ( steeghs et al . 1997 ) even when we deal with the cool disc typical of a dwarf nova . 1 . armitage p.j . , livio m. 1996 , apj 470 , 1024 2 . hirose m. , osaki y. , mineshige s. 1991 , pasj 43 , 809 3 . monaghan j.j . 1992 , ann.rev.astr.astrophys . 30 , 543 4 . murray j.r . 1996 , mnras 279 , 402 5 . savonije g.j . , papaloizou j.c.b . , lin d.n.c . 1994 , mnras 268 , 13 6 . sawada k. , matsuda t. , inoue m. , hachisu i. 1987 , mnras 224 , 307 7 . steeghs d. , harlaftis e.t . , horne k. 1997 , mnras 290 , l28 8 . yukawa h. , boffin h.m.j . , matsuda t. 1997 , mnras 282 , 321

we discuss some 3d numerical simulations of accretion discs using the sph method and a polytropic equation of state . we show that discs exist even for as large value of the polytropic index as 1.2 , and that these discs are always in hydrostatic balance . we also show that even without any inflow , spiral shocks appear in the discs .

creep is a major limitation of concrete . indeed , it has been suggested that creep deformations are logarithmic , that is , virtually infinite and without asymptotic bound , which raises safety issues @xcite . the creep of concrete is generally thought to be mainly caused by the viscoelastic and viscoplastic behavior of the cement hydrates @xcite . while secondary cementitious phases can show viscoelastic behavior @xcite , the rate and extent of viscoelastic deformations of such phases is far less significant than that calcium silicate hydrate ( c s h ) , the binding phase of the cement paste @xcite . as such , understanding the physical mechanism of the creep of c s h is of primary importance . despite the prevalence of concrete in the built environment , the molecular structure of c s h has just recently been proposed @xcite , which makes it possible to investigate its mechanical properties at the atomic scale . here , relying on the newly available model , we present a new methodology allowing us to simulate the long - term creep deformation of bulk c s h ( at zero porosity , i.e. , at the scale of the grains ) . results show an excellent agreement with nanoindentation measurements @xcite . to describe the disordered molecular structure of c s h , pellenq et al . @xcite proposed a realistic model for c s h with the stoichiometry of ( cao)@xmath0(sio@xmath1)(h@xmath1o)@xmath2 . we generated the c s h model by introducing defects in an 11 tobermorite @xcite configuration , following a combinatorial procedure . whereas the ca / si ratio in 11 tobermorite is 1 , this ratio is increased to 1.71 in the present c s h model , through randomly introducing defects in the silicate chains , which provides sites for adsorption of extra water molecules . the reaxff potential @xcite , a reactive potential , was then used to account for the reaction of the interlayer water with the defective calcium silicate sheets . more details on the preparation of the model and its experimental validation can be found in ref . @xcite and in previous works @xcite . we simulated the previously presented c s h model , made of 501 atoms , by molecular dynamics ( md ) using the lammps package @xcite . to this end , we used the reaxff potential @xcite with a time step of 0.25fs . prior to the application of any stress , the system is fully relaxed to zero pressure at 300k . shear strain and potential energy with respect to the number of loading / unloading cycles . the inset shows the shape of the applied shear stress . ] the relaxation of c s h , or of other silicate materials , takes place over long periods of time ( years ) , which prevents the use of traditional md simulations , which are limited to a few nanoseconds . to study the long - term deformations of c s h , we applied a method that has recently been introduced to study the relaxation of silicate glasses @xcite . in this method , starting from an initial atomic configuration of glass , formed by rapid cooling from the liquid state , the system is subjected to small , cyclic perturbations of shear stress @xmath3 around zero pressure . for each stress , a minimization of the energy is performed , with the system having the ability to deform ( shape and volume ) in order to reach the target stress . these small perturbations of stress deform the energy landscape of the glass , allowing the system to jump over energy barriers . note that the observed relaxation does not depend on the choice of @xmath4 , provided that this stress remains sub - yield @xcite . this method mimics the artificial aging observed in granular materials subjected to vibrations @xcite . here , in order to study creep deformation , we add to the previous method a constant shear stress @xmath5 , such that @xmath6 ( see the inset of figure [ fig : method ] ) . when subjected to shear stresses of different intensities , c s h presents a shear strain @xmath7 that : ( 1 ) increases logarithmically with the number of cycles @xmath8 ( figure [ fig : method ] ) and ( 2 ) is proportional to the applied shear stress ( see figure [ fig : strain ] ) . shear strain with respect to the number of loading / unloading cycles , under a constant shear stress of 1 , 2 , and 3 gpa . the inset shows the creep modulus @xmath9 with respect to the packing fraction @xmath10 obtained from nanoindentation @xcite , compared with the computed value at @xmath11 . ] the creep of bulk c s h can then be described by a simple logarithmic law @xmath12 , where @xmath13 is a constant analogous to a relaxation time and @xmath9 is the creep modulus . a careful look at the internal energy shows that the height of the energy barriers , through which the system transits across each cycle , remains roughly constant over successive cycles . according to transition state theory , which states that the time needed for a system to jump over an energy barrier @xmath14 is proportional to @xmath15 , we can assume that each cycle corresponds to a constant duration @xmath16 , so that a fictitious time can be defined as @xmath17 @xcite . we note that the computed creep moduli @xmath9 does not show any significant change with respect to the applied stress @xmath5 . as such , it appears to be a material property that can directly been compared to nanoindentation results extrapolated to zero porosity @xcite . as shown in the inset of figure [ fig : strain ] , we observe an excellent agreement , which suggests that the present method offers a realistic description of the creep of c s h at the atomic scale . this result also suggests that , within the linear regime ( i.e. , for sub - yield stresses , when @xmath9 remain constant ) , deformations due to cyclic creep and basic creep , with respect to the number of stress cycle or the elapsed time , respectively , should be equivalent . we reported a new methodology based on atomistic simulation , allowing us to successfully observe long - term creep deformations of c s h . creep deformations are found to be logarithmic and proportional to the applied shear stress . the computed creep modulus shows an excellent agreement with nanoindentation data , which suggests that the present methodology could be used as a predictive tool to study the creep deformations of alternative binders . mb acknowledges partial financial support for this research provisioned by the university of california , los angeles ( ucla ) . this work was also supported by schlumberger under an mit - schlumberger research collaboration and by the cshub at mit . this work has been partially carried out within the framework of the icome2 labex ( anr-11-labx-0053 ) and the a*midex projects ( anr-11-idex-0001 - 02 ) cofunded by the french program `` investissements davenir '' which is managed by the anr , the french national research agency .

understanding the physical origin of creep in calcium silicate hydrate ( c s h ) is of primary importance , both for fundamental and practical interest . here , we present a new method , based on molecular dynamics simulation , allowing us to simulate the long - term visco - elastic deformations of c s h . under a given shear stress , c s h features a gradually increasing shear strain , which follows a logarithmic law . the computed creep modulus is found to be independent of the shear stress applied and is in excellent agreement with nanoindentation measurements , as extrapolated to zero porosity .

we thank carlos wagner and james white for helpful discussions . the work of j. l. has been supported in part by doe grant de - fg05 - 93-er-40717 , and that of d.v.n . has been supported in part by doe grant de - fg05 - 91-er-40633 . 99 j. ellis , g.l . fogli , and e. lisi , cern - th/95 - 202 ( ) , and references therein . p. renton , rapporteur talk at the international symposium on lepton and photon interactions at high energies , high energy physics , beijing ( august 1995 ) , oxford preprint ounp-95 - 20 ( 1995 ) . g. altarelli and r. barbieri , ; m. boulware , d. finnel , ; a. djouadi , g. girardi , c. vergzegnassi , w. hollik and f. renard , ; g. altarelli , r. barbieri , and s. jadach , ; g. altarelli , r. barbieri , and f. caravaglios , ; g. altarelli , r. barbieri , and f. caravaglios , . j. d. wells , c. kolda , and g. l. kane , . d. garcia , r. jimenez , and j. sola , ; d. garcia and j. sola , . x. wang , , and , . g. kane , r. stuart , and j. wells , ; e. ma and d. ng , ; y. yamada , k. hagiwara , and s. matsumoto , . l. rolandi , h. dijkstra , d. strickland and g. wilson , representing the aleph , delphi , l3 and opal collaborations , joint seminar on the first results from lep 1.5 , cern , dec . 12th , 1995 . a. akhundov , d. bardin , and t. riemann , ; j. bernabeu , a. pich , and a. santamaria , ; w. beenaker and w. hollik , z. phys . c40 , 141(1988 ) ; f. boudjema , a. djouadi , and c. verzegnassi , ; a. blondel and c. verzegnassi , . j. wells and g. kane , . m. acciarri , ( l3 collaboration ) , . see , , d. decamp , ( aleph collaboration ) , phys . reports * 216 * ( 1992 ) 253 . y. okada , m. yamaguchi , and t. yanagida , prog . * 85 * ( 1991 ) 1 and ; j. ellis , g. ridolfi , and f. zwirner , and ; h. haber and r. hempfling , . and , . m. diaz and h. haber , ; r. hempfling and a. hoang , ; m. carena , j. espinosa , m. quiros , and c. wagner , ; m. carena , m. quiros , and c. wagner , . t.e . browder and k. henscheid , university of hawaii and ohio state university preprint , uh 511 - 816 - 95 and ohstpy - hep - e-95 - 010 ( 1995 ) , to appear in _ progress in nuclear and particle physics _ , 35 . j. incandela ( cdf collaboration ) , fermilab - conf-95 - 237-e ( july 1995 ) . s. mrenna and c .- p . s. abachi , ( d0 collaboration ) , search for light top squarks in @xmath86 collisions at @xmath87 " , december 1995 ( submitted to phys . j. ellis , j.s . hagelin , d.v . nanopoulos , k.a . olive and m. srednicki , . j. feng , n. polonsky , and s. thomas , . chen , m. drees , and j. gunion , . s. abachi , ( d0 collaboration ) , hep - ex/9512004 . , , x. wang , and a. zichichi , and . see , p. langacker and n. polonsky , .

we re - examine the possible magnitude of the supersymmetric contribution to @xmath0 in the light of the constraints imposed by the absence of light charginos at lep 1.5 , implementing also other available phenomenological constraints . we find the supersymmetric contribution to be @xmath1 , and discuss the extent to which this upper bound could be strengthened by future constraints on the chargino and top - squark masses . such values of @xmath2 tend to disfavor a supersymmetry explanation of the apparent @xmath3 discrepancy . = 11 # 1#2 # 1#1| # 1| # 1 # 1#1 # 1#1 versim#1#2 # 1@xmath4 # 1@xmath5 11 # 1#2#3nucl . phys . b * # 1 * ( 19#2 ) # 3 # 1#2#3phys . lett . b * # 1 * ( 19#2 ) # 3 # 1#2#3b * # 1 * ( 19#2 ) # 3 # 1#2#3phys . rev . d * # 1 * ( 19#2 ) # 3 # 1#2#3phys . rev . lett . * # 1 * ( 19#2 ) # 3 # 1#2#3phys . rep . * # 1 * ( 19#2 ) # 3 # 1#2#3mod . phys . lett . a * # 1 * ( 19#2 ) # 3 # 1#2#3int . j. mod . phys . a * # 1 * ( 19#2 ) # 3 # 1ctp - tamu-#1 # 1hep - ph/#1 # 1hep - th/#1 6.0 in 8.5 in -0.25truein 0.30truein 0.30truein cern - th/95 - 314 + doe / er/4071722 + ctp - tamu-46/95 + act-17/95 + hep - ph/9512288 0.75 cm john ellis,@xmath6 jorge l. lopez,@xmath7 and d.v . nanopoulos@xmath8 + 0.5 cm @xmath6cern theory division , 1211 geneva 23 , switzerland + @xmath7department of physics , bonner nuclear lab , rice university + 6100 main street , houston , tx 77005 , usa + @xmath9center for theoretical physics , department of physics , texas a&m university + college station , tx 778434242 , usa + @xmath10astroparticle physics group , houston advanced research center ( harc ) + the mitchell campus , the woodlands , tx 77381 , usa + 0.5 cm cern - th/95 - 314 + doe / er/4071722 + ctp - tamu-46/95 + act-17/95 + december 1995 lep 1 has , unfortunately , provided a showcase for the standard model , which has been tested successfully down to the _ per mille _ level . the measurements have proved to be sensitive to quantum corrections within the standard model , which have enabled the mass of the top quark to be predicted accurately , and may now be sensitive to the mass of the higgs boson @xcite . the only possible blots on the standard model s copybook have been suggested by the lep measurements of @xmath11 decays into @xmath12 and @xmath13 . the preliminary measurements of @xmath14 reported at the brussels and beijing conferences @xcite disagree _ prima facie _ with the standard model at the levels of 3.7 and 2.5 standard deviations , respectively . even if @xmath15 is fixed to its standard model value , at a considerable cost in @xmath16 , the lep 1 measurement of @xmath3 still disagrees with the standard model at the level of 3 standard deviations . it may well be that the apparent discrepancy is in fact due to a misestimation of the uncertainties associated with the simulation of the @xmath12 and @xmath13 final states , but it has been seductive to speculate that some new physics beyond the standard model may be coming into play . one such speculation has been supersymmetry @xcite , and two specific scenarios to explain the @xmath3 discrepancy ( but not the @xmath15 one ) have been proposed . one has invoked a light chargino @xmath17 and a light top - squark @xmath18 close to the kinematic limits already excluded by new particle searches at lep 1 @xcite , and the other a light pseudoscalar higgs boson @xmath19 @xcite . these have inspired the hope in some quarters that one or more of these supersymmetric particles might be produced at lep 2 , and conceivably already in the intermediate - energy lep 1.5 run recently completed . it should be pointed out , though , that it is has proved difficult in specific models to obtain a supersymmetric contribution to @xmath3 large enough to remove the apparent discrepancy , once one applies plausible phenomenological or theoretical constraints @xcite . preliminary results of the first part of the lep 1.5 run have now been announced by the four lep collaborations , and , to paraphrase sherlock holmes , the curious incident was that the dog did nothing " . specifically , all the four lep collaborations have reported preliminary lower limits on the mass of the lighter chargino @xcite : @xmath20 if @xmath21 ( with some dependence on the sneutrino mass ) , where the @xmath22 is the lightest neutralino , which is assumed to be the lightest supersymmetric particle ( lsp ) . many people are aware that this news is particularly disappointing for advocates of the light ( @xmath23 ) interpretation of the @xmath3 anomaly . the purpose of this note is to quantify the upper limit on the possible supersymmetric contribution to @xmath3 in the light of this preliminary lep 1.5 result , as well as recent d0 constraints on the @xmath18 mass and updates of other experimental constraints on possible sparticle masses , limits on possible new physics effects in @xmath24 and @xmath25 decay , and the absence of the lightest supersymmetric higgs boson . to set the scene for our study , we first recall that the standard model contribution to @xmath3 ( for @xmath26 ) is @xmath27 @xcite , whereas the reported experimental value ( with @xmath15 constrained to the standard model value ) is @xmath28 @xcite . this means that a value of @xmath29 would bring the supersymmetric @xmath3 prediction within the 95% c.l . interval , whilst a contribution @xmath30 would bring the prediction within one sigma of the experimental value . in this note we consider the supersymmetric contributions to @xmath3 in the regime of light chargino and top - squark masses and small values of @xmath31 , where they may be enhanced @xcite . enhancements to @xmath32 may also occur for small values of the pseudoscalar higgs mass ( @xmath33 ) and large values of @xmath31 @xcite , but this scenario now appears to be disfavored @xcite , and we do not consider it in what follows . the dominant contribution ) to be large , so as to minimize the contribution to @xmath34 from the @xmath35 loop , which is always negative . this means that our results are conservative upper bounds . ] to @xmath34 then depends on six parameters : those that parametrize the chargino sector ( @xmath36 ) , the top - squark masses ( @xmath37 ) , and their mixing angle ( @xmath38 ) . we work in the context of the general minimal supersymmetric standard model ( mssm ) , without assuming _ a priori _ any relationship among these parameters that might result from unification conditions or dynamical models . following ref . @xcite , we first sample a large number of six - plet choices of parameters , with those parameters that have the dimension of mass allowed to take random values in the interval @xmath39 , and with @xmath31 restricted to the range @xmath40 . the total sample of approximately 365k six - plets is restricted in such a way that the most elementary lep 1 lower bounds ( @xmath41 ) are satisfied . we then find a total of 1000 six - plets that yield @xmath29 . to examine in more detail the region of low values of @xmath31 , we have also generated and studied a low-@xmath31 " sample ( 91k six - plets ) , for which @xmath31 is restricted to the range @xmath42 . in order to determine the upper bound on @xmath34 , we apply a series of experimental constraints to our large six - plet sample , as follows : 1 . the invisible @xmath43 width should be less than 3.9 mev , as can be inferred from the most recent lep result @xmath44 mev @xcite . 2 . the branching ratio @xmath45 should not exceed @xmath46 @xcite . 3 . the more restrictive lep 1 lower limit on the chargino mass : @xmath47 , valid for @xmath48 and for the higgsino - like chargino @xcite required for an enhancement in @xmath34 . 4 . the lightest higgs boson should be heavier than the lep 1 limit ( @xmath49 ) . the mass of this higgs boson acquires a large quantum correction at the one - loop level , which is dominated by the top top - squark loop @xcite . casting the one - loop correction in terms of the observable top - squark parameters ( @xmath50 ) alone , one obtains @xcite @xmath51\biggr\}\nonumber\end{aligned}\ ] ] with @xmath52 and @xmath53 [ @xmath54 , @xmath55 . other one - loop corrections and the largest of the two - loop corrections are not expected to be large @xcite , and are probably no larger than uncertainties in the approximations used , so we do not incorporate them . 5 . the branching ratio @xmath56 should fall in the range @xmath57 . this interval is a conservative interpretation of the latest cleo result @xmath58 @xcite , which should cover the theoretical uncertainties in the calculation of @xmath56 , principally due to higher - order perturbative qcd corrections in the standard model contribution . 6 . the branching ratio @xmath59 has been determined by cdf to be @xmath60 @xcite . we therefore require @xmath61 , where new " includes in our case the @xmath62 decay channels , when kinematically allowed . more restrictive upper limits on @xmath63 have been considered elsewhere @xcite . 7 . the d0 collaboration has included a region in the @xmath64 space , assuming that @xmath65 @xcite . these restrictions insure that the dominant @xmath18 decay mode is via the one - loop process @xmath66 . 8 . the new lep 1.5 lower limit on the chargino mass @xmath67 , valid as long as @xmath68 @xcite . a more precise formulation of the limit must await the publication of their results by the lep collaborations : it depends on the sneutrino mass and on the wino / higgsino content of the chargino . it seems to us that the above limit is conservative , applying when the sneutrino is heavy , or when the chargino is higgsino - like , which is the case of relevance for obtaining a large value of @xmath34 . we also discuss later the effect of decreasing the restriction on the chargino - neutralino mass difference to about 5 gev , as might be achieved in the final analysis . motivated by the requirement that any stable supersymmetric relic particle should be electromagnetically neutral and have no strong interactions @xcite , we also require that neither the lightest top - squark nor the lightest chargino should be the lightest supersymmetric particle , , @xmath69 . after running our large sample of six - plets through the above set of experimental and theoretical constraints , we find that no points with @xmath70 survive . the main reason for this result is the new lep 1.5 constraint on the chargino mass . this could have been anticipated , as refs . @xcite , which did not have access to the new data , found regions of parameter space with @xmath70 , even after enforcing most of the constraints enumerated above . we conclude that a supersymmetric solution to the @xmath3 anomaly is less likely in the light of lep 1.5 . this conclusion holds for both our regular " sample and our low-@xmath31 " sample . moreover , these results rely only on the present lep 1.5 result , with the chargino - neutralino mass difference required to be more than 10 gev , and are in fact independent of the constraint on the higgs - boson mass ( item 4 above ) . we should add that our full sample contains a small fraction of points with very low values of the neutralino masses ( few gev ) , which manage to pass all lep 1 constraints ( see also @xcite ) and are not subjected to the known limits on the gluino mass as we do not impose the gut relation among gaugino masses . these points are , however , all excluded by either the @xmath56 constraint ( item 5 ) or the lep 1.5 constraint ( item 8) . next we look for the largest achievable values of @xmath34 . in fig . [ fig : rbmax ] , we show @xmath71 as a function of the lightest chargino mass ( @xmath72 ) , for both signs of @xmath73 . the top curves ( none " ) give the raw results obtained from the full sample of parameter six - plets , whereas the ( solid ) bottom curves ( all " ) give the limiting values when _ all _ the above constraints are applied , in which case we find the absolute upper limit @xmath74 of particular importance in excluding values of @xmath75 is the higgs mass constraint ( item 4 above ) . as has already been mentioned , this constraint is worthy of further theoretical refinement , and may soon be strengthened by lep itself . the effect of not enforcing this constraint is represented by the dashed lines in fig . [ fig : rbmax ] . note that this constraint is superseded by the lep 1.5 constraint for @xmath76 . we also display as dotted lines the further restriction that may be obtained should the lep 1.5 be strengthened to exclude chargino - neutralino mass differences down to about 5 gev , assuming that the lower bound on the chargino mass remains at 65 gev . we note that if it were possible to obtain an absolute lower bound of 65 gev on the chargino mass , then only values of @xmath77 would be possible . future runs at lep 2 energies should be able to probe chargino masses as large as 90 gev , which would imply @xmath78 , should no chargino signal be observed . the tevatron should also be able to constrain @xmath71 by setting lower limits on the chargino mass . indeed , d0 has just released its first limits on chargino - neutralino production and decay into trilepton final states @xcite . the limits are on the trilepton rates , , @xmath79 , which can be translated into limits on the chargino mass once one calculates the trilepton branching ratio . the latter depends on the detailed spectrum of sleptons and squarks ( which we do not consider ) , and may be enhanced if there are light sleptons @xcite , in which case the d0 limits imply @xmath80 @xcite . the possibility of light sleptons will soon be explored at lep , and the d0 sensitivity to trileptons is expected to increase significantly once the full data set is analyzed . with a view to present and future top - squark searches at lep and the tevatron , we have also studied the dependence of @xmath71 on the lightest top - squark mass . this is shown in fig . [ fig : rbmax - stop ] for the none " and all " cases ( with the higgs mass constraint included and allowing a chargino - neutralino mass difference of up to 10 gev ) . direct top - squark searches at the tevatron are underway , but so far have concentrated on top - squark decays via @xmath81 . this decay is dominant as long as @xmath82 . with this restriction , d0 has excluded a region in the @xmath64 plane @xcite . this region is not very constraining for our present purposes , but it is expected that top - squark masses as large as 130 gev could be explored with the data ( @xmath83 ) already accumulated . as fig . [ fig : rbmax - stop ] shows , a lower bound of this magnitude would impose new severe restrictions on the allowed values of @xmath34 . we have also explored the dependence of @xmath71 on @xmath56 and @xmath63 . we find that more stringent experimental limits will decrease further the size of the allowed region in parameter space , but will not necessarily impose important new restrictions on @xmath71 . requiring rather light top - squark masses may entail a degree of fine - tuning in the top - squark mass matrix , such as large values of @xmath84 . in the limit @xmath75 this situation may lead to minima of the electroweak scalar potential that break electric or color charge @xcite . we do not include these constraints in the present analysis , as these would only further constrain the allowed region of parameter space . before concluding , we note that imposing further theoretical constraints on the parameter space , such as those that follow from universal supersymmetry breaking masses at the gut scale and radiative electroweak breaking , tend to reduce @xmath71 very substantially @xcite . consulting fig . 1 in ref . @xcite , one can see that @xmath85 , after the new lep 1.5 limit is imposed . even without imposing such additional theoretical constraints , the central result ( [ absolute ] ) of our analysis suggests that the previously most plausible supersymmetric scenario for accommodating the apparent anomaly in @xmath3 is now so severely constrained that it no longer appears able to resolve this experimental discrepancy with the standard model . in the absence of any other promising explanation from beyond the standard model , it may be necessary to review carefully the calculation and simulation of the standard model contributions to @xmath3 and related measurements . lep 1.5 has done much to clarify the prospects of a supersymmetric resolution of this lep 1 anomaly , and further stages of lep should be able to cement our conclusion .

the data taking at hera , where electrons or positrons of @xmath1 collided with protons of up to @xmath2 , ended in june 2007 . each of the h1 and zeus experiments collected around @xmath3 data from the whole running period 1992 - 2007 . the largest samples are from the second data taking period 2003 - 2007 ( hera-2 ) . in comparison with hera-1 , the integrated luminosity of the @xmath4 and @xmath5 samples has a 2- and 10-fold increase , respectively . in addition , the @xmath6 and @xmath7 beams at hera-2 were longitudinally polarised . these data samples have made possible both the study of rare exclusive electroweak processes with cross section values down to @xmath8 and the search for new physics phenomena . this talk covers eight abstracts submitted to this conference from h1 and zeus on three main topics listed in the abstract . the results presented at the conference are briefly summarised here in the following sections . an excess of multi - lepton events at high @xmath9 at hera was first reported in @xcite by h1 based on hera-1 data . the dominant standard model ( sm ) processes are from the lepton pair production in photon - photon interactions , @xmath10 , where the photons are radiated from incident beam particles . the background contributions are mainly from neutral current deep inelastic scattering ( dis ) and qed compton processes where in addition to genuine electrons , hadrons or radiated photons are misidentified as electrons or muons . beyond the sm , the production of a doubly charged higgs boson @xcite or processes involving generic bosons carrying two units of lepton number ( bi - leptons ) @xcite could lead to multi - leptons events of large invariant mass . the analyses are performed in a model independent way with the following main selection cuts . take h1 @xcite as an example , each event has to have at least two central ( @xmath11 ) electron or muon candidates with the leading lepton @xmath12 , the other lepton @xmath13 and additional electrons in an extended angular region @xmath14 and additional muons in @xmath15 and @xmath16 . h1 has analysed seven topologies in @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 , @xmath22 and @xmath23 . in all the topologies , the observed event yields are found in good agreement with the predicted ones @xcite . however , when the comparison is made for the invariant mass of two highest @xmath9 leptons @xmath24 , excesses are observed in most of the topologies ( table [ table1 ] ) although the number of observed events remains statistically limited . also shown in table [ table1 ] are preliminary results from zeus on di - electron and tri - electron samples @xcite . in both samples no excess has been observed . h1 has also compared the distributions of the scalar sum of the transverse momentum ( @xmath25 ) ( see e.g. fig . [ h1](left ) for the @xmath4 data ) . at @xmath26 , 5 events have been observed in the @xmath4 sample with 0@xmath27 expected . none has been observed in the @xmath5 sample , however , while @xmath28 events are expected . therefore the excess is only shown in the @xmath4 data sample . differential cross sections as a function of the leading transverse momentum @xmath29 for electron and muon pair production are measured by h1 @xcite in a restricted phase space dominated by photon - photon interactions ( @xmath12 , @xmath13 , @xmath11 , the inelasticity variable @xmath30 and the four - momentum transfer squared @xmath31 ) . zeus has released their preliminary results @xcite for this conference in di - muon channel with a slightly different phase space cut ( @xmath32 ) . both h1 and zeus measure steeply falling cross sections in good agreement with the sm expectations . .the number of observed events and sm expectations in different multi - lepton topologies for @xmath24 . the numbers shown in parentheses correspond to the contribution from the dominant pair production in @xmath33 interactions . [ cols="^,^,^,^,^ " , ] previously observed excesses in multi - lepton events at high transverse momenta and isolated lepton events with large missing transverse energy by h1 remain true with the full hera data sample . the largest excess is up to about @xmath34 standard deviations and is however not confirmed by zeus . attempts in combining the h1 and zeus data have started and are being pursued @xcite . as the hera data taking has ended , it is unlikely that a definitive conclusion can be drawn with the combined data . future experiments will eventually tell us whether the excess is a purely statistical fluctuation or a first sign of new physics . 9 h1 collab . , a. aktas _ et al_. , _ eur . j_. c*31 * ( 2003 ) 17 [ hep - ex/0307015 ] . e. accomando and s. petrarca , _ phys . lett_. b*323 * ( 1994 ) 212 [ hep - ph/9401242 ] ; h1 collab . , a. aktas _ et al_. , _ phys . lett_. b*638 * ( 2006 ) 432 [ hep - ex/0604027 ] . f. cuypers and s. davidson , _ eur . j_. c*2 * ( 1998 ) 503 [ hep - ph/9609487 ] . h1 collab . aaron _ et al_. , to appear in _ phys . lett_. b [ arxiv:0806.3987 ( hep - ex ) ] . zeus collab . , `` multi - electron production at hera '' , zeus - prel-07 - 022 . zeus collab . , `` multi - muon search '' , zeus - prel-08 - 006 . h1 collab . , t. ahmed _ et al_. , `` observation of an @xmath35 events with high transverse momenta at hera '' , desy 94 - 248 . h1 collab . , c. adloff _ et al_. , _ eur . j_. c*5 * ( 1998 ) 575 [ hep - ex/9806009 ] , v. andreev _ et al_. , _ phys . lett_. b*561 * ( 2003 ) 241 [ hep - ex/0301030 ] , a. aktas _ et al_. , _ eur . j_. c*48 * ( 2006 ) 699 [ hep - ex/0604022 ] ; zeus collab . , j. breitweg _ et al_. , _ phys . lett_. b*471 * ( 2000 ) 411 [ hep - ex/9907023 ] , s. chekanov _ et al_. , _ phys . lett_. b*559 * ( 2003 ) 153 [ hep - ex/0302010 ] , s. chekanov _ et al_. , _ phys . lett_. b*583 * ( 2003 ) 41 [ hep - ex/0311028 ] . h1 collab . , `` events with an isolated lepton ( electron or muon ) and missing transverse momentum at hera '' , h1prelim-07 - 063 ; `` search for events with isolated tau leptons and missing transverse momentum at hera '' , h1prelim-07 - 064 . zeus collab . , s. chekanov _ et al_. , submitted to _ phys . lett _ .. h1 collab . , a. aktas _ et al_. , _ eur . j_. c*33 * ( 2004 ) 9 [ hep - ex/0310032 ] . h1 collab . , a. aktas _ et al_. , _ phys . lett_. b*599 * ( 2004 ) 159 [ hep - ex/0405070 ] . h1 collab . , `` measurement of @xmath36 production and @xmath36 polarisations at hera '' , h1prelim-07 - 161 . h1-zeus exotics working group : http://www.desy.de/h1zeus/exotics/index.html .

results on multi - lepton events at high transverse momenta , isolated lepton events with large missing transverse energy and single w production reported to this conference are based for the first time on the full data samples taken by two colliding experiments , h1 and zeus , at hera . the data correspond to an integrated luminosity of about @xmath0 from both experiments .

at lattice 2000 we discussed how to include fermionic loops contributions in numerical stochastic perturbation theory for lattice @xmath0 , an algorithm which we will refer to as unspt ( unquenched nspt ) . our main message here is that unquenching nspt results in not such a heavy computational overhead , provided only that an @xmath1 can be implemented in a fairly efficient way . @xmath1 is the main ingredient in constructing the fermion propagator by inverting the dirac kernel order by order . for a discussion of the foundations of unspt we refer the reader to @xcite . [ cols="<,<,<,<,<",options="header " , ] + the need for an efficient @xmath1 is what forced us to wait for apemille : our @xmath1 implementation mimic @xcite , which is based on a @xmath2 plus transpositions , an operation which asks for local addressing on a parallel architecture . unspt has been implemented both in single and in double precision , the former being remarkably robust for applications like wilson loops . to estimate the computational overhead of unquenching nspt one can inspect table [ table:1 ] . we report execution times of a fixed amount of sweeps both for quenched and unquenched nspt . on both columns the growth of computational time is consistent with the the fact that every operation is performed order by order . on each row the growth due to unquenching is roughly consistent with a factor @xmath3 . one then wants to understand the dependence on the volume , which is the critical one , the propagator being the inverse of a matrix : this is exactly the growth which has to be tamed by the @xmath1 . one should compare execution times at a given order on @xmath4 and @xmath5 lattice sizes . note that @xmath4 is simulated on an apemille board ( @xmath6 fpus ) , while @xmath5 on an apemille unit ( @xmath7 fpus ) . by taking this into account one easily understands that @xmath1 is doing its job : the simulation time goes as the volume also for unspt ( a result which is trivial for quenched nspt ) . notice that at this level one has only compared crude execution times : a careful inspection of autocorrelations is anyway not going to jeopardize the picture . as for the dependence on @xmath8 ( number of flavours ) , it is a parametric one : one plugs in various numbers and then proceed to fit the polynomial ( in @xmath8 ) which is fixed by the order of the computation . it is then reassuring to find the quick response to a change in @xmath8 which one can inspect in figure [ fig : nf_change ] ( which is the signal for second order of the plaquette at a given value of the hopping parameter @xmath9 ) . we now proceed to discuss some benchmark computations . a typical one is given by wilson loops . in figure [ fig:5ordplaq ] one can inspect the first five orders . ] of the basic plaquette at a given value of hopping parameter @xmath9 , for which analytic results can be found in @xcite : going even higher in order would be trivial at this stage , but with no mass counterterm ( see later ) . ] . apart for being an easy benchmark , we are interested in wilson loops for two reasons . first of all we are completing the unquenched computation of the lattice heavy quark effective theory residual mass ( see @xcite for the quenched result ) . on top of that we also keep an eye on the issue of whether one can explain in term of renormalons the growth of the coefficients of the plaquette . there is a debate going on about that ( see @xcite ) , the other group involved having also started to make use of nspt . in the renormalon framework the effect of @xmath8 can be easily inferred from the @xmath10-function , eventually resulting in turning the series to oscillating signs . in figure [ fig : mcg2 ] we show the signal for one loop order of the critical mass for wilson fermions ( two loop results are available from @xcite ) . the computation is performed in the way which is the most standard in perturbation theory , _ i.e. _ by inspecting the pole in the propagator at zero momentum . this is already a tough computation . it is a zero mode , an @xmath11 mass - cutoff is needed and the volume extrapolation is not trivial . on top of that one should keep in mind that also gauge fixing is requested . the coefficients which are known analytically can be reproduced . still one would like to change strategy in order to go to higher orders ( which is a prerequisite of all other high order computations ) . the reason is clear : we have actually been measuring the propagator @xmath12 , while the physical information is actually coded in @xmath13 ( one needs to invert the series and huge cancellations are on their way ) . notice anyway that the fact that the critical mass is already known to two - loop makes many interesting computations already feasible . benchmark computations in unspt look promising , since the computational overhead of including fermionic loops contributions is not so huge . this is to be contrasted with the heavy computational effort requested for non perturbative unquenched lattice qcd . this in turn suggests the strategy of going back to perturbation theory for the ( unquenched ) computation of quantities like improvement coefficients and renormalisation constants . the critical mass being already known to two loops , many of these computations are already feasible at @xmath14 order . + we have only discussed the implementation of the algorithm on the apemille architecture . we can also rely on a @xmath15 implementation for pc s ( clusters ) which is now at the final stage of development . 9 f. di renzo , l. scorzato , . t. lippert , k. schilling , f. toschi , s. trentmann , r. tripiccione , . b. alles , a. feo , h. panagopoulos , . f. di renzo , l. scorzato , . see f. di renzo , l. scorzato , and r. horsley , p.e.l . rakow , g. schierholz , . e. follana , h. panagopoulos , ; s. caracciolo , a. pelissetto , a. rago , .

the inclusion of fermionic loops contribution in numerical stochastic perturbation theory ( nspt ) has a nice feature : it does not cost so much ( provided only that an fft can be implemented in a fairly efficient way ) . focusing on lattice @xmath0 , we report on the performance of the current implementation of the algorithm and the status of first computations undertaken .

future galaxy surveys will provide new opportunities to verify the current standard cosmological model , and also to constrain modified gravity theories , invoked to explain the present accelerated expansion of the universe . before studying general parametrizations of dark energy , its however important to understand first which quantities can be really observed . from this direction recently @xcite shown that cosmological measurements can determine , in addition to the expansion rate @xmath8 , only three additional variables @xmath9 , @xmath10 and @xmath11 , given by @xmath12 with @xmath2 is the growth function , @xmath3 is the galaxy bias with respect to the dark matter density contrast , and @xmath13 is the dark matter density contrast today . the functions @xmath14 ( the anisotropic stress @xmath15 ) and @xmath16 ( the clustering of dark energy @xmath17 ) , describe the impact of the dark energy on cosmological perturbations . in @xcite , a fisher analysis was made using galaxy clustering , weak lensing and supernovae probes , in order to find the expected accuracy with which an euclid - like survey can measure the anisotropic stress @xmath14 , in a model - independent way . + in this work we want to obtain some results on the intrinsic degeneracy on galaxy clustering measurements , using the quantities @xmath10 and @xmath9 . we use a flat @xmath18cdm fiducial model , with @xmath19 , @xmath20 , @xmath21 , @xmath22 , @xmath23 , @xmath24 , euclid - like survey specifications are used @xcite : we divided the redshift range @xmath25 $ ] in 5 bins of width @xmath26 and one of width @xmath27 ; a spectroscopic error @xmath28 , and a fraction of sky @xmath29 ; the bias @xmath3 in the fiducial is assumed to be unity . observations of the growth rate @xmath4 from large scale structures using redshift space distortions ( rsd ) , give a direct way to test different dark energy models , @xcite , @xcite , @xcite . let us consider now the galaxy power spectrum in redshift space @xmath30 whit @xmath31 , and we explicitly use @xmath32 . the fisher matrix is in general @xmath33 where @xmath34 , and @xmath35 is the effective volume of the survey @xmath36 @xmath37 being the galaxy number density in each bin . we want to study the dependence on the angular integration in the fisher matrix for the set of parameters @xmath38 . the derivatives of the power spectrum are @xmath39 we consider two cases depending on the behavior of @xmath35 , equation ( [ veff ] ) : 1 . `` enough data '' @xmath40 , then we have @xmath41 and the fisher matrix could be written as @xmath42 where @xmath43 being @xmath44 and @xmath45 . shot - noise dominated @xmath46 , then @xmath47 and since we are interested only in the @xmath48 dependence , we can write @xmath49 . then the fisher matrix becomes @xmath50 with @xmath51 and @xmath7 in the three cases : orange line @xmath35 , blue line @xmath41 , and green line @xmath49.,title="fig : " ] and @xmath7 in the three cases : orange line @xmath35 , blue line @xmath41 , and green line @xmath49.,title="fig : " ] + and @xmath7 in the three cases : orange line @xmath35 , blue line @xmath41 , and green line @xmath49.,title="fig : " ] and @xmath7 in the three cases : orange line @xmath35 , blue line @xmath41 , and green line @xmath49.,title="fig : " ] + and @xmath7 in the three cases : orange line @xmath35 , blue line @xmath41 , and green line @xmath49.,title="fig : " ] and @xmath7 in the three cases : orange line @xmath35 , blue line @xmath41 , and green line @xmath49.,title="fig : " ] we notice that in the two limiting cases above , we can move the matrices @xmath52 and @xmath53 outside of the integral , as for the fiducial model @xmath6 and @xmath7 do not depend on @xmath54 . this means that , although the absolute size of the error ellipse depends on the integral , the relative size and orientation do not . in other words , we can obtain ` generic expectations ' for the shape of the degeneracy between @xmath6 and @xmath7 from galaxy clustering surveys . these results are quite representative for the full range of @xmath55 and @xmath56 , i.e. galaxy surveys have generically a slightly negative correlation between @xmath55 and @xmath56 , and they can always measure @xmath56 about 3.7 to 4.7 times better than @xmath55 , see figure [ fig1 ] . in comparisson to the results of @xcite , we remove the dependence on @xmath57 , eq . ( [ eq : directobs ] ) , which is a quantity that depends on inflation or other primordial effects . , a.g . and a.v . acknowledge support from dfg through the project trr33 `` the dark universe '' , a.g . also acknowledges support from daad through program `` forschungsstipendium fr doktoranden und nachwuchswissenschaftler '' . m.k . acknowledges financial support from the swiss nsf .

from the galaxy power spectrum in redshift space , we derive semi - analytical results on the generic degeneracy of galaxy clustering measurements . defining the observables @xmath0 and @xmath1 , ( being @xmath2 the growth function , @xmath3 the bias , @xmath4 the growth rate , and @xmath5 the amplitude of the power spectrum ) , we perform a fisher matrix analysis to forecast the expected precision of these quantities for a euclid - like survey . among the results we found that galaxy surveys have generically a slightly negative correlation between @xmath6 and @xmath7 , and they can always measure @xmath7 about 3.7 to 4.7 times better than @xmath6 .

in a recent paper moitsheki et al@xcite argued that a method based on lie algebras is suitable for obtaining the solution to nonlinear ordinary differential equations that appear in simple models for heat transfer . they compared the analytical solutions with other results coming from perturbation approaches like homotopy perturbation method ( hpm ) and homotopy analysis method ( ham)@xcite . it is worth noticing that there is an unending controversy between the users of those fashionable perturbation approaches that arose some time ago@xcite . the purpose of this paper is to determine the usefulness of the results for the heat transfer systems provided by the lie algebraic method and those perturbation approaches . in sec . [ sec : exact ] we analyze the exact solutions arising from lie algebras , in sec . [ sec : taylor ] we outline the application of the well known taylor series approach , in sec . [ sec : virial ] we derive a simple accurate analytical expressions for one of the models and in sec . [ sec : conclusions ] we summarize our results and draw conclusions . the first example is the nonlinear ordinary differential equation@xcite @xmath0u^{\prime \prime } ( x)+\epsilon u^{\prime } ( x)^{2 } & = & 0 \nonumber \\ u(0)=1,\;u(1 ) & = & 0 \label{eq : ex_1}\end{aligned}\ ] ] where the prime denotes differentiation with respect to the variable @xmath1 . this equation is trivial if one rewrites it in the following way @xmath2^{\prime } = 0$]@xcite and the solution is @xmath3x}-1}{\epsilon } \label{eq : u_ex_1}\ ] ] moitsheki et al@xcite derived exactly this result by means of a rather lengthy algebraic procedure . it is clear that in this case the lie algebraic method gives us the same answer that we can obtain in a simpler way . for the second example @xmath4 the authors derived the simple analytical expression@xcite @xmath5 they argued correctly that it satisfies @xmath6 but they were wrong when they stated that `` however , @xmath7 only if @xmath8 '' . notice that the function @xmath9 that comes from such value of @xmath10 does not have the correct behaviour at @xmath11 . therefore , in this case the lie algebraic approach led to a wrong result . other authors have applied hpm and ham to the equation@xcite @xmath0u^{\prime } ( x)+u(x ) & = & 0 \nonumber \\ u(0 ) & = & 1 \label{eq : ex_3}\end{aligned}\ ] ] with the trivial solution @xmath12+x=0 \label{eq : u_ex_3}\ ] ] in the following two sections we discuss some of these problems from different points of view . if the variable of the nonlinear equation is restricted to a finite interval , one can try a straightforward power series solution @xmath13 and obtain the unknown model parameter from the boundary conditions . in the case of the example ( [ eq : u_ex_1 ] ) the radius of convergence of this series is @xmath14 $ ] and therefore the approach will be useful for small and moderate values of @xmath10 . as @xmath10 increases the rate of convergence of the taylor series method decreases because the radius of convergence approaches unity from above . however , this example is trivial and of no interest whatsoever for the application of a numerical or analytical method . this reasoning also applies to example ( [ eq : ex_3 ] ) although in this case we do not have an explicit solution @xmath15 but @xmath16 . the example ( [ eq : ex_2 ] ) is more interesting because there appears to be no exact solution , and for this reason we discuss it here . the unknown parameter is @xmath17 and the partial sums for the taylor series about @xmath11@xmath18}(x)=\sum_{j=0}^{n}u_{j}(u_{0})x^{j } \label{eq : u_x_series}\ ] ] enable one to obtain increasingly accurate estimates @xmath19}$ ] as @xmath20 increases . such estimates are roots of @xmath21}(1)=1 $ ] . although the rate of convergence decreases as @xmath10 increases it is sufficiently great for most practical purposes . notice that the ham perturbation corrections for this model are polynomial functions of @xmath1@xcite whereas the hpm has given polynomial functions of either @xmath1@xcite or @xmath22@xcite . however , there is no doubt that the straightforward power series approach is simpler and does not require fiddling with adjustable parameters@xcite . the analysis of the nontrivial equations for heat transfer models may be easier if we have simple approximate analytical solutions instead of accurate numerical results or cumbersome perturbation expressions . in the case of the models ( [ eq : ex_1 ] ) and ( [ eq : ex_3 ] ) there is no doubt that the exact analytical expressions should be preferred . for that reason , in what follows we concentrate on the seemingly nontrivial model ( [ eq : ex_2 ] ) . we have recently shown that the well known virial theorem may provide simple analytical solutions for some nonlinear problems@xcite . in particular , we mention the analysis of a bifurcation problem that appears in simple models for combustion@xcite . the only nontrivial problem outlined above is a particular case of nonlinear ordinary differential equations of the form @xmath23 the hypervirial theorem is a generalization of the virial one . if @xmath24 is an arbitrary differentiable weight function , the hypervirial theorem provides the following suitable expression for our problem ( [ eq : gen_nonlin ] ) : @xmath25^{\prime } dx & = & w(u(1))u^{\prime } ( 1)-w(u(0))u^{\prime } ( 0 ) \nonumber \\ & = & \int_{0}^{1}\left [ \frac{dw}{du}(u^{\prime } ) ^{2}+w(u)f(u)\right ] dx \label{eq : vt_gen}\end{aligned}\ ] ] in the particular case of the example ( [ eq : ex_2 ] ) we have @xmath26 dx \label{eq : vt_ex_2}\ ] ] when @xmath27 we obtain the virial theorem . here we also consider the even simpler choice @xmath28 that we will call hypervirial although it is just a particular case . since @xmath29 we try the ansatz @xmath30 that satisfies the boundary conditions in equation ( [ eq : ex_2 ] ) . it follows from equation ( [ eq : vt_ex_2 ] ) that the adjustable parameter @xmath31 is a root of @xmath32 when @xmath27 and @xmath33 when @xmath28 . [ fig : ht1 ] shows @xmath34 for some values of @xmath10 and also the accurate result obtained from the taylor series discussed in sec . [ sec : taylor ] . we appreciate that the accuracy of the analytical expression ( [ eq : u_app ] ) decreases as @xmath10 increases . however , if one takes into account the simplicity of equation ( [ eq : u_app ] ) the agreement is remarkable . besides , the hypervirial theorem with @xmath35 proves to be more accurate than the virial theorem . it is curious that there is no such test for the hpm or ham@xcite . as a particular example we consider @xmath36 ( the preferred parameter value for both ham and hpm calculations@xcite ) . from the partial sums of the taylor series with @xmath37 we obtain @xmath38 . the analytical function ( [ eq : u_app ] ) yields @xmath39 , @xmath40 for @xmath41 and @xmath42 , @xmath43 for @xmath35 that is a reasonable estimate of the unknown parameter . again we see that the hypervirial approach is better than the virial one . [ fig : ht2 ] shows accurate values of @xmath15 given by the taylor series with @xmath44 , our approximate analytical virial expression @xmath45 and equation ( [ eq : u_ex_2 ] ) for @xmath46 . it seems that the accuracy of @xmath45 is somewhat between the ham results of 5th and 10th order@xcite . on the other hand , the equation ( [ eq : u_ex_2 ] ) derived by the lie algebraic method@xcite exhibits a wrong behaviour . finally , in fig . [ fig : ht2b ] we compare the numerical , virial ( @xmath41 ) and hypervirial ( @xmath35 ) approaches to the function @xmath15 in a wider scale . we conclude that the virial theorem is not always the best choice for obtaining approximate solutions to nonlinear problems . the purpose of this paper has been the discussion of some recent results for the nonlinear equations arising in heat transfer phenomena . the oversimplified models considered here may probably be of no utility in actual physical or engineering applications . notice that the authors did not show any sound application of those models and the only reference is a pedagogical article cited by rajabi et al@xcite . however , it has not been our purpose to discuss this issue but the validity of the methods for obtaining exact and approximate solutions to simple nonlinear equations . it seems that the particular application of the lie algebraic method by moitsheki et al@xcite has only produced the exact result of a trivial equation and a wrong result for a nontrivial one . therefore , we believe that the authors failed to prove the utility of the technique and it is not surprising that they concluded that their results did not agree with the ham ones@xcite ( see fig . [ fig : ht2 ] ) . we have also shown that under certain conditions the well known straightforward taylor series method is suitable for the accurate treatment of such nontrivial equations . it is simpler than both ham and hpm@xcite and as accurate as the numerical integration routine built in a computer algebra system@xcite . finally , we have shown that the well known hypervirial theorem may provide simple analytical expressions that are sufficiently accurate for a successful analysis of some of those simple models for heat transfer systems . it is surprising that our results suggest that the virial theorem@xcite may not be the best choice .

we analyze some exact and approximate solutions to nonlinear equations for heat transfer models . we prove that recent results derived from a method based on lie algebras are either trivial or wrong . we test a simple analytical expression based on the hypervirial theorem and also discuss earlier perturbation results .

the strange and antistrange quark distributions of the nucleon are of great interest . it has been known for some time that non - perturbative processes involving the meson cloud of the nucleon may break the symmetry between the strange and antistrange quark distributions . this asymmetry affects the extraction of @xmath4 from neutrino dis processes@xcite . a precise understanding on the cross - secrion for @xmath5 production at the large hadron collider ( lhc ) depends on the strange sea distributions at small @xmath6 region . however , the strange sea distributions are not well determined compared with those for the light quark sea . the hermes collaboration recently presents their measurement of helicity averaged and helicity dependent parton distributions of the strange quark sea in the nucleon from charge kaon production in deep - inelastic scattering on the deuteron@xcite . the severest constrain on the strange and antistrange distributions before the hermes measurement comes from the neutrino(antineutrino)-nucleon deep inelastic scattering ( dis ) in which two muons are produced in the final state , i.e. @xmath7 . most data for such processes are provided by the ccfr@xcite and nutev@xcite collaborations . there are two dominant mechanisms for the quark sea production in the nucleon : ( i ) gluons splitting into quak - antiquark pairs , and ( ii ) contributions from the meson - baryond components in the nucleon . while the sea distributions generated through mechanism ( i ) can be assumed to be flavour independent ( su(3 ) flavour symmetric ) , i.e. @xmath8 and @xmath9 and quark - antiquark symmetric , i.e. @xmath10 , the sea distributions generated through mechanism ( ii ) violate these symmetries . mechanism ( ii ) provides a natural explanation for the observed su(2 ) flavour asymmetry among the sea distributions , i.e. @xmath11@xcite , and predicts a strange - antistrange asymmetry@xcite . assuming su(3 ) flavour symmetry and quark - antiquark symmetry for the sea distributions generated via mechanism ( i ) , we can construct a quantity ( x)=(x)+(x)-s(x)-(x ) , [ delta ] which has a leading contribution from mechanism ( ii ) , and can be calculated using non - perturbative models describing that mechanism . we present a calculation of @xmath3 in the meson cloud model ( mcm)@xcite by considering fock states involving mesons in the pseudoscalar and vector octets and baryons in the octet and decuplet . combining our calculation for @xmath3 with results for the light antiquark sea distributions from global pdf fits we can calculate the total strange distribution @xmath12 and the strange sea suppression factor @xmath13 $ ] the wave function for the physical nucleon can be written as * k * _ ) ; m^^(1-y,-*k * _ ) ) . [ nmcm ] 2 in eq . ( [ nmcm ] ) the first term is for a bare " nucleon , @xmath14 is the wave function renormalization constant , and @xmath15 is the wave function of the fock state containing a baryon ( @xmath16 ) with longitudinal momentum fraction @xmath17 , transverse momentum @xmath18 , and helicity @xmath19 , and a meson ( @xmath20 ) with momentum fraction @xmath21 , transverse momentum @xmath22 , and helicity @xmath23 . the probability of finding a baryon with momentum fraction @xmath17 ( also known as fluctuation function in the literature ) can be calculated from the wave function @xmath15 , f_bm / n ( y ) = _ ^ ^_0 d k_^2 ^^_bm(y , k_^2 ) ^*^_bm(y , k_^2 ) . [ fbmn ] the probability of finding a meson with momentum fraction @xmath17 is given by f_mb / n(y ) = f_bm / n ( 1-y ) . [ fmbn ] the wave functions and thereby the fluctuation functions can be derived from effective meson - nucleon lagrangians employing time - order perturbation theory in the infinite momentum frame@xcite . the mesons and baryons could contribute to the hard scattering processes such as the deep inelastic scattering , provided that the lifetime of a virtual baryon - meson fock state is much longer than the interaction time in the hard process . the fock states we consider include @xmath24 , @xmath25 , and @xmath26 , x ( x ) & = & z , [ deltas ] + x(x ) & = & z \ { ( f_n / n+f_/n+f_n / n+f_/n+f_n / n ) v_. - ( f_k / n + f_k^*/n ) s^ + ( f_k / n + f_k^*/n ) s^ + & & . - ( f_k /n+f_k /n + f_k^ * /n+f_k^ * /n ) ^k } . [ delta_mcm ] 2 in eqs . ( [ deltas ] ) and ( [ delta_mcm ] ) @xmath27 denotes the convolution of two functions , i.e. @xmath28 . the calculation details can be found in refs . @xcite . the light quark sea distributions are well decided by the global pdf fits to all available experimental data . combining the global fit results for @xmath29 and our calculation for the @xmath3 we could have an estimation on the strange sea distributions @xmath30= x\left [ \dbar(x)+\ubar(x)\right]_{fit}-x\delta(x ) . \label{xs+}\ ] ] in fig . 1 we show our calculated difference between strange and anti - strange quark distributions with and without including the contributions from fock states involving @xmath31 mesons . we can see that the contributions from @xmath32 and @xmath33 are of similar magnitude to those from the lower mass fock states . the calculated results for @xmath34 together with the hermes measurement@xcite and the results from mstw2008@xcite , cteq6.6@xcite , cteq6.5@xcite and cteq6l@xcite are shown in fig . 2 . the hermes data for @xmath34 are obtained by using hermes measurement for @xmath35 which is a leading - oder analysis and cteq group s pdfs for @xmath36 at the leading - order , .i.e . the shaded area represents the allowed range for the @xmath37 distribution estimated by the cteq group@xcite by applying the @xmath38 confidence criteria on the dimuon production data sets , i.e. by requiring the momentum fraction carried by the strange sea to be in the range of @xmath39 . it can be seen that our calculations are much smaller that that given in the mstw2008 , cteq6l and the central values of the cteq6.5 for the region of @xmath40 while the agreement with the hermes results are reasonably well except for the region around @xmath41 . the calculation results agree with that obtained using the cteq6.6 pdf set . it is noticed that our calculations for @xmath34 are independent of any global pdf sets for the proton . the agreement between our calculations and the cteq6.6 results is remarkable . the results for the total strange and antistrange distributions is given in fig . 3 . in this study the @xmath42 distribution from the cteq6.6 set is used . it can be found that our calculations agree with the hermes data and the results from cteq6.6 very well for the region of @xmath43 , but are larger that that from the mstw2008 and cteq6.5 . our calculations for @xmath37 becomes negative for @xmath44 which is unreasonable . the reason for this could be that the model calculations over estimate @xmath34 or @xmath45 is under estimated in the cteq6.6 set , or both . we calculated the difference between the strange and antistrange quark distributions and the difference between the light antiquark distributions and the strange and anstistrange distributions using the meson cloud model . we estimated the total strange and antistrange distributions by combining our calculations for the difference with the light antiquark distributions determined from global parton distribution functions fits . our calculations for the strange sea distributions agree with the hermes measurements and cteq6.6 set but larger than that given in cteq6.5 and mstw2008 . 00 g. p. zeller _ ( nutev collaboration ) , . a. airapetian , _ et . al . _ , hermes collaboration , . a. o. bazarko , _ et . al . _ , ccfr collaboration , . m. goncharov _ ( nutev collaboration ) , . for recent reviews , see e.g. , s. kumano , ; j. speth and a. w. thomas , . a. i. signal and a. w. thomas , . cao and a. i. signal , . a. w. thomas , . h. holtmann , a. szczurek and j. speth , . cao and a. i. signal , . cao and a. i. signal , . f. bissey , f .- cao , and a. i. signal , . h. chen , f .- cao and a. i. signal , in preparation . a. d. martin , w. j. stirling , r. s. thorne , and g. watt , arxiv:0901.0002 [ hep - ph ] . p. m. nadolsky , _ et . al . arxi:0802.00007 [ hep - ph ] . h. l. lai , _ et . al . _ , . w .-

the difference between the strange and antistrange quark distributions , @xmath0 , and the combination of light quark sea and strange quark sea , @xmath1 , are originated from non - perturbative processes , and can be calculated using non - perturbative models of the nucleon . we report calculations of @xmath2 and @xmath3 using the meson cloud model . combining our calculations of @xmath3 with relatively well known light antiquark distributions obtained from global analysis of available experimental data , we estimate the total strange sea distributions of the nucleon . # 1#2#3#4#1 , # 3 , * # 2 * : # 4 strange and antistrange quark distributions , nucleon meson cloud model 2

( 4 ) of the main text , we give the result of @xmath124 for the special case that drift occurs along the @xmath2-direction ( @xmath65 ) and detection at @xmath66 ( @xmath67 ) . here , we provide the result for a general case : @xmath127 \\ - k_{\mathrm{di},x } -2 k_{\mathrm{dr},x } + \frac{2}{k_\mathrm{f}^2 } \left [ k_{\mathrm{di},x } k_{\mathrm{dr},y}^2 + 2 k_{\mathrm{di},y } k_{\mathrm{dr},y } k_{\mathrm{dr},x } + k_{\mathrm{dr},y}^2 k_{\mathrm{dr},x } - 3 k_{\mathrm{di},x } k_{\mathrm{dr},x}^2 - k_{\mathrm{dr},x}^3 \right ] \end{pmatrix } \ , .\ ] ] @xmath129 + 2 k_{\mathrm{dr},y } \left[1 + \left(\frac{k_{\mathrm{dr},y}}{k_\mathrm{f}}\right)^2 \right ] \\ k_{\mathrm{di},x } \left [ 1 - \left(\frac{2 k_{\mathrm{dr},y}}{k_\mathrm{f } } \right)^2 \right ] \end{pmatrix } \ , .\ ] ] for @xmath128 evm , @xmath136 evm and @xmath137 evm , respectively . in all cases , @xmath138 evm , @xmath139 evm and @xmath140 km / s ( violet dashed line ) . we find good agreement between the simulation and the model ( green solid lines ) for the entire parameter range . [ si_fig1 ] ] in the main text , we discuss the validity of the model for cases away from the psh symmetry , i.e. , away from @xmath87 , by comparing the model with spin - precession maps obtained from numerical monte - carlo simulations . we state that , as long as drift occurs along @xmath2 , we obtain good agreement between simulation and model . in fig . [ si_fig1 ] , we show the corresponding simulations for three different cases between @xmath141 ( isotropic ) and @xmath142 ( psh ) . the model of eqs . ( 5 ) and ( 6 ) of the main text ( green solid lines ) correctly predicts the simulated spin dynamics for the entire parameter range for drift along @xmath2 . equation ( 1 ) in the main text contains six independent fit parameters . suitable starting values for the fitting are obtained in the following way . for the amplitude @xmath38 we choose the value of @xmath143 . the drift velocity , @xmath13 , is defined by the shift of the spin packet in time and its starting value is estimated manually . the spin diffusion constant , @xmath39 , is determined by the broadening of the gaussian envelope function and we start with a typical value for samples from the same wafer . for the dephasing time , @xmath40 , we use 1 ns as a starting value . the most important parameters for the presented study are @xmath10 , the temporal precession frequency , and @xmath17 , the spatial wavenumber . both quantities are little affected by the other fit parameters . starting values for both of them are obtained from a line - cut through the data at a fixed time ( a fixed position ) for @xmath17 ( for @xmath10 ) . before calculating the mean - squared error between eq . ( 1 ) and the measured @xmath29 , we perform a one - dimensional convolution of eq . ( 1 ) with the gaussian intensity profiles of the pump and probe laser spots along @xmath2 . this step is very important , because its neglect distorts particularly the value of @xmath10 . all fit parameters are then constrained to a reasonable range . to determine each parameter s fit value and confidence interval , we vary that parameter in small steps through its full range . at each step , all other parameters are optimized to minimize the mean - squared error between the data and eq . ( 1 ) by a nelder - mead simplex search algorithm . the value of the parameter with the smallest error defines the fit value . for all fit parameters , we find a single minimum . the confidence interval , as shown in fig . 2 in the main text , is then defined by an increase of the mean - squared error by 5 % from its minimal value . the mean - squared error is taken over approximately 3000 data points ( typically 35 steps of @xmath3 , 85 steps of @xmath2 or @xmath90 ) .

space- and time - resolved measurements of spin drift and diffusion are performed on a gaas - hosted two - dimensional electron gas . for spins where forward drift is compensated by backward diffusion , we find a precession frequency in absence of an external magnetic field . the frequency depends linearly on the drift velocity and is explained by the cubic dresselhaus spin - orbit interaction , for which drift leads to a spin precession angle twice that of spins that diffuse the same distance . drift and diffusion of charge carriers in semiconductor nanostructures are the foundation of information technology . the spin of the electron is being investigated as an additional or complementary degree of freedom that can enhance the functionality of electronic devices and circuits @xcite . in the presence of spin - orbit interaction ( soi ) , the spins of moving electrons precess about effective magnetic fields that depend on the electron momentum vector , @xmath0 @xcite . in a two - dimensional electron gas ( 2deg ) , this precession has been proposed as a gate - tunable switching mechanism @xcite . spin diffusion and spin drift have been studied using optical @xcite and electrical techniques @xcite . a local spin polarization expands diffusively into a spin mode with a spatial polarization pattern that is characteristic of the strength and symmetry of the soi @xcite . an additional drift induced by an electric field does not modify the spatial precession period in the case of linear soi @xcite . this is because spins that travel a certain distance and direction precess on average by the same angle , irrespective of how the travel is distributed between diffusion and drift . therefore , no spin precession occurs for quasi - stationary electrons , i.e. for electrons where drift is compensated by diffusion . . ( a ) measured spin polarization @xmath1 vs. @xmath2 for different @xmath3 at an electric field @xmath4 kv / m . the data is offset according to @xmath3 and normalized to the maximum spin polarization , @xmath5 . circles are experimental data and solid lines are fits with eq . ( [ eq : fit ] ) . ( b ) colorscale plot of @xmath6 for @xmath4 kv / m . the violet dashed line marks the center of the spin packet . the gray solid lines are contour lines of a global fit as explained in the text . the solid green line indicates the slope of the lines of equal spin phase . it is tilted because spin precession from drift is different from that from diffusion owing to cubic soi . ( c ) colorscale plot of @xmath6 for @xmath7 kv / m , where the slope of the green line is reversed . inset : schematic layout of the cross - shaped mesa structure . four ohmic contacts allow the application of electric fields along the @xmath8 $ ] and the @xmath9 $ ] direction . [ fig2 ] ] in this letter , we experimentally observe such unexpected drift - induced spin precession of stationary electron spins in the absence of an external magnetic field . using an optical pump - probe technique , we investigate the spatiotemporal dynamics of locally excited spin polarization in an n - doped gaas quantum well . spin polarization probed at a fixed position is found to precess with a finite frequency , @xmath10 . this is identified as a consequence of cubic soi , which affects spin drift and spin diffusion differently . a simple model predicts that drifting spins precess twice as much as spins that diffuse the same distance . this difference leads to a dependence @xmath11 , where @xmath12 is the cubic soi coefficient and @xmath13 the drift velocity . we demonstrate quantitative agreement between model and experiment , and extract a @xmath12 in agreement with literature values . monte - carlo simulations confirm the validity of the model and pinpoint deviations that occur when the drift - induced soi field is small compared with that from diffusion into a perpendicular direction . this finding highlights the role of nonlinear soi in spin transport and is relevant for spintronics applications . plotted against the applied electric field . dots are the fit values obtained from the measured @xmath14 . the solid line is the drift velocity calculated from the measured current @xmath15 via @xmath16 . ( b ) values for the spatial wavenumber , @xmath17 . dots are the fit values and the red line is the model of eq . ( [ eq : q ] ) with @xmath18 evm . ( c ) values for the precession frequency , @xmath10 . dots are fit values and the red line is the model of eq . ( [ eq : omg ] ) with @xmath19 evm . confidence intervals in all plots are defined as a 5% increase of the fit error . [ fig3 ] ] the sample consists of a 12-nm - thick gaas quantum well in which the soi is tuned close to the persistent spin helix ( psh ) symmetry @xcite . there , the effective magnetic field from linear soi is strongly anisotropic , such that diffusing spins exhibit a strong spatial precession along the @xmath20 $ ] direction and no precession along @xmath21 $ ] @xcite . the 2deg has a sheet density of @xmath22 with one occupied subband and a mobility of @xmath23 , as determined by a van - der - pauw measurement at 4 k after illumination . further details on the sample structure are given in ref . [ ] . a cross - shaped mesa structure [ cf . inset in fig . [ fig2](c ) ] with a width @xmath24 was fabricated by photo lithography and wet - chemical etching . we applied an in - plane electric field @xmath25 to the 2deg along @xmath2 via two ohmic contacts , which are 800 @xmath26 m apart . spins oriented along the @xmath27-axis were locally excited in the center of the mesa at time @xmath28 by an optical pump pulse . at varying time - delay , @xmath3 , the transient spin polarization along the @xmath27-axis , @xmath29 , was measured using the pump - probe technique described in @xcite with a spatial resolution of @xmath30 . the time - averaged laser power of the pump ( probe ) beam was @xmath31 ( @xmath32 ) at a repetition rate of 80 mhz . the sample temperature was 20 k. figure [ fig2](a ) shows data for three different time delays , @xmath3 , at @xmath4 kv / m . the spatially precessing spins are well described by a cosine oscillation in a gaussian envelope , which broadens with time because of diffusion . the center of the envelope shifts along @xmath33 because the electrons drift in the applied electric field . figs . [ fig2](b ) and [ fig2](c ) show colorscale plots of @xmath29 for @xmath4 kv / m and @xmath7 kv / m , respectively . the motion of the center of the spin packet is marked by a violet dashed line . remarkably , the position of constant spin precession phase shifts along @xmath2 in time , as indicated by the solid green lines . this corresponds to a finite temporal precession frequency @xmath10 for spins that stay at a constant position @xmath2 . for a positive @xmath25 [ fig . [ fig2](b ) ] , the spin packet moves towards the negative @xmath2-axis , and the tilt @xmath34 of constant spin phases is negative . both the drift direction and the tilt change their sign when the polarity of @xmath25 is reversed [ fig . [ fig2](c ) ] . we model @xmath1 by multiplying the gaussian envelope by @xmath35 and a decay factor @xmath36 : @xmath37 \cos \left ( \omega t + q y \right ) \exp \left ( - t/\tau \right ) \end{split } \label{eq : fit}\end{aligned}\ ] ] the amplitude @xmath38 , @xmath13 , the diffusion constant @xmath39 , the dephasing time @xmath40 , @xmath10 and the wavenumber @xmath17 are treated as fit parameters . detailed information on the fitting procedure is given in the supplementary information . to avoid deviations due to heating effects and other initial dynamics @xcite not captured in this simple model , we fit the data from @xmath41 . the decrease of the spatial precession period in time is a known effect of the finite size of the pump and probe laser spots @xcite , and is accounted for by convolving eq . ( [ eq : fit ] ) with the gaussian intensity profiles of the laser spots . the experiment is perfectly described by this model , as evident from the good overlap of the symbols ( experiment ) with the solid lines ( fits ) in fig . [ fig2](a ) , and from the fitted gray lines that mark @xmath42 in the colorscale plots of figs . [ fig2](b - c ) . the fit parameters obtained for different values of @xmath25 are shown in fig . [ fig3 ] . in fig . [ fig3](a ) , @xmath13 obtained from @xmath14 is compared with values deduced from the measured current @xmath15 using @xmath16 , where @xmath43 is the elementary electron charge . the good agreement shows that the spin packet follows the stream of drifting electrons in the channel and that no parallel conductance obscures the interpretation of our data . in figs . [ fig3](b - c ) , we summarize the values obtained for @xmath17 and @xmath10 . while @xmath17 shows no significant dependence on @xmath13 , we find a linear dependence of @xmath10 on @xmath13 with a negative slope . . ( b ) the fermi circle is shifted by the drift vector @xmath44 . ( c ) exemplary map of @xmath14 generated from eq . ( [ eq : fit ] ) . electrons with an average @xmath45 drift along the violet dashed line . electrons measured away from this line additionally experience a diffusive motion . because of the unequal contributions of drift and diffusion to spin precession , the phase of quasi - stationary electron spins ( for example , those on the solid green line ) depends on how the travel is divided between drift and diffusion . this leads to a precession in time , as seen in the lower panel ( shown for spins at @xmath46 ) . [ fig1 ] ] next , we show that the drift - induced @xmath10 is a consequence of cubic soi . considering a degenerate 2deg in a @xmath47-oriented quantum well with one occupied subband , the soi field is given by @xcite @xmath48 k_y\\ \left[- \alpha + \beta_1 + \beta_3 \frac{2 ( k_y^2 - k_x^2)}{k_\mathrm{f}^2 } \right ] k_x \end{pmatrix } \ , . \label{eq : soi}\ ] ] here , @xmath49 is the rashba - coefficient , and @xmath50 and @xmath12 are the linear and cubic dresselhaus coefficients , respectively . in the degenerate limit , the relevant electrons are those at the fermi energy , @xmath51 , where @xmath52 is the reduced planck s constant , @xmath53 is the effective electron mass and @xmath54 is the fermi wave - vector . figure [ fig1](a ) sketches two different diffusive paths of electrons that travel the same distance @xmath55 . on those paths , the electrons scatter many times and thereby sample different @xmath56-states . because we consider electrons that travel along @xmath57 , they occupy states with @xmath56-vectors along @xmath57 more often than along the opposite direction . assuming isotropic scattering , this occupation is modeled by a weighting function @xmath58 such that the average momentum is @xmath59 , with @xmath60 and @xmath61 . the drift of the electron gas is accounted for by a shift of the fermi circle by @xmath44 [ fig . [ fig1](b ) ] . because of its dependence on @xmath56 [ eq . ( [ eq : soi ] ) ] , the soi field changes after each scattering event . its average is given by @xmath62 . instead of deriving the spin mode of the system @xcite , we describe the spin dynamics by assuming that spins injected at @xmath28 and @xmath63 precess about @xmath64 . for drift along the @xmath2-direction ( @xmath65 ) and detection at @xmath66 ( @xmath67 ) , we obtain ( see supplementary information for the general case ) @xmath68 this is a surprising result , because in the last term , which is proportional to @xmath12 , drift ( @xmath69 ) leads to a spin precession angle twice as large as that induced by diffusion ( @xmath70 ) . as illustrated in fig . [ fig1](c ) , this leads to a precession in time for spins located at a constant position @xmath71 . without diffusion , the electrons follow @xmath72 ( violet dashed line ) and reach @xmath46 at a given time . spins that reach @xmath71 earlier ( later ) will in addition diffuse along ( against ) @xmath73 and therefore acquire a different precession phase . to calculate the corresponding frequency @xmath10 , we insert @xmath74 into eq . ( [ eq : omgmean ] ) and obtain @xmath75 , with @xmath76 we have defined @xmath77 and @xmath78 . the wavenumber @xmath17 is not modified by drift to first order . in contrast , the precession frequency @xmath10 depends linearly on @xmath13 and is proportional to the cubic dresselhaus coefficient , @xmath12 . this induces a temporal precession for quasi - stationary electrons [ cf . lower panel in fig . [ fig1](c ) ] . the tilt of the green solid lines in figs . [ fig2](b - c ) therefore directly visualizes the unequal contributions of drift and diffusion to the spin precession for nonlinear soi . we note that spins that follow @xmath79 precess with a frequency @xmath80 , recovering the result of ref . [ ] , which is valid for measurements that do not spatially resolve the spin distribution . we find a remarkable agreement between eqs . ( [ eq : q ] ) and ( [ eq : omg ] ) and the measured values for @xmath17 and @xmath10 [ figs . [ fig3](b - c ) ] . from @xmath17 , we obtain @xmath81 evm , which is equal to previous results from a similar sample @xcite . the slope of @xmath10 vs. @xmath13 is directly proportional to @xmath12 . we get @xmath19 evm , which agrees perfectly with the measured sheet electron density of @xmath82 m@xmath83 and a bulk dresselhaus coefficient of @xmath84 evm@xmath85 @xcite , by considering that @xmath86 . equations ( [ eq : q ] ) and ( [ eq : omg ] ) were derived assuming spin precession about an averaged @xmath64 . for drift along @xmath2 , this is appropriate for the psh situation ( @xmath87 ) , where soi is large for @xmath88 and small for @xmath89 [ cf . eq . ( [ eq : soi ] ) ] . the spin helix is described by a strong spatial spin precession along @xmath2 and no precession along @xmath90 @xcite . the investigated sample slightly deviates from the psh symmetry , because @xmath91 as determined from measurements in an external magnetic field @xcite : @xmath92 . for drift along @xmath90 , the model predicts a finite spatial spin precession with @xmath93 . however , when we apply the electric field along the @xmath90 axis and measure @xmath94 , no precession is visible [ fig . [ fig4](a ) ] . the absence of precession can be explained by the large anisotropy of the soi . the small soi field induced by drift along @xmath90 can not destabilize the spin helix along @xmath2 , which leads to the suppression of @xmath95 . a similar effect has been predicted in a purely diffusive situation @xcite . it is not accounted for in our simple model , where for drift along @xmath90 , the fields for @xmath88 average to zero and the fields induced by drift along @xmath90 appear dominant , even though electrons tracked at @xmath96 also occupy states with @xmath88 . we compare the measured and modeled spin dynamics with a numerical monte - carlo simulation that takes the precession about all axes into account correctly . we set @xmath97 evm , @xmath98 evm and @xmath99 evm . using eq . ( [ eq : soi ] ) , we calculate , in small time steps of 0.1ps , the traces of 500,000 electron spins that isotropically scatter on a fermi circle ( scattering time @xmath100 ps , @xmath101 ) displaced along the @xmath102 direction by @xmath103 . the result is shown in fig . [ fig4](b ) . as in the experiment , spin precession is absent . in fig . [ fig4](c ) , the simulation data is shown for @xmath104 and @xmath105 evm . for this almost isotropic soi @xcite , the model predicts both the temporal and the spatial precession period remarkably well ( green lines ) . the transition from isotropic soi to a psh situation , for drift along @xmath90 , is summarized in fig . [ fig4](d ) . it shows the wavenumber @xmath95 obtained from monte - carlo simulations as a function of @xmath49 . the value of @xmath106 was varied to keep @xmath107 constant at @xmath108 evm . the psh situation is realized at @xmath109 evm , where the model correctly predicts @xmath110 . between there and @xmath111 evm , spin precession along @xmath90 is completely suppressed , in contrast to the linearly increasing @xmath95 of the simple model ( red solid line ) . at smaller values of @xmath49 , towards the isotropic case , the simulated @xmath95 gradually approaches the model s prediction . in contrast , spin precession for drift along @xmath2 is correctly described by eqs . ( [ eq : q ] ) and ( [ eq : omg ] ) for the entire range between the isotropic and the psh case ( see supplementary information ) . note that in wire structures narrower than the soi length , spin precession perpendicular to the wire is suppressed @xcite , and we expect drift - induced spin precession to occur along the wire in any crystallographic direction for generic soi . . ( a ) measured @xmath112 for @xmath113 kv / m . no precession is visible , although for our sample we expect @xmath114 , for which our model predicts a precession ( green dashed lines mark @xmath115 ) . ( b ) numerical monte - carlo simulation data of @xmath116 for @xmath117 evm and @xmath118 evm . as in ( a ) , no precession pattern is observed although it is predicted by the model ( green solid line ) . ( c ) numerical monte - carlo simulation data of @xmath116 for @xmath119 evm and @xmath120 evm . here , the soi is almost isotropic and the model ( green solid lines ) describes the precession pattern well . ( d ) when @xmath49 is gradually increased from zero , the @xmath95 observed in the simulation ( blue circles ) initially follows @xmath121 ( red line ) . in a finite range around @xmath87 ( psh ) , precession along @xmath90 is suppressed ( @xmath122 ) . the total strength of soi in all simulations [ ( b)-(d ) ] is kept constant at @xmath123 evm . [ fig4 ] ] in conclusion , we experimentally observed and theoretically explained that , for quasi - stationary electrons , current induces a temporal spin - precession frequency that is directly proportional to the drift velocity and the strength of cubic soi . the origin of this effect is that drift motion in a cubic soi system leads to a precession angle twice as large as that induced by diffusive motion . further work is needed to analytically describe the spin precession for drift along the axis of weak soi in an anisotropic situation . the occupation of a second subband or anisotropic scattering could modify the proportionality constant between @xmath10 and @xmath12 . the temporal precession observed should hold universally for cubic soi , e.g. , also in hole gases in group iv @xcite and iii - v semiconductors @xcite , or charge layers in oxides like perovskites @xcite . moreover , the effect demonstrated must be considered when designing spintronic devices based on such systems . for read - out schemes with finite - sized contacts , it may lead to a temporal smearing of the spin packet and by that to signal reduction . this can be suppressed by designing a small diffusion constant . the effect itself presents a means to manipulate quasi - stationary spins via soi and to directly quantify the strength of the cubic dresselhaus soi . we acknowledge financial support from the nccr qsit of the swiss national science foundation , f.g.g.h . acknowledges financial support from grants no . 2013/03450 - 7 and 2014/25981 - 7 of the so paulo research foundation ( fapesp ) , g.j.f . acknowledges financial support from fapemig and cnpq , and m.k . from the japanese ministry of education , culture , sports , science , and technology ( mext ) in grant - in - aid for scientific research nos . 15h02099 and 25220604 . we thank r. allenspach , a. fuhrer , t. henn , f. valmorra , and r. j. warburton for helpful discussions , and u. drechsler for technical assistance . 37ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/revmodphys.76.323 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop _ _ ( , ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1103/physrevlett.76.4793 [ * * , ( ) ] http://www.nature.com/nature/journal/v397/n6715/abs/397139a0.html [ * * , ( ) ] link:\doibase 10.1103/physrevlett.94.236601 [ * * , ( ) ] link:\doibase 10.1126/science.1195816 [ * * , ( ) ] link:\doibase 10.1103/physrevb.83.241306 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.68.106 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevb.75.125307 [ * * , ( ) ] link:\doibase 10.1103/physrevb.73.075306 [ * * , ( ) ] \doibase http://dx.doi.org/10.1063/1.2717526 [ * * , ( ) , http://dx.doi.org/10.1063/1.2717526 ] link:\doibase 10.1103/physrevb.82.155324 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.109.246603 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.90.146801 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.97.236601 [ * * , ( ) ] http://www.nature.com/nphys/journal/v8/n10/abs/nphys2383.html [ * * , ( ) ] link:\doibase 10.1103/physrevb.90.201306 [ * * , ( ) ] link:\doibase 10.1103/physrevb.92.235304 [ * * , ( ) ] link:\doibase 10.1103/physrevb.88.085303 [ * * , ( ) ] link:\doibase 10.1103/physrevb.89.045304 [ * * , ( ) ] link:\doibase 10.1103/physrevb.82.235320 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevb.92.045308 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevb.61.13115 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.113.086601 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevb.65.155303 [ * * , ( ) ] link:\doibase 10.1103/physrevb.71.165312 [ * * , ( ) ] \doibase http://dx.doi.org/10.1016/j.sse.2013.01.016 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.108.206601 [ * * , ( ) ]

we consider the same model that we discussed in the main text . namely we take a toy model where the dynamics is driven by @xmath43 for the first half period and @xmath44 for the second half period . the time - evolution operator for the single period @xmath93 is given by @xmath94 we show the time - evolution of @xmath95 for several system sizes and periods in fig . [ suppl1 ] . the initial state is chosen as the all spin - down state . each graph of fig . [ suppl1 ] shows that @xmath95 remains finite when the system size is small , while it eventually tends to zero when the system size is large . this implies that a large system eventually reaches the state of infinite temperature , which is consistent with the floquet eth . by comparing the three graphs of fig . [ suppl1 ] , we find that the timescale of the heating becomes longer as the period of the external field decreases . this is also consistent with our result on the timescale of the heating . the arrows in the figures indicate the expectation value of @xmath48 in the equilibrium state of the 0th - order truncated floquet hamiltonian @xmath40 , that is , @xmath96 with @xmath97 . the temperature is determined from the expectation value of @xmath40 at @xmath42 . in this case , @xmath41 and @xmath98 . we can see that in the first stage of the relaxation , @xmath95 relaxes to @xmath99 , which indicates that a quasi - stationary state observed in this model is actually described by the equilibrium state of the truncated floquet hamiltonian . we next demonstrate the numerical evidence that the fm - expansion can diverge in this model . in fig . [ suppl2 ] , we show the operator norms of @xmath100 as a function of @xmath10 . it looks convergent up to some @xmath10 but it starts to diverge when @xmath10 exceeds this value . as far as we computed , the divergence of the fm expansion occurs for @xmath101 when @xmath102 . it is emphasized that the divergence begins at a higher order term than our estimation @xmath68 . although the theorem presented in the main text becomes meaningless when @xmath103 because @xmath60 becomes negative , the numerical simulations given here and in the main text show that exponentially slow heating is observed even in that case . from this observation , we must conclude that although our rigorous analysis clearly shows that the timescale of heating is extremely slow in the high frequency regime for general spin systems , it does not give accurate quantitative details . numerical investigation is necessary in order to make a quantitatively accurate prediction for a given specific model . for ( a ) : @xmath104 , ( b ) : @xmath105 , and ( c ) @xmath106 . the arrows indicate the equilibrium value with respect to @xmath40 , i.e. @xmath85 with @xmath97 . the temperature is determined by the expectation value of @xmath40 in the initial state ( @xmath41 in this case).,width=302 ] th order term of the fm expansion ( left ) and the @xmath10th order truncated floquet hamiltonian.,width=453 ] here , we provide the proof of the theorem . as a preliminary , we define the `` @xmath30-locality '' and the `` @xmath18-extensiveness '' as the properties of operators . we say that an operator @xmath107 is @xmath108-local if it is decomposed as a=_x:|x|k_aa_x , where @xmath27 is a set of lattice sites and @xmath26 is the number of the sites in @xmath27 , see setup in the main text . this operator @xmath107 is said to be @xmath109-extensive if _ x : xi , let @xmath107 be a @xmath108-local and @xmath109-extensive operator and let @xmath110 be a @xmath111-local and @xmath112-extensive operator . then we readily find that the commutator of @xmath107 and @xmath110 is @xmath113-local and @xmath114$]-extensive . using this iteratively leads to that the multiple commutator in eq . ( [ eq : fm ] ) is @xmath57-local and @xmath115$]-extensive . from this we find that @xmath51 is @xmath57-local and @xmath116-extensive with @xmath117 we can derive useful inequality for the ( multiple ) commutators of @xmath108-local and @xmath109-extensive operator @xmath107 and @xmath111-local operator @xmath118 : 2g_ak_b , [ eq : inequality ] where @xmath119 . more generally , we can show that for any @xmath120-local and @xmath121-extensive operators @xmath122 , _ i=1^n2g_a_ik_i , [ eq : multi_inequality ] where @xmath123 . by applying this inequality to eq . ( [ eq : fm ] ) , it is shown that the coefficient of the fm expansion @xmath51 can be decomposed as @xmath124 , where @xmath125 is an operator acting on the sites in @xmath27 , with t^n_x:|x|(n+1)kw_xt^n2gn_v . [ eq : omega ] obviously @xmath126 and thus eq . ( [ eq : bound_omega ] ) is also derived . in order to prove the theorem , we first consider the time evolution of a local operator @xmath127 in the single period . the exact time evolution of the operator @xmath127 in the heisenberg picture is given by o(t)=u^(t)ou(t)=e^i_0^tdtl(t)o , [ eq : o(t ) ] where @xmath128 $ ] is the liouville operator . we define the approximate time evolution under the truncated floquet hamiltonian @xmath65 as ^(n_0)(t)=e^ih_f^(n_0)toe^-ih_f^(n_0)t = e^il_f^(n_0)to , [ eq : o(t) ] where @xmath129 $ ] . we can show the following lemma : * lemma*. _ assume that @xmath79 , @xmath21 , and @xmath2 are @xmath30-local and @xmath18-extensive . then , for an arbitrary @xmath130-local operator @xmath131 and the period @xmath132 , the following inequality holds : o(t)-^(n_0)(t)16gk2 ^ -(n_0-i)t , [ eq : theorem ] where @xmath133 and @xmath68 . in particular , for @xmath134 , the following stronger bound exists : h_0(t)-_0^(n_0)(t)8g^2k2 ^ -n_0n_vt , [ eq : theorem_h0 ] where @xmath19 is the number of sites subjected to the periodic driving . _ note that eqs . ( [ eq : o(t ) ] ) and ( [ eq : o(t) ] ) are rewritten as follows @xmath135 \tilde{o}^{(n_0)}(t ) = e^{il_f^{(n_0)}t}o = \sum_{n=0}^{\infty}t^n\mathcal{\tilde{a}}_n^{(n_0 ) } { \cal o } \ , , \end{array } \label{heise2}\end{aligned}\ ] ] where @xmath136 $ ] and @xmath137 $ ] , and @xmath138 is the coefficient in the dyson expansion given as @xmath139 the coefficient @xmath140 is given by @xmath141 where @xmath142 $ ] and @xmath143 is the indicator function defined by @xmath144 and @xmath145 . the truncated fm expansion is exact up to @xmath146 in the sense that _ n=_n^(n_0 ) . by using this fact , we have @xmath147 we bound @xmath148 and @xmath149 from above , using eq . ( [ eq : multi_inequality ] ) . first , we show from eqs . ( [ eq : dyson ] ) and ( [ eq : multi_inequality ] ) that @xmath148 is bounded as @xmath150 by using @xmath151\leq 2^{n+i}$ ] and @xmath152 , we have _ n = n_0 + 1^t^n_no8gkt2^i - n_0 . [ eq : an ] for @xmath134 , we can give a stronger bound . because @xmath153=[v(t_1),h_0]=-l_0v(t_1)$ ] , where @xmath154 $ ] , we have @xmath155 because @xmath21 is @xmath30-local , it is written as @xmath156 , where @xmath157 is an operator acting non - trivially only on the domain @xmath27 . by almost the same calculation , we have _ n = n_0 + 1^t^n_nh_04gkt2 ^ -n_0v_0 , [ eq : anh0 ] where @xmath158 . because @xmath21 is @xmath18-extensive , @xmath159 if the driving is applied to @xmath19 sites . by using eqs . ( [ eq : multi_inequality ] ) and ( [ eq : gn ] ) with @xmath162 , because @xmath163 for @xmath164 , we obtain l_l_1 l_l_ro(2gk)^r(2gkn_0)^n - r . by using @xmath165\leq 2^{n+i}$ ] and @xmath166 $ ] , we obtain @xmath167^{n-1}4gk\overline{o}.\end{aligned}\ ] ] because @xmath60 is the maximum integer not exceeding @xmath168 , we have @xmath169 and thus _ n = n_0 + 1^t^n_n^(n_0)o8gkt2^i - n_0 . [ eq : an2 ] by substituting eqs . ( [ eq : an ] ) and ( [ eq : an2 ] ) into eq . ( [ eq : o_bound ] ) , we complete the proof of lemma ( [ eq : theorem ] ) . for @xmath134 , we have @xmath170 and thus @xmath171 . clearly , @xmath172 has no contribution , and for @xmath173 , we can use eq . ( [ eq : omega ] ) . as @xmath174 , we have @xmath175 . applying eq . ( [ eq : multi_inequality ] ) and the upper bound of @xmath176 , we obtain _ n = n_0 + 1^t^n_n^(n_0)h_04g^2ktn_v2 ^ -n_0 . [ eq : anh02 ] using eqs . ( [ eq : anh0 ] ) and ( [ eq : anh02 ] ) , we obtain lemma ( [ eq : theorem_h0 ] ) . from the relation @xmath177 , we note the inequality for any positive integer @xmath67 : @xmath178 applying lemma and using eq . ( [ eq : omega ] ) , we obtain @xmath179 by using @xmath180 and @xmath181 for @xmath182 , we have @xmath183 by combining this and eq . ( [ eq : bound_h0 ] ) with eq . ( [ eq : diff_hf ] ) , we obtain the theorem h_f^(n_0)(t)-h_f^(n_0)16g^2k2 ^ -n_0n_vt , [ eq : exp_slow ] where @xmath66 . this completes the proof of theorem .

we discuss the universal nature of relaxation in isolated many - body quantum systems subjected to global and strong periodic driving . our rigorous floquet analysis shows that the energy of the system remains almost constant up to an exponentially long time in frequency for arbitrary initial states and that an effective hamiltonian obtained by a truncation of the floquet - magnus expansion is a quasi - conserved quantity in a long timescale . these two general properties lead to intriguing classification on the initial stage of relaxation , one of which is similar to the prethermalization phenomenon in nearly - integrable systems . _ introduction. _ in periodically driven many - body quantum systems , excited states as well as the ground state participate in the dynamics , and nontrivial macroscopic phenomena can appear . recent years have witnessed remarkable experimental developments , such as the discoveries of the higgs mode in the oscillating order parameter of the superconducting material under a terahertz laser @xcite , and the floquet topological states in the periodically driven cold atom @xcite . periodic driving in isolated quantum systems sometimes generates unexpected dynamical phenomena even if the instantaneous hamiltonian at each time step is simple . to name only a few , dynamical localization @xcite , coherent destruction of tunneling @xcite , dynamical freezing @xcite , and dynamical phase transitions @xcite are remarkable far - from - equilibrium phenomena that can not be captured within linear - response analysis . on the other hand , as recently discussed in the context of _ thermalization _ , careful consideration is necessary on the true steady state in driven many - body systems @xcite . thermalization in isolated quantum systems has become one of critical subjects in modern physics @xcite . the first study was made by von neumann early in 1929 @xcite , and now we are on the new stage by incorporating many concepts including quantum entanglement @xcite and experiments @xcite . in the case without driving fields , the notion of the eigenstate thermalization hypothesis ( eth ) is a key idea @xcite that states that each energy eigenstate is indistinguishable from the microcanonical ensemble with the same energy . as a generalization of eth to periodically driven systems , the floquet eth was proposed , which states that all the floquet eigenstates look the same and are indistinguishable from the infinite - temperature ( i.e. , completely random ) state @xcite . this leads to the conclusion that in general periodically driven many - body systems will eventually reach the steady state of infinite temperature , although several exceptions exist @xcite . the question that follows is on the time scale to reach the steady state . recent experiments seem to urge us to clarify the general aspects of the time scale especially for the strong amplitude of global driving , where nontrivial transient dynamics is anticipated . we note that most nontrivial dynamical phenomena in driven systems are far - from - equilibrium effects that can not be analyzed within linear - response analysis . hence , in this paper , we for the first time aim to find the universal nature of the relaxation to the steady state under _ strong and global driving_. this direction is clearly crucial for a deeper understanding of thermalization and for analyzing the stability of transient dynamics in experiments . for this aim , we focus on the floquet hamiltonian @xmath0 which plays a central role in periodically driven systems : @xmath1 where @xmath2 is the hamiltonian of the system , @xmath3 is the time - ordering operator , and @xmath4 is the period of the driving ( @xmath5 throughout this paper ) . the floquet hamiltonian is an effective hamiltonian that contains full information on the stroboscopic dynamics . the floquet - magnus ( fm ) expansion is a formal expression for the floquet hamiltonian : @xmath6 @xcite . the explicit form of @xmath7 is given in eq . ( [ eq : fm ] ) below . however , it has recently been recognized that using full series expansion is problematic since it is not convergent in general . the convergence radius shrinks as the system size increases @xcite . instead we here use the technique of truncation in the fm expansion , which was recently developed for describing the floquet hamiltonian for transient time scales @xcite : @xmath8 here , @xmath9 is the @xmath10th order truncated floquet hamiltonian . there are several studies which show that the time - evolution by the truncated floquet hamiltonian is reliable up to a certain long time @xmath11 for the driving with high frequency @xmath12 @xcite ; @xmath13 for the friedrichs model on the continuous space @xcite and @xmath14 $ ] for lattice systems when driving is local @xcite or interactions are short - ranged @xcite . in this paper , we use the truncation technique for high frequency driving . with this technique , two findings are mainly presented . we show as the first result that in the case of a high - frequency driving , the truncated floquet hamiltonian is a quasi - conserved quantity ( a quantity that is almost conserved in a long timescale ) . we also show as the second result that energy absorption rate per one site is bounded for an arbitrary amplitude of driving and for arbitrary initial states : @xmath15 \ , , \label{firstresult}\end{aligned}\ ] ] where @xmath16 and @xmath17 are respectively the total energy and the number of lattice sites , and @xmath18 is the maximum energy per one site . the driving field is applied to @xmath19 sites . this provides a criterion on stability of transient quantum dynamics in experiments . these two findings lead to intriguing classification on the relaxation processes , one of which is similar to the prethermalization phenomenon seen in non - driven nearly - integrable systems @xcite , see refs . @xcite for recent relevant numerical calculations . _ setup and numerical example. _ we consider a quantum spin system defined on a lattice with @xmath17 sites in arbitrary dimension , whose hamiltonian is written as @xmath20 the driving field @xmath21 is applied to @xmath22 sites and satisfies the periodicity in time @xmath23 with zero average over the single period . we mainly focus on the regime of high - frequency @xmath12 . each lattice site @xmath24 has its own spin . the basic assumption on the hamiltonian is that it is expressed in the form of h(t)=_x:|x|kh_x(t ) , [ eq : k - local ] where @xmath25 is a set of the lattice sites with @xmath26 being the number of sites in @xmath27 , and @xmath28 is an operator acting on the sites in @xmath27 . in addition , we assume that the single site energy is bounded in the sense that _ x : xih_x(t)g [ eq : g ] with some fixed positive constant @xmath18 , where @xmath29 denotes the operator norm . the form of eq . ( [ eq : k - local ] ) means that the hamiltonian contains at most @xmath30-body interactions . for most physical applications , we can consider the case of @xmath31 . in the case of spin-(1/2 ) systems , the most general form of the hamiltonian ( [ eq : k - local ] ) with @xmath31 is h(t)=_i=1^n_i(t)_i + _ i < j^n_,=x , y , zj_ij^(t)_i^_j^ , [ eq : h_spin ] where @xmath32 is the pauli matrix of @xmath33th spin , @xmath34 is the local magnetic field at @xmath33th site , and @xmath35 denotes the interaction between @xmath33th and @xmath36th spins . we can explicitly confirm that this hamiltonian can be brought into the form of eq . ( [ eq : k - local ] ) by putting @xmath37 and @xmath38 . and @xmath39 . the dotted line in ( b ) is the expectation value in the equilibrium state of @xmath40 at the inverse temperature @xmath41 , which is determined from the expectation value of @xmath40 at @xmath42.,width=302 ] to make clear physical phenomena that we address , we show a numerical example with a toy model that has been used to show the floquet eth in @xcite . we consider dynamics over one cycle , taking @xmath43 for the first half period and @xmath44 for the second half period , where @xmath45 $ ] with the periodic boundary condition and @xmath46 . we calculate the time - evolution of the @xmath47-component of the first spin @xmath48 setting all spin - down state as the initial state . floquet eth implies that a steady state in the long - time limit is a random state , and hence , when it is satisfied , the expectation value of any local spin operator eventually reaches zero . in fig.[fig1 ] , the time - evolution for a sufficiently large system size is shown . figure [ fig1](a ) , ( b ) and ( c ) are respectively time - evolution of @xmath48 in the large timescale , the initial stage , and the transient timescale . fig.[fig1](a ) shows a vanishing expectation value that is a clear indication of the floquet eht . crucial observation is that after the initial relaxation ( fig.[fig1](b ) ) , the expectation value is almost constant for finite transient timescales , and the timescales depend on the period @xmath4 ( fig.[fig1](c ) ) . this implies that the heating process is seemingly suppressed during this timescale . this is somewhat similar to the prethermalization phenomenon in nondriven nearly - integrable systems . in experimental situations , this transient time behavior is crucial , and hence we address the mechanism of the behavior and consider the period dependence on the timescale . _ timescale of the heating process. _ we use the fm expansion for analyzing the energy absorption and the relaxation process . the fm expansion is the formal expansion of the floquet hamiltonian given by @xmath49 with @xmath50 and the @xmath10th order coefficient @xmath51 for @xmath52 being given by @xcite @xmath53}\theta[\sigma]!(n-\theta[\sigma ] ) ! \over i^n(n+1)^2n ! t^{n+1 } } \int_0^tdt_{n+1 } \dots\int_0^{t_2}dt_1 [ h(t_{\sigma(n+1)}),[h(t_{\sigma(n)}),\dots,[h(t_{\sigma(2)}),h(t_{\sigma(1)})]\dots ] ] , \label{eq : fm}\end{aligned}\ ] ] where @xmath54 is a permutation and @xmath55=\sum_{i=1}^n\theta(\sigma(i+1)-\sigma(i))$ ] with @xmath56 is the step function . it is believed that the fm expansion is divergent in many - body interacting systems @xcite . see the supplementary material for the numerical demonstration of the divergence @xcite . this divergence is not merely a mathematical phenomenon but is now thought to be an indication of heating process due to periodic driving @xcite . we define the @xmath10th order truncation of the fm expansion as in eq . ( [ trfm ] ) and show that for general spin systems the timescale of the heating is exponentially slow in frequency . to this end , we start with an intuitive explanation on our analysis . from eq . ( [ eq : fm ] ) , @xmath51 has at most @xmath57-spin effective interactions because of the multiple commutators in eq . ( [ eq : fm ] ) , which describes the collective flip of @xmath57 spins . since the energy exchange between a quantum system and the external periodic field is quantized into integer multiples of @xmath58 and the energy of each spin is bounded by @xmath18 , @xmath59 spins must flip cooperatively in order to absorb or emit the single `` energy quantum '' . such a process is taken into account only in the terms higher than the @xmath60th order in the fm expansion with @xmath61 . indeed , each term of the fm expansion is rigorously bounded from above as _ nt^n2gn_v . [ eq : bound_omega ] this is given by estimating norms of the multiple commutators taking account that the hamiltonian has at most @xmath30-body interaction and the energy per site is bounded by @xmath18 @xcite . equation ( [ eq : bound_omega ] ) shows that the fm expansion ( [ trfm ] ) looks convergent up to @xmath62 and h_f^(n)-h_f^(n_0)= n_v(t^n+1 ) ( n < n_0 ) , [ eq : convergent ] but grows rapidly for @xmath63 . therefore , we can eliminate the heating effect most efficiently by truncating the fm expansion at @xmath64 . the timescale of the heating is thus evaluated by comparing the difference between the exact time evolution and the approximate time evolution under the @xmath60th order truncated floquet hamiltonian . it is expected that higher - order terms ( i.e. simultaneous flip of a large number of spins ) would matter only in the later stage of the time evolution . we now make the above argument mathematically rigorous . we can prove the following theorem : * theorem . * _ the @xmath60th order truncated floquet hamiltonian @xmath65 is almost conserved up to an exponentially long time in frequency in the sense that _ ^ -n_0n_vt , [ eq : conserved ] _ where @xmath66 with a positive integer @xmath67 , @xmath68 , and @xmath69 is the @xmath60th order truncated floquet hamiltonian at time @xmath70 in the heisenberg picture with @xmath71 . _ this is derived by evaluating the norm of the dyson - expansion for the time - evolution operators in the left hand side taking into account that the hamiltoanin is written as eq . ( [ eq : k - local ] ) with eq . ( [ eq : g ] ) . see the supplementary material for more details on the derivation @xcite . combined with eq . ( [ eq : convergent ] ) , this theorem leads to h_f^(n)(t)-h_f^(n)16g^2k2 ^ -n_0n_vt+n_v(t^n+1 ) for any @xmath72 . in particular , by substituting @xmath73 , we obtain h_0(t)-h_0 . [ eq : exp_slow_heating ] it is noted that the term of @xmath74 in eq . ( [ eq : exp_slow_heating ] ) is independent of @xmath70 . thus , the energy density remains constant within a small fluctuation of @xmath74 until an exponentially long time in frequency . equation ( [ eq : conserved ] ) provides _ a lower bound _ on the timescale during which @xmath65 can be an approximately conserved quantity . this quasi - conserving property lasts during the timescale larger than @xmath75 . similarly , eq . ( [ eq : exp_slow_heating ] ) implies that the lower bound of the timescale of heating is an exponentially long time in frequency . this is a main result ( [ firstresult ] ) . the exponentially long timescale of the energy relaxation was shown for short - range interacting spin systems in the linear - response regime in ref . @xcite , but it should be emphasized that eq . ( [ eq : exp_slow_heating ] ) has been obtained without assuming short - range interactions and the linear - response argument . see ref . @xcite for a recent numerical result . it is remarked that for local driving with @xmath76 , a much stronger result was shown in ref . @xcite , i.e. , e^-i_0^th(s)ds - e^-ih_f^(n_0)tt [ eq : local ] for @xmath66 . this inequality implies that for any bounded operator that may be highly nonlocal , the fm truncated hamiltonian gives the accurate time evolution up to an exponentially long time . in the case of global driving @xmath77 , this strong inequality ( [ eq : local ] ) is not satisfied for sufficiently large systems , but even in this case , we can utilize the finite order truncation of the fm expansion to discuss the relaxation process as is argued below . _ relaxation process. _ our rigorous result enables us to discuss possible scenarios on the initial stage of relaxation . according to the floquet eth @xcite , the steady state in the long - time limit induced by the floquet hamiltonian ( [ fldef ] ) is a state of infinite temperature . full fm series expansion in general diverges in large quantum systems and hence it is not useful @xcite . however , the truncated floquet hamiltonian @xmath65 is a quasi - conserved quantity and plays a crucial role in the relaxation process . we make a remark on the degree of nonlocality on the quasi - conserved quantity . the @xmath60th order truncated floquet hamiltonian has effective @xmath78-body interactions , and hence the nonlocality looks large . however , for a high frequency driving , higher order contributions in the fm expansion are very small , since @xmath4 is small . the dominant contribution is in fact the original hamiltonian @xmath79 . hence , nonlocality of the truncated floquet hamiltonian is not very strong . eigenstates for the truncated floquet hamiltonian @xmath65 thus should satisfy the usual eth , not the floquet eth . in addition , we should note that from eq . ( [ eq : convergent ] ) , @xmath80 for any @xmath72 . hence these truncated floquet hamiltonians are not independent but almost the same . practically one can approximate the quasi - conserved quantity @xmath65 by @xmath81 . taking account of those , we discuss a scenario on the initial stage of relaxation . since the quasi - conserved quantity exists with long lifetime , the system relaxes to _ a quasi - stationary state _ characterized by the quasi - conserved quantity , which will be close to a state corresponding to the ( micro)canonical ensemble @xmath82 of the effective hamiltonian @xmath65 set by the initial state . approximately one can use @xmath83 ( the equilibrium ensemble of @xmath79 ) instead of @xmath82 because @xmath80 for any @xmath72 . the initial stage of relaxation can be classified into two cases , i.e. , ( i ) the case where the relaxation to the quasi - stationary state is faster than the energy relaxation , and ( ii ) the case where both relaxation times are comparable . in the case ( i ) , the system first reaches the quasi - stationary state , and then relaxes to the true steady state . this is highly related to the prethermalization phenomenon in the isolated nearly - integrable systems @xcite , where the system first relaxes to a quasi - stationary state corresponding to the generalized gibbs ensemble and next relaxes to the true steady state . this is what we numerically observed in fig.[fig1 ] ( b ) and ( c ) . remarkably , in fig . [ fig1 ] ( b ) and ( c ) , @xmath84 in the quasi - stationary state , which is close to @xmath85 ( the dotted line in fig . [ fig1 ] ( b ) ) at the inverse temperature @xmath41 that is determined from the expectation value of @xmath40 at @xmath42 . this fact indicates that the quasi - stationary state is actually described by @xmath83 in this model . in the case ( ii ) , on the other hand , the relaxation process towards the quasi - stationary state and that towards the true steady state are indistinguishable , and hence stable quasi - stationary behavior is not observed in the initial stage of relaxation . because the timescale of energy relaxation becomes longer exponentially as the frequency increases , we expect to find the case ( i ) for sufficiently high - frequencies unless there is some special reason such as conservation laws @xcite , strong quenched disorder @xcite , diverging timescale due to quantum criticality @xcite , and so on . our analysis deals with general spin models , which makes clear why the heating is slow in a precise manner and leads us to the universal scenario of relaxation processes . however , in our evaluation , the single - site energy is overestimated and the effect of quantum interference is underestimated . hence , the divergence of the fm expansion presumably begins at a higher order than our estimation @xmath86 . we stress that our estimation on the timescale is _ a rigorous lower bound _ that can be exponentially large in frequency , and hence the actual timescale of the heating will be longer than our estimation is typically about @xmath87 hz , @xmath31 , and then the condition @xmath88 implies @xmath89 khz , which has been achieved in experiment [ a. zenesini , h. lignier , d. ciampini , o. morsch , and e. arimondo , http://link.aps.org/doi/10.1103/physrevlett.102.100403[phys . rev . lett . * 102 * , 100403 ( 2009 ) ] ] . according to our estimation , the heating timescale in this case is about 1 msec , which is a typical timescale of cold - atom experiments . ] . in order to obtain a quantitatively accurate estimate for a specific model , we will have to study the quantum dynamics of the given model numerically . related to the above remark , we emphasize that our result does not tell us about the true steady state . it should be an infinite - temperature state if the floquet eth holds . however , another possibility is not excluded ; there might be an energy - localized phase @xcite with vanishing energy - absorption rate . it is an open problem to understand the precise condition of the floquet eth . _ summary. _ in summary , we have considered the quantum dynamics of general driven spin systems that have at most @xmath30-body interactions and a bounded single - site energy @xmath18 . we have rigorously shown the theorem stating that the truncated floquet hamiltonian is a quasi - conserved quantity and the rate of energy absorption is exponentially small in frequency . this finding enables us to classify the initial stage of relaxation . it is emphasized that we need not assume short - range interactions in the hamiltonian ( [ eq : h_spin ] ) . for instance , @xmath90 , which corresponds to the heisenberg all - to - all couplings , satisfies the condition of eq . ( [ eq : g ] ) with a fixed value of @xmath18 even in the thermodynamic limit . therefore , the result in this paper is applicable to most physically - relevant spin models . however , as seen in eq . ( [ eq : g ] ) , our argument excludes bosonic systems . we expect that our analysis will help to understand even for bosonic systems . we are grateful to naomichi hatano and hal tasaki for critical reading of the manuscript . t.m . was supported by the jsps core - to - core program `` non - equilibrium dynamics of soft matter and information '' and jsps kakenhi grant no . 15k17718 . t.k . acknowledges the support from jsps grant no . 2611111 . k.s . was supported by mext grant no . . _ note added . _ recently , closely related results in a different approach have appeared @xcite . 49ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1126/science.1254697 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.111.185301 [ * * , ( ) ] link:\doibase 10.1038/nphys2790 [ * * , ( ) ] link:\doibase 10.1038/nature13915 [ * * , ( ) ] link:\doibase 10.1038/nphys3171 [ * * , ( ) ] link:\doibase 10.1103/physrevb.34.3625 [ * * , ( ) ] link:\doibase 10.1016/s0370 - 1573(98)00022 - 2 [ * * , ( ) ] link:\doibase 10.1103/physreva.77.010101 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.67.516 [ * * , ( ) ] link:\doibase 10.1103/physrevb.82.172402 [ * * , ( ) ] link:\doibase 10.1103/physrevb.90.174407 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.107.060403 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.108.043003 [ * * , ( ) ] link:\doibase 10.1088/0953 - 4075/47/2/025501 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.109.257201 [ * * , ( ) ] link:\doibase 10.1016/j.aop.2013.02.011 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.112.150401 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.115.030402 [ * * , ( ) ] link:\doibase 10.1016/j.aop.2014.11.008 [ * * , ( ) ] link:\doibase 10.1103/physreva.43.2046 [ * * , ( ) ] link:\doibase 10.1103/physreve.50.888 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.80.1373 [ * * , ( ) ] link:\doibase 10.1038/nature06838 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.83.863 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.108.110401 [ * * , ( ) ] link:\doibase 10.1007/bf01339852 [ * * , ( ) ] link:\doibase 10.1038/nphys444 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.80.885 [ * * , ( ) ] link:\doibase 10.1103/physrevx.4.041048 [ * * , ( ) ] link:\doibase 10.1103/physreve.90.012110 [ * * , ( ) ] link:\doibase 10.1103/physreve.90.052105 [ * * , ( ) ] link:\doibase 10.1016/j.physrep.2008.11.001 [ * * , ( ) ] link:\doibase 10.1080/00018732.2015.1055918 [ * * , ( ) ] link:\doibase 10.1103/physreva.91.020101 [ * * , ( ) ] link:\doibase 10.1016/j.aop.2016.01.012 [ * * , ( ) ] http://arxiv.org/abs/1509.05386 [ ( ) ] http://arxiv.org/abs/1510.03405 [ ( ) ] link:\doibase 10.1103/physrevlett.93.142002 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.100.175702 [ * * , ( ) ] link:\doibase 10.1126/science.1224953 [ * * , ( ) ] link:\doibase 10.1103/physrevb.84.054304 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.115.205301 [ * * , ( ) ] link:\doibase 10.1103/physreve.93.012130 [ * * , ( ) ] link:\doibase 10.1016/0003 - 4916(69)90351 - 0 [ * * , ( ) ] @noop link:\doibase 10.1103/physrevlett.115.256803 [ * * , ( ) ] http://arxiv.org/abs/1512.02119 [ ( ) ] link:\doibase 10.1103/physrevlett.95.245701 [ * * , ( ) ] * supplementary material for + `` rigorous bound on energy absorption and generic relaxation in periodically driven quantum systems '' * + takashi mori@xmath91 , tomotaka kuwahara@xmath91 and keiji saito @xmath92 + @xmath91_department of physics , graduate school of science , university of tokyo , bunkyo - ku , tokyo 113 - 0033 , japan _ + @xmath92_department of physics , keio university , yokohama 223 - 8522 , japan _ +

the diffuse galactic emission ( dge ) arises from interactions of cosmic - rays ( crs ) with interstellar gas and radiation field in the galaxy . due to the smooth nature of the interstellar radiation field and the cr flux after propagation , the fine structure of the dge is determined by the structure of the interstellar gas . getting the distribution of the interstellar gas correct is therefore crucial when modeling the dge . it is generally assumed that galactic crs are accelerated in interstellar shocks and then propagate throughout the galaxy ( see e.g. * ? ? ? * for a recent review . ) . in this paper , cr propagation and corresponding diffuse emission is calculated using the galprop code ( see * ? ? ? * and references within . ) . we use the so - called conventional galprop model @xcite , where the cr injection spectra and the diffusion parameters are chosen such that the cr flux agrees with the locally observed one after propagation . the gas distribution is given as galacto - centric annuli and the diffuse emission is calculated for those same annuli . the distribution of h i is determined from the 21-cm lab line survey @xcite while distribution of molecular hydrogen , h@xmath1 , is found using the co ( @xmath2 ) survey of @xcite assuming @xmath3 . while converting observations of the 21-cm h i line to column density is theoretically possible , it is not practically feasible . to correctly account for the optical depth of the emitting h i gas , one must know its spin temperature , @xmath0 ( see e.g. * ? ? ? * ) . under the assumption of a constant @xmath0 along the line of sight , the column density of h i can be calculated from the observed brightness temperature @xmath4 using @xmath5 where @xmath6 is the background continuum temperature and @xmath7 @xmath8 k ( km / s)@xmath9 . the assumption of a constant @xmath0 along the line of sight is known to be wrong for many directions in the galaxy ( see e.g. * ? ? ? the @xmath0 values derived in this paper are therefore only a global average and should not be taken at face value . figure [ fig : tsratio ] shows how changing @xmath0 affects @xmath10 in a non - linear way , mainly affecting areas with @xmath4 close to @xmath0 in the galactic plane . this figure was created under the assumption of a fixed @xmath0 for the whole galaxy that is known to be wrong but has been used for dge analysis from the days of cos - b @xcite . note that for equation ( [ eq : opticaldepthcorrection ] ) to be valid the condition @xmath11 must hold . when generating the gas annuli , this condition is forced by clipping the value of @xmath4 . while the assumption of a constant spin temperature @xmath12 for the whole galaxy may have been sufficient for older instrument , it is no longer acceptable for a new generation experiment like fermi - lat @xcite . this has been partially explored for the outer galaxy in @xcite . in this paper we will show a better assumption for @xmath0 can be easily found and also show that direct observations of @xmath0 using absorption measurement of bright radio sources are needed for accurate dge modeling . in galactic coordinates . the figure clearly shows the non - linearity of the correction that can be as high as a factor of 2 in this case.,width=283 ] we assume the source distribution of cr nuclei and electrons are the same . cr propagation is handled by galprop and we use the conventional model so that after the propagation the cr spectra agree with local observations . the galprop diffuse emission is output in galacto - centric annuli , split up into different components corresponding to different processes ( bremsstrahlung , @xmath13-decay , and inverse compton scattering ) . to allow for radial variations in cr intensity we perform a full sky maximum likelihood fit , preserving the spectral shape of each component . we allow for one global normalization factor for the electron to proton ratio . additionally , we also allow for radial variation in the @xmath14 factor . this accounts for uncertainties in the cr source distribution and @xmath14 factor . the maximum likelihood fits were performed on the whole sky using the gardian package @xcite after preparing the fermi - lat data with the science tools . we use the same dataset as @xcite that has special cuts to reduce cr background contamination compared to the standard event selection @xcite . in addition to the dge model , we also include all sources from the 1 year fermi - lat source list @xcite and an isotropic component to account for egb emission and particle contamination . this fit is performed for different assumptions of @xmath0 and a likelihood ratio test is used to compare the quality of the fits . the simplest assumption is that of a constant @xmath0 for the whole galaxy and it deserves some attention for historical reasons . it will also serve as a baseline model for comparison with other assumptions . to get an approximation for the best model , we scan @xmath0 from 110 k to 150 k in 5 k steps . our results show that @xmath15 gives the maximum likelihood for this setup . one of the problems with the constant global @xmath0 approximation , apart from the fact that observations of the interstellar gas have shown it to be wrong , is that the maximum observed brightness temperature in the lab survey is @xmath16150 k which is greater than our best fit global @xmath0 . this is solved by clipping the observations when generating the gas annuli , which is not an optimal solution . a different possibility is to use the assumption @xmath17 here , @xmath18 is the maximum observed brightness temperature for each line of sight . this ensures @xmath0 is always greater than @xmath4 . scanning the values of @xmath19 and @xmath20 with a step size of 10 k and 5 k , respectively , gives us a maximum likelihood for @xmath21 and @xmath22 . while this assumption still does not account for the complexity of the interstellar medium , the log likelihood ratio between the best fit linear relation model and the best fit constant @xmath0 model is of the order of 1000 , a significant change . the most accurate @xmath0 estimates come from observations of h i in absorption against bright radio sources . we gathered over 500 lines of sight with observed @xmath0 from the literature @xcite . this covers about 0.2% of the pixels in the lab survey , allowing for accurate column density estimates only in those pixels . after taking our best fit linear relation model and correcting the pixels with known @xmath0 the fit was redone for the whole sky . note that we did not change the values of @xmath23 and @xmath20 . the log likelihood ratio of 105 tells us that this model is worse than the best fit linear relation . this is not unexpected , since the gamma rays are generated from cr interactions with the gas and if the gas distribution is wrong , we wo nt get the correct cr distribution from the fit . to limit the uncertainty involved with the linear relation assumption , we did another fit , limiting ourselves to the region @xmath24 , @xmath25 that covers the observations made in the canadian galactic plane survey ( cgps ) where the density of @xmath0 observations is the highest and is large enough to get a good fit to the lat data . the fit in this region results in a log likelihood ratio of 28 indicating a statistically significant improvement in the fit . this is despite the observed @xmath0 lines of sight only covering 25% of the fitted region and the values of @xmath19 and @xmath20 not being adjusted after correcting for known @xmath0 values . our small exercise here has shown that for accurate dge modeling we need to know more about the distribution of gas in the galaxy , especially the h i distribution . the standard constant @xmath0 assumption is not sufficient for current instruments and small adjustments cause large differences in the quality of the resulting model . we also show that direct observations of @xmath0 help in creating a better model of the dge . unfortunately , direct observations of @xmath0 are difficult since they require high resolution telescopes and bright radio continuum sources . some assumptions will therefore have to be made for the regions in between bright radio sources . it must be stated here that all of the above results are model dependent . the fermi - lat data can only provide us with the intensity of gamma - rays from a particular direction of the sky . uncertainties in our modeling of contribution other than those directly related to the h i distribution will affect the value obtained for @xmath0 . we are currently studying the systematic effects this will have on our results . we also note that even for the best fit models , the residuals show signs of structure , strongly indicating our models are less than perfect .

the diffuse high - energy gamma - ray emission of the milky way arises from interactions of cosmic - rays ( crs ) with interstellar gas and radiation field in the galaxy . the neutral hydrogen ( h i ) gas component is by far the most massive and broadly distributed component of the interstellar medium . using the 21-cm emission line from the hyperfine structure transition of atomic hydrogen it is possible to determine the column density of h i if the spin temperature ( @xmath0 ) of the emitting gas is known . studies of diffuse gamma - ray emission have generally relied on the assumption of a fixed , constant spin temperature for all h i in the milky way . unfortunately , observations of h i in absorption against bright background sources has shown it to vary greatly with location in the milky way . we will discuss methods for better handling of spin temperatures for galactic diffuse emission modeling using the fermi - lat data and direct observation of the spin temperature using h i absorption .