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for fixed integers @xmath0 and @xmath1 , we consider the admissible sequences of @xmath2 lattice paths in a colored @xmath3 square given in @xcite . each admissible sequence of paths can be associated with a partition @xmath10 of @xmath4 . in section
[ paths ] , we show that the number of self - conjugate admissible sequences of paths associated with @xmath10 is equal to the number of standard young tableaux of shape @xmath10 , and thus can be calculated using the hook length formula .
we extend this result to include the non - self - conjugate admissible sequences of paths and show that the number of all such admissible sequences of paths is equal to the sum of squares of the number of standard young tableaux of partitions of @xmath4 with height less than or equal to @xmath11 . using the rsk correspondence in @xcite ,
it is shown in ( @xcite , corollary 7.23.12 ) that the sum of squares of the number of standard young tableaux of partitions of @xmath4 with height less than or equal to @xmath11 is equal to the number of @xmath6-avoiding permutations of @xmath7 . in section [ multiplicities ]
, we apply our results to the representation theory of the affine kac - moody algebra @xmath8 .
let @xmath12 , @xmath13 and @xmath14 denote the simple roots , simple coroots , and fundamental weights respectively .
note that @xmath15
. for @xmath16 , set @xmath17 and @xmath18 . as shown in @xcite , @xmath19
are maximal dominant weights of the irreducible @xmath8-module @xmath9 .
we show that the multiplicity of the weight @xmath19 in @xmath9 is the number of @xmath6-avoiding permutations of @xmath7 , which proves conjecture 4.13 in @xcite .
for fixed integers @xmath0 and @xmath1 , consider the @xmath3 square containing @xmath20 unit boxes in the fourth quadrant so that the top left corner of the square is at the origin .
we assign color @xmath21 to a box if its upper left corner has coordinates @xmath22 .
this gives the following @xmath3 colored square @xmath23 : a lattice path @xmath25 on @xmath23 is a path joining the lower left corner @xmath26 to the upper right corner @xmath27 moving unit lengths up or right . for two lattice paths @xmath28 on @xmath23
we say that @xmath29 if the boxes above @xmath30 are also above @xmath25 .
now , we draw @xmath2 lattice paths , @xmath31 on @xmath23 such that @xmath32 . for integers
@xmath33 , where @xmath34 , @xmath35 , we define @xmath36 to be the number of @xmath37-colored boxes between @xmath38 and @xmath39 .
we define @xmath40 to be the number of @xmath37-colored boxes below @xmath41 and @xmath42 to be the number of @xmath37-colored boxes above @xmath43 .
denote by @xmath49 the set of all admissible sequences of @xmath2 paths .
notice that there are @xmath4 0-colored boxes in @xmath23 and hence for any admissible sequence of paths , @xmath50 .
in addition , it follows from definition [ pathsdef](2 ) that @xmath51 for any admissible sequence of paths .
thus , we can and do associate an admissible sequence of paths @xmath44 on @xmath23 with a partition @xmath52 of @xmath4 . in this case , we say that this admissible sequence of paths is of type @xmath10 and often draw @xmath10 as a young diagram .
figure [ adseq](a ) is an element of @xmath53 , where @xmath54 and @xmath55 are shown in figures [ adseq](b ) , [ adseq](c ) , and [ adseq](d ) , respectively .
notice that this admissible sequence of paths is of type @xmath56 . | for @xmath0 and @xmath1 , we consider certain admissible sequences of @xmath2 lattice paths in a colored @xmath3 square .
we show that the number of such admissible sequences of lattice paths is given by the sum of squares of the number of standard young tableaux of partitions of @xmath4 with height @xmath5 , which is also the number of @xmath6-avoiding permutations of @xmath7 .
finally , we apply this result to the representation theory of the affine lie algebra @xmath8 and show that this quantity gives the multiplicity of certain maximal dominant weights in the irreducible module @xmath9 . |
a magnitude limited complete census of variable stars in nearby dwarf galaxies allows important contributions to the star formation history of these systems . measurements of some variable stars can supply improved distance determinations for the host galaxies , others will provide important constraints for the population analysis .
different classes of variables can further improve the understanding of the star formation history of these system , functioning as tracers of star formation during different epochs .
we expect the data set of our long term monitoring program to be especially well suited to study the contents of red long - period variables and to re - investigate the paucity of cepheids with @xmath1 days as reported by sandage & carlson ( 1985 ) .
we selected a sample of six local group dwarf irregular galaxies which are visible with the 0.8 m telescope of our institute at mt .
the names and additional data from the literature compilation by mateo ( 1998 ) are shown in table 1 .
.names , variable star counts , absolute @xmath2-band brightness in mag , and current distance estimation in kpc for the dwarf galaxies observed in our project .
the data are taken from the literature compilation by mateo ( 1995 ) .
for leo a the data are from the work of dolphin et .
al ( 2002 ) and from this work . [ cols="<,<,^,^,^,^,^ " , ] @xmath3 this work the observations so far were carried out in @xmath4 and @xmath2-band , sparsely sampling a three year period starting with test observations in 1999 .
this part of the data set should be sensitive for long period variable stars with periods up to @xmath5 days .
additional observations in @xmath4 , @xmath2 and @xmath6-band were obtained during 3 observing campaigns at the 1.23 m telescope on calar alto densely sampling three two week long periods .
these observations should provide a ground for a search for variable stars with shorter periods ranging from @xmath7 days up to @xmath8 days .
the acquired data were bias subtracted , flat - fielded and cosmic ray rejected .
then , the images from one night were astrometrically aligned to a common reference frame and combined with individual weights proportional to their @xmath9 . for each epoch , consisting of all the stacked images of a single night , a difference image against a common deep reference frame was created using an implementation ( gssl & riffeser , 2002 , 2003 ) of the alard algorithm ( alard & lupton , 1998 ) .
finally , these difference images were convolved with a stellar psf . to extract lightcurves from the reduced data ,
first all pixels deviating significantly ( @xmath10 ) from the reference image in a minimum number of epochs @xmath11 were flagged , utilizing the complete per - pixel error propagation of our data reduction pipeline .
then , using these coordinates as input , values and associated errors are read from the difference images and the lightcurve data are assembled . to search for periodic signals in the extracted difference fluxes , a lomb ( 1976 ) algorithm using the interpretation from scargle ( 1982 )
is applied .
the photometric calibration was conducted using the hst data published by schulte - ladbeck et al .
for the galaxies leo a , and ugca 92 , we have a very good monitoring and a large fraction of the data passed already the pipeline .
the leo a data set serves as test case : a total of 26 variable star candidates were detected . among them
, we identified 16 secure long period variables ( typical average values @xmath12 , and @xmath13 period [ days ] @xmath14 ) , and we have 8 further candidates for lpvs .
in addition we were able to identify two good candidates for @xmath0 cephei stars with best fitting periods of 6.4 and 1.69 days .
the later candidate was previously described by dolphin et al .
( 2002 ) as c2-v58 with a period of 1.4 days . the dolphin et al .
period solution fails in deriving a reliable lightcurve with our data , yet , applying our period value to their data set yields reasonable results .
the phase convolved lightcurves for the two @xmath0 cephei variables are shown in figure 1 .
the color magnitude diagram shown in the left panel of figure 2 is based upon the hst data published by tolstoy et al .
( 1996 ) and schulte - ladbeck et al . flagged by bigger symbols
are those variables from our sample that lie inside the hst field of view , two @xmath0 cephei variables in the instability strip ( crosses ) and the candidates for long term variability ( triangles ) in the regime of the red giants .
tolstoy et al .
( 1996 ) based on ground - based data found a distance modulus for leo a of 24.2 and a resulting distance of 690 kpc ( see also schulte - ladbeck et al . ) .
this result got further support by the search for short periodic variables with the wiyn telescope within 3 consecutive days in dec . 2000 ( dolphin et al .
our data complement this dataset for longer periods .
the right hand panel of figure 2 shows the period - luminosity ( pl ) relation of the smc shifted to the distance determined by tolstoy et al .
the short period variables measured by dolphin coincide with the shown pl relation .
the overplotted values for the two cepheids from our survey ( crosses ) support this relation also in the regime of longer periods .
we presented preliminary results for our survey for variable stars in a sample of irregular local group dwarf galaxies . for the leo a dwarf galaxy , the best analysed case so far
, we already identified a total of 26 candidates for variability , 16 of these as long period variables and 2 @xmath0 cephei stars .
we compared the later with the period - luminosity relation and the short period variables discussed by dolphin et al .
we found , that our cepheids fully support their findings and the resulting distance estimate for leo a. this result is further in good agreement with the trgb distance ( tolstoy et al .
, schulte - ladbeck et al . ) .
the location of the lpvs in the color - magnitude diagram indicate that most of them are early asymptotic giant branch stars .
while a complete census of these intermediate age stars is missing for most of the local group members , a proper statistic of their appearance can guide the reconstruction of the star formation history at the age of several gyr by - passing the age metalicity degeneracy inherent to color magnitude diagram studies .
we like to thank drs .
i. drozdovsky , c. maraston , r.e .
schulte - ladbeck , and e. tolstoy for helpful discussion .
we acknowledge the support of the calar alto and wendelstein staff .
j. fliri and a. riffeser carried out some of our observations .
the project is supported by the deutsche forschungsgemeinschaft grant ho 1812/3 - 1 and ho 1812/3 - 2 .
alard , c. & lupton , r. h. , , 503 , 325 dolphin , a. e. et al .
2002 , , 123 , 3154 gssl c. a. & riffeser a. 2002 , , 381 , 1095 gssl , c. a. & riffeser , a. 2003 , asp conf .
295 , 229 lomb n. r. 1976 , , 39 , 447 mateo m. l. 1998 , , 36 , 435 sandage , a. & carlson , g. 1985 , , 90 , 1464 scargle j. d. 1982 , , 263 , 835 schulte - ladbeck r. et al .
2002 , , 124 , 896 tolstoy e. et al .
1996 , , 116 , 1244 | dwarf galaxies in the local group provide a unique astrophysical laboratory . despite their proximity some of these systems still lack a reliable distance determination as well as studies of their stellar content and star formation history .
we present first results of our survey of variable stars in a sample of six local group dwarf irregular galaxies . taking the leo a dwarf galaxy as an example we describe observational strategies and data reduction .
we discuss the lightcurves of two newly found @xmath0 cephei stars and place them into the context of a previously derived p - l relation .
finally we discuss the lpv content of leo a. |
there are reasons to believe that cosmic rays ( crs ) around the ankle at @xmath0 gev are dominated by extragalactic protons @xcite .
scattering processes in the cosmic microwave background ( cmb ) limit the propagation of ultra high energy ( uhe ) charged particles in our universe .
a continuation of a power - like cr spectrum above the greisen - zatsepin - kuzmin ( gzk ) cutoff @xcite at about @xmath1 gev is only consistent with the proton dominance if the sources lie within the proton attenuation length of about 50 mpc .
very few astrophysical accelerators can generate crs with energies above the gzk cutoff ( see e.g. @xcite for a review ) and so far none of the candidate sources have been confirmed in our local environment .
it has been speculated that decaying superheavy particles , possibly some new form of dark matter or remnants of topological defects , could be a source of uhe crs , but also these proposals are not fully consistent with the cr spectrum at lower energies @xcite .
the observation of gzk excesses has led to speculations about a different origin of uhe crs .
berezinsky and zatsepin @xcite proposed that _
cosmogenic _ neutrinos produced in the decay of the gzk photopions could explain these events assuming a strong neutrino nucleon interaction .
we have followed this idea in ref .
@xcite and investigated the statistical goodness of scenarios with strongly interacting neutrinos from optically thin sources using cr data from agasa @xcite and hires @xcite ( see fig . [ cr ] ) and limits from horizontal events at agasa @xcite and contained events at rice @xcite .
-branes , and string excitations ( see ref .
@xcite ) . ]
the flux of uhe extragalactic protons from distant sources is redshifted and also subject to @xmath2 pair production and photopion - production in the cmb which can be taken into account by means of propagation functions .
the resonantly produced photopions provide a _ guaranteed _ source of cosmogenic uhe neutrinos observed at earth . in astrophysical accelerators inelastic scattering of the beam protons off the ambient photon gas in the source will also produce photopions which provide an additional source of uhe neutrinos . the corresponding spectrum will in general depend on the details of the source such as the densities of the target photons and the ambient gas @xcite .
we have used the flux of crs from _ optically thin _ sources using the luminosities given in ref .
@xcite in the goodness - of - fit test . for a reasonable and consistent contribution of extragalactic neutrinos in vertical crs
one has to assume a strong and rapid enhancement of the neutrino nucleon interaction .
the realization of such a behavior has been proposed in scenarios beyond the ( perturbative ) sm ( see ref .
@xcite ) . for convenience
, we have approximated the strong neutrino nucleon cross section in our analysis by a @xmath3-behavior shown in fig .
[ fig ] , parameterized by the energy scale and width of the transition , and the amplification compared to the standard model predictions .
our analysis showed that uhe crs measured at agasa and hires can be interpreted to the 90% cl as a composition of extragalactic protons and strongly interacting neutrinos from optically thin sources in agreement with experimental results from horizontal events at agasa and contained events at rice ( see fig .
[ fig ] ) .
the pierre auger observatory combines the experimental techniques of agasa and hires as a hybrid detector . with a better energy resolution , much higher statistics and also stronger bounds on horizontal showers
it will certainly help to clarify our picture of uhe crs in the future .
the author would like to thank the organizers of the erice school on nuclear physics 2005 _ `` neutrinos in cosmology , in astro , particle and nuclear physic '' _ for the inspiring workshop and vihkos ( _ `` virtuelles institut fr hochenergiestrahlungen aus dem kosmos '' _ ) for support .
m. ahlers , a. ringwald , and h. tu , _ astropart .
( to appear ) , preprint astro - ph/0506698 .
v. berezinsky , a. z. gazizov and s. i. grigorieva , preprint hep - ph/0204357 ; v. berezinsky , a. z. gazizov and s. i. grigorieva , .
m. ahlers _
et al . _ , .
k. greisen , ; g. t. zatsepin and v. a. kuzmin , .
d. f. torres and l. a. anchordoqui , .
d. v. semikoz and g. sigl , .
v. s. beresinsky and g. t. zatsepin , .
m. takeda _
et al . _ [ agasa ] , .
d. j. bird _
et al . _
[ hires ] , ; r. u. abbasi _ et al . _ [ hires ] , ; r. u. abbasi _ et al . _ [ hires ] , . s. yoshida _
_ [ agasa ] , . | the origin and chemical composition of ultra high energy cosmic rays is still an open question in astroparticle physics .
the observed large - scale isotropy and also direct composition measurements can be interpreted as an extragalactic proton dominance above the _ ankle _ at about @xmath0 gev .
photopion production of extragalactic protons in the cosmic microwave background predicts a cutoff at about @xmath1 gev in conflict with excesses reported by some experiments . in this report
we will outline a recent statistical analysis @xcite of cosmic ray data using strongly interacting neutrinos as primaries for these excesses . |
in solid - core photonic crystal fibers ( pcf ) the air - silica microstructured cladding ( see fig . [ fig1 ] ) gives rise to a variety of novel phenomena @xcite including large - mode area ( lma ) endlessly - single mode operation @xcite .
though pcfs typically have optical properties very different from that of standard fibers they of course share some of the overall properties such as the susceptibility of the attenuation to macro - bending .
macrobending - induced attenuation in pcfs has been addressed both experimentally as well as theoretically / numerically in a number of papers @xcite . however , predicting bending - loss is no simple task and typically involves a full numerical solution of maxwell s equations as well as use of a phenomenological free parameter , _
e.g. _ an effective core radius . in this paper
we revisit the problem and show how macro - bending loss measurements on high - quality pcfs can be predicted with high accuracy using easy - to - evaluate empirical relations .
predictions of macro - bending induced attenuation in photonic crystal fibers have been made using various approaches including antenna - theory for bent standard fibers @xcite , coupling - length criteria @xcite , and phenomenological models within the tilted - index representation @xcite . here
, we also apply the antenna - theory of sakai and kimura @xcite , but contrary to refs .
@xcite we make a full transformation of standard - fiber parameters such as @xmath1 , @xmath2 , and @xmath0 @xcite to fiber parameters appropriate to high - index contrast pcfs with a triangular arrangement of air holes . in the large - mode area
limit we get ( see appendix ) @xmath3 for the power - decay , @xmath4 , along the fiber . for a conversion to a db - scale @xmath5 should be multiplied by @xmath6 . in eq .
( [ alpha_lma ] ) , @xmath7 is the bending radius , @xmath8 is the effective area @xcite , @xmath9 is the index of silica , and @xmath10 is the recently introduced effective v - parameter of a pcf @xcite .
the strength of our formulation is that it contains no free parameters ( such as an arbitrary core radius ) and furthermore empirical expressions , depending only on @xmath11 and @xmath12 , have been given recently for both @xmath8 and @xmath13 @xcite . from the function
@xmath14 we may derive the parametric dependence of the critical bending radius @xmath15 .
the function increases dramatically when the argument is less than unity and thus we may define a critical bending radius from @xmath16 where @xmath17 . typically the pcf is operated close to cut - off where @xmath18 @xcite so that the argument may be written as @xmath19 this dependence was first reported and experimentally confirmed by birks
_ et al . _
@xcite and recently a pre - factor of order unity was also found experimentally in ref .
we have fabricated three lma fibers by the stack - and - pull method and characterized them using the conventional cut - back technique .
all three fibers have a triangular air - hole array and a solid core formed by a single missing air - hole in the center of the structure , see fig .
[ fig1 ] . for the lma-20 macro - bending loss has been measured for bending radii of r=8 cm and r=16 cm and
the results are shown in fig .
the predictions of eq .
( [ alpha_lma ] ) are also included .
it is emphasized that the predictions are based on the empirical relations for @xmath8 and @xmath13 provided in refs . @xcite and @xcite respectively and therefore do not require any numerical calculations .
similar results are shown in figs .
[ fig3 ] and [ fig4 ] for the lma-25 and lma-35 fibers , respectively .
the pcf , in theory , exhibits both a short and long - wavelength bend - edge .
however , the results presented here only indicate a short - wavelength bend - edge .
the reason for this is that the long - wavelength bend - edge occurs for @xmath20 @xcite . for typical lma - pcfs
it is therefor located in the non - transparent wavelength regime of silica .
in conclusion we have demonstrated that macro - bending loss measurements on high - quality pcfs can be predicted with good accuracy using easy - to - evaluate empirical relations with only @xmath21 and @xmath22 as input parameters .
since macro - bending attenuation for many purposes and applications is the limiting factor we believe that the present results will be useful in practical designs of optical systems employing photonic crystal fibers .
the starting point is the bending - loss formula for a gaussian mode in a standard - fiber @xcite @xmath23 where @xmath8 is the effective area , @xmath24 is the core radius , @xmath7 is the bending radius , and the standard - fiber parameters are given by @xcite @xmath25 substituting these parameters into eq .
( [ alpha1 ] ) we get @xmath26 in the relevant limit where @xmath27 . here ,
@xmath28 and @xmath29 in eqs . ( [ alpha_lma ] ) and ( [ v_pcf ] ) have been introduced . for large - mode area fibers we make a further simplification for the isolated propagation constant ; using that @xmath30 we arrive at eq .
( [ alpha_lma ] ) .
m. d. nielsen acknowledges financial support by the danish academy of technical sciences . | we report on an easy - to - evaluate expression for the prediction of the bend - loss for a large mode area photonic crystal fiber ( pcf ) with a triangular air - hole lattice .
the expression is based on a recently proposed formulation of the v - parameter for a pcf and contains no free parameters .
the validity of the expression is verified experimentally for varying fiber parameters as well as bend radius . the typical deviation between the position of the measured and the predicted bend loss edge is within measurement uncertainty . 10 url # 1`#1`urlprefix[2][]#2 j. c. knight , `` photonic crystal fibres , '' nature * 424 * , 847851 ( 2003 ) .
t. a. birks , j. c. knight , and p. s. j. russell , `` endlessly single mode photonic crystal fibre , '' opt . lett .
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t. srensen , j. broeng , a. bjarklev , e. knudsen , and s. e. b. libori , `` macro - bending loss properties of photonic crystal fibre , '' electron . lett . * 37 * , 287289 ( 2001 ) .
t. srensen , j. broeng , a. bjarklev , t. p. hansen , e. knudsen , s. e. b. libori , h. r. simonsen , and j. r. jensen , `` spectral macro - bending loss considerations for photonic crystal fibres , '' iee proc .- opt .
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( chapman & hall , new york , 1983 ) .
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express * 10 * , 341348 ( 2002 ) .
http://www.opticsexpress.org/abstract.cfm?uri=opex-10-7-341 .
n. a. mortensen , j. r. folkenberg , m. d. nielsen , and k. p. hansen , `` modal cut - off and the @xmath0parameter in photonic crystal fibers , '' opt . lett . * 28 * , 18791881 ( 2003 ) .
m. d. nielsen , n. a. mortensen , j. r. folkenberg , and a. bjarklev , `` mode - field radius of photonic crystal fibers expressed by the @xmath0parameter , '' opt
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* 28 * , 23092311 ( 2003 ) . m. d. nielsen and n. a. mortensen , `` photonic crystal fiber design based on the @xmath0parameter , '' opt .
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http://www.opticsexpress.org / abstract.cfm?uri = opex-11 - 21 - 2762% [ http://www.opticsexpress.org / abstract.cfm?uri = opex-11 - 21 - 2762% ] . |
in @xcite a database containing a solution of the 3d incompressible navier - stokes ( ns ) equations is presented .
the equations were solved numerically with a standard pseudo - spectral simulation in a periodic domain , using a real space grid of @xmath0 grid points .
a large - scale body force drives a turbulent flow with a taylor microscale based reynolds number @xmath1 . out of this solution ,
@xmath2 snapshots were stored , spread out evenly over a large eddy turnover time .
more on the simulation and on accessing the data can be found at http://turbulence.pha.jhu.edu . in practical terms
, we have easy access to the turbulent velocity field and pressure at every point in space and time .
one usual way of visualising a turbulent velocity field is to plot vorticity isosurfaces see for instance the plots from @xcite .
the resulting pictures are usually very `` crowded '' , in the sense that there are many intertwined thin vortex tubes , generating an extremely complex structure .
in fact , the picture of the entire dataset from @xcite looks extremely noisy and it is arguably not very informative about the turbulent dynamics . in this work ,
we follow a different approach .
first of all , we use the alternate quantity @xmath3 first introduced in @xcite .
secondly , the tool being used has the option of displaying data only inside clearly defined domains of 3d space .
we can exploit this facility to investigate the multiscale character of the turbulent cascade . because vorticity is dominated by the smallest available scales in the velocity
, we can visualize vorticity at scale @xmath4 by the curl of the velocity box - filtered at scale @xmath4 .
we follow a simple procedure : * we filter the velocity field , using a box filter of size @xmath5 , and we generate semitransparent surfaces delimitating the domains @xmath6 where @xmath7 ; * we filter the velocity field , using a box filter of size @xmath8 , and we generate surfaces delimitating the domains @xmath9 where @xmath10 , but only if these domains are contained in one of the domains from @xmath6 ; and this procedure can be used iteratively with several scales ( we use at most 3 scales , since the images become too complex for more levels ) .
additionally , we wish sometimes to keep track of the relative orientation of the vorticity vectors at the different scales . for this purpose
we employ a special coloring scheme for the @xmath11 isosurfaces : for each point of the surface , we compute the cosine of the angle @xmath12 between the @xmath13 filtered vorticity and the @xmath5 filtered vorticity : @xmath14 the surface is green for @xmath15 , yellow for @xmath16 and red for @xmath17 , following a continuous gradient between these three for intermediate values .
the opening montage of vortex tubes is very similar to the traditional visualisation : a writhing mess of vortices . upon coarse - graining
, additional structure is revealed .
the large - scale vorticity , which appears as transparent gray , is also arranged in tubes . as a next step ,
we remove all the fine - scale vorticity outside the large - scale tubes . the color scheme for the small - scale vorticity
is that described earlier , with green representing alignment with the large - scale vorticity and red representing anti - alignment .
clearly , most of the small - scale vorticity is aligned with the vorticity of the large - scale tube that contains it .
we then remove the fine - grained vorticity and pan out to see that the coarse - grained vortex tubes are also intricately tangled and intertwined . introducing a yet larger scale , we repeat the previous operations
. the relative orientation properties of the vorticity at these two scales is similar to that observed earlier .
next we visualize the vortex structures at all three scales simultaneously , one inside the other .
it is clear that the small vortex tubes are transported by the larger tubes that contain them .
however , this is not just a passive advection .
the small - scale vortices are as well being distorted by the large - scale motions . to focus on this more clearly
, we now render just the two smallest scales .
one can observe the small - scale vortex tubes being both stretched and twisted by the large - scale motions .
the stretching of small vortex tubes by large ones was suggested by orszag and borue @xcite as being the basic mechanism of the turbulent energy cascade .
as the small - scale tubes are stretched out , they are `` spun up '' and gain kinetic energy . here , this phenomenon is clearly revealed .
the twisting of small - scale vortices by large - scale screw motions has likewise been associated to helicity cascade @xcite .
the video thus allows us to view the turbulent cascade in progress .
next we consider the corresponding view with three levels of vorticity simultaneously .
since the ratio of scales is here 1:15:49 we are observing less than two decades of the turbulent cascade .
one must imagine the complexity of a very extended inertial range with many scales of motion .
not all of the turbulent dynamics is tube within tube . in our last scene
we visualize in the right half domain all the small - scale vortices , and in the left domain only the small - scale vortices inside the larger scale ones . in the right half ,
the viewer can observe stretching of the small - scale vortex structures taking place externally to the large - scale tubes .
the spin - up of these vortices must contribute likewise to the turbulent energy cascade .
6ifxundefined [ 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 10.1080/14685240802376389 [ * * ( ) , 10.1080/14685240802376389 ] @noop * * ( ) , in http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1592886[__ ] ( ) p. @noop _ _ , ( ) link:\doibase 10.1017/s0022112097008306 [ * * , ( ) ] http://journals.cambridge.org / production / action / cjogetfulltext?fulltextid=4% 00523 [ * * , ( ) ] | the jhu turbulence database @xcite can be used with a state of the art visualisation tool @xcite to generate high quality link : anc / dfdsubmissionquarterres.mpg[fluid dynamics videos ] . in this work
we investigate the classical idea that smaller structures in turbulent flows , while engaged in their own internal dynamics , are advected by the larger structures .
they are not advected undistorted , however .
we see instead that the small scale structures are sheared and twisted by the larger scales .
this illuminates the basic mechanisms of the turbulent cascade . |
in recent years electron transfer ( et ) between molecular adsorbates and semiconductor nanomaterials and surfaces has been subject of much research @xcite .
the injection of an electron into the conduction band is a prototype reaction for a lot of electrochemical and photoelectrochemical interfacial processes such as photography , solar energy conversion , quantum dot devices , etc .
interfacial et between discrete molecular levels and a conducting surface is the simplest of all surface reactions : it involves only the exchange of an electron , and so no bonds are broken @xcite .
the ultrafast nature of the charge injection from adsorbed molecules to the conduction band of semiconductor surfaces was shown in recent experiments @xcite . the theoretical description of such experiments demands an adequate treatment of the et dynamics to be able to describe short time - scale phenomena such as coherences .
this can be done within the reduced density matrix ( rdm ) description used in the present contribution .
recently @xcite the electron injection from a chromophore to a semiconductor conduction band was described using the time - dependent schrdinger equation , thus neglecting relaxation processes .
the neglect of relaxation processes was motivated by the experimental finding that injected electrons relax only within 150 fs in the perylene - tio@xmath0 system . here
we include relaxation to be able to treat a larger class of experiments where , for example , the adsorbed molecule is surrounded by a liquid environment , and longer times .
in the rdm theory the full system is divided into a relevant system part and a heat bath .
therefore the total hamiltonian consists of three terms the system part @xmath1 , the bath part @xmath2 , and the system - bath interaction @xmath3 : @xmath4 the rdm @xmath5 is obtained from the density matrix of the full system by tracing out the degrees of freedom of the environment .
this reduction together with a second - order perturbative treatment of @xmath3 and the markov approximation leads to the redfield equation @xcite : @xmath6 + { \mathcal r } \rho = { \mathcal
l } \rho .
\label{eq : redfield}\ ] ] in this equation @xmath7 denotes the redfield tensor .
if one assumes bilinear system - bath coupling with system part @xmath8 and bath part @xmath9 @xmath10 one can take advantage of the following decomposition @xcite : @xmath11 + [ \lambda\rho , k]+ [ k,\rho\lambda^{\dagger } ] .
\label{eq : pf - form}\ ] ] the @xmath12 operator can be written in the form @xmath13 where @xmath14 is the operator @xmath8 in the interaction representation .
the system bath interaction is taken to be linear in the reaction coordinate as well as in the bath coordinates .
neither the rotating wave nor the secular approximation have been invoked .
the so - called diabatic damping approximation which has numerical advantages @xcite is not used because it could lead to wrong results in the present system studied @xcite . in the following
we direct our attention to et between an excited molecular state and a conduction band .
the hamiltonian modeling this system consists of the ground and one excited state of the molecule and a quasi - continuum describing the conduction band together with one vibrational coordinate @xmath15 here @xmath16 can be equal to @xmath17 for the ground state , @xmath18 for the excited state , and @xmath19 for the quasi - continuum . as in ref .
@xcite we choose the frequency of the vibrational mode to be @xmath20 .
the coupling between the excited state and the continuum states is assumed to be constant : @xmath21 .
a box - shaped uniform density of states is used . instead of modeling the excitation from the ground state
explicitly we assume a @xmath22-pulse .
the excited state potential energy surface is shifted 0.1 along the reaction coordinate with respect to the ground state potential energy surface .
this results in an initial vibrational wave packet on the excited state with significant population in the lowest 4 - 5 vibrational states .
the shift between the excited state energy surface and the continuum parabola is 0.2 .
the thermal bath is characterized by its spectral density @xmath23 . because all system oscillators have the same frequency the coupling to the bath
can be given by one parameter @xmath24 in the diabatic damping approximation . denoting the effective mass of the harmonic oscillator by @xmath25 the strength of the damping
is chosen as @xmath26 . to be able to study the effects of dissipation
we do not model the quasi - continuum with such a large number of electronic states as in ref .
@xcite . in that work
a band of width 2 ev was described using an energy difference of 2.5 mev leading to 801 electronic surfaces .
these calculations are already demanding using wave packet propagation but almost impossible using direct density matrix propagation .
for doing such a large system one would have to use the monte carlo wave function scheme @xcite .
we use a much simpler model and describe only that part of the conduction band which really takes part in the injection process .
the total width of the conduction band may be significantly larger . in the following ,
a band of width 0.75 ev is treated with 31 electronic surfaces . in each of these electronic states
five vibrational states are taken into account .
we are aware that this is only a minimal model but hope that it catches the effects of dissipation on the electron injection process .
here we look at two different populations arising in the process of electron injection .
the time - dependent population of the electronic states in the conduction band is calculated as the sum over the vibrational levels of each electronic surface @xmath27 . as a second quantity
we look at the time - dependent population of the vibrational levels of the excited molecular state @xmath28 .
these two probability distributions give some hints on the effect of dissipation .
figure 1 shows the electronic population for the quasi - continuum , i.e. the probability distribution of the injected electron , versus the energy of the conduction band .
as described above , the four lowest vibrational states are populated significantly at @xmath29 .
the structure arising in the upper panel of fig . 1
was already explained by ramakrishna et al .
it can be estimated using the golden rule .
the electronic probabilities in the quasi - continuum are given as @xmath30 where @xmath31 is the initial vibronic distribution in the excited state and @xmath32 and @xmath33 are the vibronic parts of the wave packet in the excited and quasi - continuum states , respectively .
the energy @xmath34 denotes the middle of the band . turning on dissipation two
effects can be seen .
first , the vibrational populations in the excited state of the molecule no longer only decay into the quasi - continuum states but also relax within the excited state ( see fig . 2 ) .
second , the vibrational populations also relax within the quasi - continuum states .
the recurrences back into the excited state become much smaller .
only those parts of the wave packet which are still high enough in energy can go back to the molecule . in summary , we extended the work by ramakrishna , willig , and may @xcite by including relaxation processes into the description of electron injection into the conduction band of a semiconductor .
this will , at least , become important for modeling electron injection in the presence of a fluid surrounding the attached molecule . | electron injection from an adsorbed molecule to the substrate ( heterogeneous electron transfer ) is studied .
one reaction coordinate is used to model this process .
the surface phonons and/or the electron - hole pairs together with the internal degrees of freedom of the adsorbed molecule as well as possibly a liquid surrounding the molecule provide a dissipative environment , which may lead to dephasing , relaxation , and sometimes excitation of the relevant system . in the process studied the adsorbed molecule is excited by a light pulse .
this is followed by an electron transfer from the excited donor state to the quasi - continuum of the substrate .
it is assumed that the substrate is a semiconductor .
the effects of dissipation on electron injection are investigated . electron transfer , density matrix theory , molecules at surfaces |
the open connectome project ( located at http://openconnecto.me ) aims to annotate all the features in a 3d volume of neural em data , connect these features , and compute a high resolution wiring diagram of the brain , known as a connectome .
it is hoped that such work will help elucidate the structure and function of the human brain .
the aim of this work is to automatically annotate axoplasmic reticula , since it is extremely time consuming to hand - annotate them .
specifically , the objective is to achieve an operating point with high precision , to enable robust contextual inference .
there has been very little previous work towards this end @xcite .
axoplasmic reticula are present only in axons , indicating the identity of the surrounding process and informing automatic segmentation .
the brain data we are working with was color corrected using gradient - domain image - stitching techniques @xcite to adjust contrast through the slices .
we use this data as the testbed for running our filters and annotating axoplasmic reticula .
the bilateral filter @xcite is a non - linear filter consisting of one 2d gaussian kernel @xmath0 , which decays with spatial distance , and one 1d gaussian kernel @xmath1 , which decays with pixel intensity : @xmath2_p = \frac{1}{w_p}\sum_{q\in s}g_{\sigma_{s}}(||p - q||)g_{\sigma_{r}}(i_p - i_q)i_q,\\ & \hspace{4mm}\textrm{where } w_p = \sum_{q\in s}g_{\sigma_{s}}(||p - q||)g_{\sigma_{r}}(i_p - i_q ) \end{split}\ ] ] is the normalization factor .
this filter smooths the data by averaging over neighboring pixels while preserving edges , and consequently important detail , by not averaging over pixels with large intensity difference . applying this filter
accentuates features like axoplasmic reticula in our data .
even with a narrow gaussian in the intensity domain , the bilateral filter causes some color bleeding across edges .
we try to undo this effect through laplacian sharpening .
the laplacian filter computes the difference between the intensity at a pixel and the average intensity of its neighbors .
therefore , adding a laplacian filtered image to the original image results in an increase in intensity where the average intensity of the surrounding pixels is less than that of the center pixel , an intensity drop where the average is greater , and no change in areas of constant intensity .
hence , we use the 3x3 laplacian filter to highlight edges around dark features such as axoplasmic reticula .
we use a morphological region growing algorithm on our filtered data to locate and annotate axoplasmic 26.5 mm @xmath3 26.5 mm @xmath3 26.5 mm @xmath3 26.5 mm @xmath3 26.5 mm 26.5 mm 2 reticula .
we implement this by iterating over the filtered image and looking for dark pixels , where a dark pixel is defined as a pixel with value less than a certain specified threshold .
when a dark pixel is found , we check its 8-neighborhood to determine if the surrounding pixels are also below the threshold .
then , we check the pixels surrounding these , and we do this until we find only high intensity pixels , or until we grow larger than the diameter of an axoplasmic reticula .
the thresholds we use in our algorithm are biologically motivated and tuned empirically .
finally , we track our annotations through the volume to verify their correctness and identify axoplasmic reticula that were missed initially . for each slice , we traverse the annotations and check if an axoplasmic reticulum is present in the corresponding xy - location ( with some tolerance ) in either of the adjacent slices .
if a previously annotated axoplasmic reticulum object is present , we confirm the existing annotation .
otherwise , the adjacent slice locations are checked for axoplasmic reticula with a less restrictive growing algorithm , and new annotations are added in the corresponding slice . if no axoplasmic reticulum object is found in either of the adjacent slices , then we assume the annotation in the current slice to be incorrect , and delete it .
we qualitatively evaluated our algorithm on 20 slices from the kasthuri11 dataset , and quantitatively compared our results against ground truth from a neurobiologist .
our algorithm annotates axoplasmic reticulum objects with 87% precision , and 52% recall .
these numbers are approximate since there is inherent ambiguity even among expert annotators .
our current algorithm is designed to detect transverally sliced axoplasmic reticula . in future work , we plan to extend our morphological region growing algorithm to also find dilated axoplasmic reticula , and to incorporate a more robust tracking method such as kalman or particle filtering .
additionally , our algorithm can be adapted to annotate other features in neural em data , such as mitochondria , by modifying the morphological region growing algorithm . | * _ abstract _ : * in this paper , we present a new pipeline which automatically identifies and annotates axoplasmic reticula , which are small subcellular structures present only in axons .
we run our algorithm on the kasthuri11 dataset , which was color corrected using gradient - domain techniques to adjust contrast .
we use a bilateral filter to smooth out the noise in this data while preserving edges , which highlights axoplasmic reticula .
these axoplasmic reticula are then annotated using a morphological region growing algorithm . additionally , we perform laplacian sharpening on the bilaterally filtered data to enhance edges , and repeat the morphological region growing algorithm to annotate more axoplasmic reticula .
we track our annotations through the slices to improve precision , and to create long objects to aid in segment merging .
this method annotates axoplasmic reticula with high precision .
our algorithm can easily be adapted to annotate axoplasmic reticula in different sets of brain data by changing a few thresholds .
the contribution of this work is the introduction of a straightforward and robust pipeline which annotates axoplasmic reticula with high precision , contributing towards advancements in automatic feature annotations in neural em data . + 2 |
nuclei in interaction with external fields display a wide variety of collective vibrations known as giant resonances , associated with various degrees of freedom and multipolarities .
the giant isovector dipole resonance and the giant isoscalar quadrupole resonance are the most studied examples in this class of phenomena .
a particular mode , that is associated with vibrations in the number of particles , has been predicted in the 70s@xcite and discussed , under the name of giant pairing resonance , in the middle of the 80 s in a number of papers@xcite .
this phenomenon , despite some early efforts aimed to resolve some broad bump in the high - lying spectrum in ( p , t ) reactions@xcite , is still without any conclusive experimental confirmation . for a discussion , in particluar in connection with two - particle transfer reactions , on many aspects of pairing correlations in nuclei
we refer to a recent review@xcite .
we have studied the problem of collective pairing modes at high excitation energy in two neutron transfer reactions with the aim to prove the advantage of using unstable beam as a new tool to enhance the excitation of such modes @xcite .
the main point is that with standard available beams one is faced with a large energy mismatch that strongly hinders the excitation of high - lying states and favours the transition to the ground state of the final system .
instead the optimum q - value condition in the ( @xmath3he,@xmath4he ) stripping reaction suppresses the ground state and should allow the transition to 10 - 15 mev energy region .
we have performed particle - particle rpa calculations on lead and bcs+rpa on tin , as paradigmatic examples of normal and superfluid systems , evaluating the response to the pairing operator .
subsequently the two - neutron transfer form factors have been constructed in the framework of the macroscopic model@xcite and used in dwba computer codes .
we have estimated cross - sections of the order of some millibarns , dominating over the mismatched transition to the ground state .
recently we added similar calculations on other much studied targets to give some guide for experimental work .
the formal analogy between particle - hole and particle - particle excitations is very well established both from the theoretical side@xcite and from the experimental side for what concern low - lying pairing vibrations around closed shell nuclei and pairing rotations in open shells .
the predicted concentration of strength of a @xmath5 character in the high - energy region ( 8 - 15 mev for most nuclei ) is understood microscopically as the coherent superposition of 2p ( or 2h ) states in the next major shell above the fermi level .
we have roughly depicted the situation in fig .
( [ fig1 ] ) . in closed shell nuclei the addition of a pair of particles ( or holes ) to the next major shell , with a total energy @xmath6 , is expected to have a high degree of collectivity .
also in the case of open shell nuclei the same is expected for the excitation of a pair of particles with @xmath7 energies .
for normal nuclei the hamiltonian with a monopole strength interaction reads : @xmath8 where @xmath9 annihilates a pair of particles coupled to @xmath10 total angular momentum . getting rid of all the technicalities of the solution of the pp - rpa equations ( that may be found in the already cited work by the author ) we merely state that the pairing phonon may be expressed as a superposition of 2p ( or 2h ) states with proper forward and backward amplitudes ( @xmath11 and @xmath12 ) .
the pair transfer strength , that is a measure of the amount of collectivity of a each state @xmath13 , is given by : @xmath14 .
\label{p5}\ ] ] this quantity is plotted in the first column of fig .
( [ fig2 ] ) for the removal ( upper panel ) and addition mode ( lower panel ) . in the same figure
are reported the pairing strength parameters for the states of @xmath1sn . to obtain these last quantities for superfluid spherical
nuclei one has to rewrite the hamiltonian according to the bcs transformation and has to solve more complex rpa equations . in this case
the pairing strength for the addition of two particles is given , for each state @xmath13 , by : @xmath15_{00}|0\rangle = \sum_{j } \sqrt{2j+1 } [ u^{2}_{j } x_{n}(j ) + v^{2}_{j}y_{n}(j)]\ ] ] where the @xmath16 and @xmath17 are the usual occupation probabilities .
the amount of collectivity is a clear signal of the structural existence of giant pairing vibrations in the high - lying energy region .
we also report here a number of analogous results for other commonly studied targets = 9.4pc = 9.4pc = 9.4pc with the aim of giving some indications to experimentalists on the reasons why we think that lead and tin are some of the most promising candidates .
we have studied two isotopes of calcium with closed shells .
even if the absolute magnitudes of the @xmath18 is lower , it is worthwhile to notice that some enhancement is seen in the more neutron - rich @xmath19ca with respect to @xmath20ca .
an important role in this change is certainly due to the different shell structure of the two nuclei as well as to the scheme that we implemented to obtain the set of single particle levels .
the latter is responsible for the collectivity of the removal modes in both ca isotopes and also for the difficulty in finding out a collective state in the addition modes .
we display also results for @xmath21zr where the strength is much more fragmented and the identification of the gpv is more difficult . in the work of broglia and bes estimates for the energy of the pairing resonance are given as @xmath22 mev and @xmath23 mev for normal and superfluid systems respectively .
our figures follow roughly these prescriptions based on simple arguments ( and much more grounded in the case of normal nuclei ) as evident from table [ ta1 ] .
.comparison of position of gpv between our calculation and the broglia and bes estimate .
[ cols="^,^,^",options="header " , ] = 13.8pc = 13.8pc these cross - sections have been derived for sharp states , and we refer to the numbers in the last table when speaking of order of magnitude estimates . obviously cross - section in the high - lying energy region have a finite ( and large ) width that should be inserted for a more realistic description of the spectrum .
we have chosen a simple scheme that gives a lorentzian distribution with a width that grows quadratically with the excitation energy , @xmath24 , with @xmath25 adjusted to give a width of 4 mev for the gpv .
this could seem rather arbitrary since there is no reason for an _ a priori _ assignment of this quantity .
we have been brought to this simple prescription because other collective states ( of different nature ) lying in the same energy region display similar values for their width , and it is reasonable to assume some rule to narrow the low - energy states and to broaden the high - energy ones .
the final achievements for the four reactions studied in detail are presented in figure [ fig4 ] where the areas corresponding to the cross - sections given above have been shaded to give a feeling of the relative magnitudes of the transition to the ground states and to the gpv s . it is worthwhile to note that in the case of pb there is a considerable gain in using unstable beams , while in sn is much less evident .
one sees the need for unstable helium when compares the magnitude for the pairing resonance in the right a ) and b ) panels with the peak at zero energy : in the first panel the transition to the ground state is extremely hindered .
a @xmath3he beam is currently available ( or it will be available in the very near future ) in many radioactive ion beams facilities around the world and the calculations that we have presented could allow a planning for future experiments aimed to study the not yet completely unraveled role of pairing interaction in common nuclei , using exotic weakly bound nuclei as useful tools .
the author wishes to gratefully acknowledge discussions with andrea vitturi , hugo sofia and wolfram von oertzen on various aspects of theoretical and experimental nuclear physics .
the participation at the _ vii international school - seminar on heavy ion physics , dubna , russia _ 2002 has been supported by the infn .
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c.h.dasso and a.vitturi , prl 596341987 . | we investigate the possible signature of the presence of giant pairing states at excitation energy of about 10 mev via two - particle transfer reactions induced by neutron - rich weakly - bound projectiles . performing particle - particle rpa calculations on @xmath0pb and bcs+rpa calculations on @xmath1sn
, we obtain the pairing strength distribution for two particles addition and removal modes .
estimates of two - particle transfer cross sections can be obtained in the framework of the macroscopic model. the weak - binding nature of the projectile kinematically favours transitions to high - lying states . in the case of @xmath2
reaction we predict a population of the giant pairing vibration with cross sections of the order of a millibarn , dominating over the mismatched transition to the ground state . |
the schwinger - dyson ( sd ) equation is one of the most popular approaches to investigate the non - perturbative features of quantum field theory .
the analyses by making use of the sd equation for quark propagator are well - known .
recently , the coupled sd equations for the gluon and ghost propagators in yang - mills theory have been studied mainly in the lorentz ( landau ) gauge.@xcite in this paper , we derive the sd equations for the @xmath0 yang - mills theory in the maximal abelian ( ma ) gauge and solve them analytically in the infrared ( ir ) asymptotic region .
the ma gauge is useful to investigate the yang - mills theory from the view point of the dual superconductivity . in the ma gauge , in contrast to the ordinary lorentz gauge
, we must explicitly distinguish the diagonal components of the fields from the off - diagonal components .
this is indeed the case even in the perturbative analysis in the uv region.@xcite therefore , we must take account of the four propagators for the diagonal gluon , off - diagonal gluon , diagonal ghost and off - diagonal ghost
. numerical behaviors of gluon propagators in the ma gauge are also investigated on a lattice simulation.@xcite
first , we derive the sd equations from the @xmath0 yang - mills action in the ma gauge@xcite . the graphical representation of sd equations are shown in figure [ fig : sde ] .
= .001 in ( 6000,1800 ) ( 0,-200)(0,500)(0,150)(450,300)(600,160)(800,200)(1250,300)(1400,160)(1600,0)(2000,350)(2200,160)(2400,160)(3600,160)(3800,160)(0,1000)(0,150)(450,300)(600,160)(800,200)(1250,300)(1400,160)(1600,100)(2000,350)(2200,160)(2400,160)(3600,160)(3800,160)(0,1500)(0,150)(0,250)(450,300)(600,160)(800,200)(1000,250)(1250,300)(1400,160)(1600,0)(1570,230)(2200,160)(2400,0)(2370,230)(3000,160)(3200,160)(4400,160)(4600,160)(0,0)(0,150)(0,250)(450,300)(600,160)(800,200)(1000,250)(1250,300 ) for the diagonal gluon propagator , we adopt the landau gauge so that the diagonal gluon propagator @xmath1 has only the transverse part @xmath2 where we defined the form factor @xmath3 . while , the off - diagonal gluon propagator @xmath4 has both the transverse and longitudinal parts @xmath5\delta^{ab},\ ] ] where we defined the form factors @xmath6 and @xmath7 .
the form factor @xmath8 for the off - diagonal ghost propagator @xmath9 is defined @xmath10 the diagonal ghost propagator is decoupled from the other fields so that we omit it hereafter .
now , we write down the sd equations : @xmath11 @xmath12 and @xmath13 here the contributions from the two - loop graphs have been omitted .
the full form of sd equations will be given in a separate paper@xcite .
@xmath14 is the full vertex function for the diagonal gluon , off - diagonal ghost and off - diagonal antighost interaction , while @xmath15 is the full vertex function for an interaction of the diagonal gluon and two off - diagonal gluons , and the superscript `` @xmath16 '' means a _ bare _ propagator or vertex function . in the ma gauge
, we obtain the slavnov - taylor ( st ) identities @xmath17 @xmath18
in order to solve the sd equations analytically , we employ the following approximations .
@xmath19 we neglect the two - loop contributions . instead of the full vertex functions ,
we adopt modified vertex functions which are compatible with the st identities .
we adopt approximations for vertex functions as @xmath20 and @xmath21 here , we adopt the feynman gauge for the off - diagonal gluon for simplicity , that is , @xmath22 and @xmath23 . substituting the bare form factors , which are @xmath24 , into the right hand side of the ansatz ( [ eq : acc ] ) and ( [ eq : aaa ] )
, we obtain the bare vertex functions .
moreover , these ansatz are compatible with the st identities ( [ eq : sti - c ] ) and ( [ eq : sti - a ] ) in the limit of @xmath25 . in the momentum integration
, we use the higashijima - miransky approximation@xcite as @xmath26
now we adopt the ansatz for the form factors in the ir region : @xmath27 g(p^2 ) = b(p^2)^v+\cdots,\\[1 mm ] f_{\rm t}(p^2 ) = c(p^2)^w+\cdots . \end{array } \label{eq : ir solutions}\ ] ] substituting the ansatz ( [ eq : ir solutions ] ) for the form factors , and the ansatz ( [ eq : acc ] ) and ( [ eq : aaa ] ) for vertex functions into the sd equations ( [ eq : diagonal gluon ] ) , ( [ eq : off - diagonal ghost ] ) and ( [ eq : off - diagonal gluon ] ) , and comparing the leading term in the both sides of each equation , we obtain the following results for @xmath22 . from eqs .
( [ eq : off - diagonal ghost ] ) and ( [ eq : off - diagonal gluon ] ) , we obtain the relations @xmath28 and @xmath29 . in the case of @xmath30 and @xmath31 , from the eq .
( [ eq : diagonal gluon ] ) , we obtain the relation @xmath32 so that @xmath33 is less than @xmath34 . in the case of @xmath35 and @xmath31 , we need redefine the form factor @xmath8 as @xmath36 with @xmath37 since contributions from the leading term of @xmath8 are canceled each other in the ansatz ( [ eq : acc ] ) .
therefore we need the information of next leading term of the form factor @xmath8 . in this case
we obtain the relation @xmath38 from the eq .
( [ eq : diagonal gluon ] ) so that @xmath33 is also less than @xmath34 .
next , we consider the case of @xmath30 and @xmath39 . as well as the above case , we need redefine the form factor @xmath6 as @xmath40 with @xmath41 and we obtain the relation @xmath42 ( @xmath43 ) .
similarly , in the case of @xmath44 , we obtain the relation @xmath45 ( @xmath43 ) .
the results are summarized in table [ tbl : feynman gauge ] .
@xmath32 & @xmath42 @xmath35 & @xmath38 & @xmath45 [ tbl : feynman gauge ] in the gauge other than the feynman gauge , that is , @xmath46 , the calculation and discussion are very tedious
. however , the qualitative results are identical to the above case except for the following one point . in this case , even if @xmath39 , there occurs no cancellation as in the above two cases 2c and 2d .
this is because the off - diagonal gluon propagator has the momentum dependent tensor structure for @xmath46 , while it is proportional to @xmath47 for @xmath22 .
therefore , we obtain the relation @xmath48 in the case of @xmath39 .
( see table [ tbl : not feynman gauge ] . )
@xmath30 & @xmath32 & @xmath48 @xmath35 & @xmath38 & @xmath48 [ tbl : not feynman gauge ]
in the ir limit , the form factors of each propagator behave as @xmath49 @xmath50 @xmath51 therefore the solution shows that the diagonal gluon propagator is enhanced in the ir limit , while the off - diagonal gluon and off - diagonal ghost propagators are suppressed in the ir region .
our results are compatible with a hypothesis of abelian dominance@xcite . | we derive the schwinger - dyson equations for the @xmath0 yang - mills theory in the maximal abelian gauge and solve them in the infrared asymptotic region .
we find that the infrared asymptotic solutions for the gluon and ghost propagators are consistent with the hypothesis of abelian dominance . |
it is common accepted that braking of pulsars is caused by the magneto - dipole radiation of the rotating magnetic star . in this case
the rate of losses of the neutron star rotation energy can be equated to the power of its magneto - dipole radiation : @xmath1 + where _ i _ is the moment of inertia of the neutron star , @xmath2 - the angular speed of its rotation , @xmath3 - its magnetic moment , @xmath0 - the angle between the rotation axis and the magnetic moment , _ c _ - speed of light . for standard parameters of neutron stars : masses of order of the solar mass ( @xmath4 ) and radii _ r _ of order of @xmath5 cm we can put _ i _ = @xmath6 . for the magnetic moment
we have @xmath7 + here @xmath8 is the magnetic induction at the magnetic pole , @xmath9 ?
the induction at the magnetic equator . instead of @xmath2 the rotation period @xmath10
is usually measured and we can obtain from ( 1 ) and ( 2 ) : @xmath11 + this equality is used usually to calculate magnetic inductions of pulsars assuming that @xmath12 for all objects . the known catalogs ( see , for example manchester et al
. , 2005 ) contain as a rule @xmath9 instead of @xmath8 .
here we propose to decline the assumption on the constancy of @xmath13 and use some estimations of this parameter to calculate more accurate values of pulsar magnetic inductions .
in a number of our works ( malov & nikitina , 2011a , b , 2013 ) some methods for calculations of the angle @xmath0 have been put forward and applied to some catalogs of pulsars ( keith et al . , 2010 ; van ommen et al . , 1997 ; weltevrede & johnston , 2008 ) at approximately 10 , 20 and 30 cm .
basic equations for this aim are ( manchester & taylor , 1977 ) : @xmath14 @xmath15 + here @xmath16 is the angle between the line of sight and the rotation axis , @xmath17 - the angular radius of the emission cone , @xmath18 - a half of the angular width of the observed pulse , @xmath19 - the position angle of the linear polarization , @xmath20 - longitude . the simplest case for the calculations of the angle @xmath0 is realized when the line of sight passes through the center of the emission cone , i.e. @xmath21 + in this case we can use the dependence of the observed pulse width @xmath22 at the @xmath23 level on the rotation period and determine the lower boundary in the corresponding diagram to obtain @xmath24 + as the result we have from ( 4 ) , ( 5 ) and ( 7 ) ( malov & nikitina , 2011a ) : @xmath25 + the values of angles calculated by this method are denoted as @xmath26 and given in the table 1 .
usually polarization measurements are made inside the pulse longitudes only . in this case
we can use the maximal derivative of the position angle . from ( 5 ) we have @xmath27 we can obtain from the dependence of @xmath22 on _ p _ by the least squares method @xmath28 + the third equation for the calculations of the angle @xmath0 is ( 4 ) . from these three equations we obtain @xmath29y^2 + 2c(d - b^2)y+c^2d^2-b^2(1+c^2)=0.\\\ ] ] + here @xmath30
+ we can transform the equation ( 9 ) to the following form @xmath31 + then finding the value of y from the equation ( 11 ) we can calculate @xmath0 from ( 13 ) .
we have calculated values of @xmath0 by this method and list them in the table 1 as @xmath32 . here
we correct the misprint in the equation ( 11 ) made in our papers ( malov & nikitina , 2011a , b , 2013 ) .
there is an additional way to calculate angles @xmath0 .
this way uses observable values of position angles and shapes of average profiles for individual pulsars . in this case , original equations form the closed system for calculations of the angles @xmath17 , @xmath16 and @xmath0 : @xmath33 as the observed pulsar profiles have various forms , the coefficient _
n _ has a different value depending on a profile structure .
we put arbitrary the following values of _ n _ ( fig.1 ) . if the ratio of the intensity @xmath34 in the center of the pulse to the maximal intensity @xmath35 is zero then @xmath36 . for @xmath37 @xmath38 , @xmath39 @xmath40 , @xmath41 @xmath42 , and for @xmath43 @xmath44 .
it is worth noting that the solution of the system ( 14 ) can be obtained numerically for any value of _
n_. for example , if @xmath45 , the solution for @xmath46 can be obtained from the equation : @xmath47 at n = 2 : @xmath48 y^4 + 2c \left [ c^2 ( 1 + d - 2d^2 ) - 2 - d \right ] y^3 + \left [ 2dc^4 ( 1 - d ) - \right .
. - c^2 ( 2d^2 - 6d + 7 ) + 5 \right ] y^2 + 2c \left [ c^2 d^2 + d(1 + c^2 ) - 2 ( c^2 - 1 ) \right ] y + c^2 d^2 ( 1 + c^2 ) - ( c^2 - 1)^2 = 0;\\ \end{array}\ ] ] at n = 3/2 : @xmath49 \sqrt{\frac{1 + \frac{c + y}{\sqrt{c^2 + 2cy + 1}}}{2 } } - c y^2 ( 1 - d ) - y - cd = 0;\ ] ] at n = 5/4 : @xmath50 this method gives angles @xmath51 ( see the table 1 ) . for some pulsars calculations
were made by one method only . when it was possible we used two or all three methods . in these cases ,
the mean value of the angle @xmath0 has been calculated .
the resulting values @xmath52 are listed in the table 1 .
some other authors ( for example , kuzmin & dagkesamanskaya , 1983 ; kuzmin et al . , 1984 ;
lyne & manchester , 1988 ) carried out calculations of the angle @xmath0 earlier for the shorter samples of pulsars using some additional assumptions .
we will use further our estimations to calculate magnetic inductions at the surface of the neutron stars .
the distribution of the angles @xmath0 from the table 1 ( fig.2 ) shows that the majority of pulsars have rather small inclinations of the magnetic moments .
these pulsars are old enough , and we can conclude that they evolve to the aligned geometry .
the average characteristic age for our sample of pulsars is @xmath53 years .
we must note however that the angles calculated by the method * _ 1 ) _ * are the lower limits of this parameter .
this explains partly the predominance of the small values of @xmath0 . from the table 1.,width=453 ]
.values of the angle @xmath0 ( deg ) . [ cols="^,^,^,^,^,^,^,^,^,^,^ " , ]
1 . some methods for calculations of the angle @xmath0 between rotation and magnetic axes were applied to obtain the values of @xmath0 for 376 radio pulsars .
the distribution of these values shows the predominance of small inclinations of the magnetic axes . 2 .
magnetic inductions at the surface of 375 pulsars considered were calculated .
there is no the measured derivative @xmath54 for the pulsar j1713 - 3949 and it is excluded from the consideration .
the distribution of the calculated magnetic inductions can be described by the gaussian with the maximal value of @xmath55 and the width in the logarithmic scale nearly 1 .
the calculated inductions are higher than the catalog equatorial inductions with the mean value of the ratio of these quantities of 5 . for the pulsar j1410 - 7404 @xmath56 . the maximal value of the ratio @xmath57 for the pulsar j2007 + 0809 .
this work has been carried out with the financial support of basic research program of the presidium of the russian academy of sciences * _ transitional and explosive processes in astrophysics _ * ( p-41 ) .
we thank a.v.biryukov for very useful comments and discussions .
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mnras , 287 , 1210 weltevrede p. , johnston s. , 2008 , mnras , 391 , 1210 | we used the magneto - dipole radiation mechanism for the braking of radio pulsars to calculate the new values of magnetic inductions at the surfaces of neutron stars . for this aim
we estimated the angles @xmath0 between the rotation axis and the magnetic moment of the neutron star for 376 radio pulsars using three different methods .
it was shown that there was the predominance of small inclinations of the magnetic axes . using the obtained values of the angle @xmath0 we calculated the equatorial magnetic inductions for pulsars considered .
these inductions are several times higher as a rule than corresponding values in the known catalogs .
* keywords * magnetic fields ; methods : data analysis ; methods : statistical ; _ ( stars : ) _ pulsars : general |
one of the most promising solutions to the hierarchy problem is the randall - sundrum ( rs ) model @xcite . in this model
there is a single extra dimension compactified on @xmath1 with the non - factorizable metric of @xmath2 @xmath3 here @xmath4 is the extra - dimensional coordinate , and @xmath5 is the inverse of the @xmath6 curvature , @xmath7 .
two branes define the boundaries of the extra dimension .
one , at @xmath8 , is called the uv , or planck , brane .
the other , at @xmath9 , is the ir , or tev , brane . picking @xmath10 , which is natural in realistic stabilization mechanisms ,
solves the hierarchy problem @xcite . in the original rs model
the sm was confined to the ir brane , and only gravity propagated in the bulk @xcite .
it has since been realized that both gauge and fermion fields can live in the bulk in a realistic model @xcite .
these models are realistic , but the parameter space can be strongly reduced by precision electroweak constraints .
much of this problem can be traced to the fact that the massive gauge fields receive a contribution to their mass from the bulk geometry which does not respect the custodial @xmath11 .
this can be fixed by expanding the gauge group to @xmath12 , which dramatically improves the electroweak fit @xcite .
the breaking of this extended electroweak symmetry proceeds in two stages : on the uv brane @xmath13 ; on the ir brane @xmath14 , where @xmath15 is the diagonal of the @xmath16 groups .
this paper investigates the properties of the higgs sector that accomplishes this breaking .
we now ask what drives the breaking on each brane . on the planck brane
all degrees of freedom will have planck scale masses , so we can ignore them .
we can then implement the breaking with boundary conditions to good approximation .
this leads to the boundary conditions at @xmath8 @xmath17 here @xmath18 and @xmath19 are ratios of 5d gauge couplings : @xmath20 , and @xmath21 . on the tev brane
, the masses will be tev scale , so we should look at the higgs sector in detail . the simplest structure that will create
the breaking pattern is a real higgs that is a bidoublet under @xmath22 .
this leads to the boundary conditions at @xmath9 @xmath23 note that in the @xmath24 limit we obtain the usual higgsless boundary conditions , and this model reduces to the higgsless model in @xcite
. we will use this parameter , @xmath25 to interpolate between the sm limit ( @xmath26 ) , and the higgsless limit .
[ fig : wroot ] to write down the effective 4d theory , we expand the 5d fields into kaluza klein ( kk ) fields , @xmath27 we can now obtain the gauge boson wavefunctions by solving the equation of motion subject to the boundary conditions ( [ eq : gaugebcr ] ) and ( [ eq : gaugebcrp ] ) .
this produces a spectrum of eigenvalues corresponding to the excitations of the gauge fields .
the lowest masses in each of the charged and neutral sectors will correspond to the @xmath28 and @xmath29 bosons .
the neutral sector also contains a zero mode , corresponding to the photon .
fig [ fig : wroot ] shows the eigenvalue for the @xmath28 as a function of the parameter @xmath25 .
[ fig : wcoup ]
one interesting feature of this model is that the @xmath28 and @xmath29 wavefunctions are suppressed near the ir brane , as can be seen by inspecting the boundary conditions
. this suppression increases for increasing @xmath25 .
this means that the coupling of massive gauge bosons to the higgs will generically be suppressed .
[ fig : wcoup ] shows the coupling of the @xmath28 to the higgs . for values of @xmath25 near unity
the lep bounds on the higgs mass can be dramatically reduced .
( for larger values of @xmath25 the model is effectively higgsless . )
the fermion sector of this model is more complicated .
again , the higgs vev induces mixed boundary conditions that link left and right handed fields to give the fermions masses .
however , there are two new degrees of freedom . first
, since 5d fermions are achiral , ther can always be a mass term in the bulk @xmath30 .
the main effect of this term is to shift the location of the fermion zero mode in the bulk . by changing this parameter
we can cause the zero mode to be localized either near the uv or ir brane , and also can change the degree of this localization .
this allows us to control the overlap of the zero mode with the ir brane , and consequently the strength with which the fermion interacts with the higgs . in this way
the hierarchy of fermion masses can be generated by order one changes in the 5d masses .
the second complication arises from the @xmath31 symmetry which enforces that , for example , @xmath32 if unbroken .
this mass relation can be modified by mixing with new fermions localized to the planck brane , where the @xmath31 is broken . for full details , see @xcite . note that there are tree - level corrections to precision electroweak observables , coming largely from the kk excitations of the gauge bosons .
unfortunately , the magnitude of these corrections is highly sensitive to the configuration of the fermion sector . for the specific configuration studied in @xcite
we find the constraint @xmath33 .
there are , however , special points in the fermion parameter space where the constraint becomes trivial , so a wide range of @xmath25 should be considered .
the final interesting shift in higgs properties is in the couplings to massless gauge bosons , _
i.e. _ gluons and photons .
the coupling of the higgs to gluon pairs is induced through top loops . however , in this model the kk excitations also couple to the higgs .
furthermore , note that we have arranged small 4d yukawa couplings for the other fermions by small wavefunction overlaps with the would - be zero modes .
the 5d yukawa couplings are all order 1 , and the excited states have _ no _ wavefunction suppression .
hence there are large contributions to the higgs - glue - glue coupling from the kk excitations of _ all _ colored fermions .
this leads to an enhancement in that coupling , as seen in fig .
[ fig : hgg ] .
there are similar corrections to the higgs - gamma - gamma coupling .
the situation there is more complicated , however , since there are also contributions from @xmath28 boson loops , which are dominant in the sm , and the higgs coupling to @xmath28s is suppressed .
we can now look at the behavior of the higgs branching ratios , as shown in fig .
[ fig : widthbr ] . note in particular the dominance of @xmath34 over a wide range , and the late onset of @xmath35 .
this is driven by the @xmath31 symmetry , which gives a large enhancement of the @xmath36-quark yukawa , and the suppression of the gauge boson couplings .
note also the reduction in the @xmath37 mode .
this will make discovery at the lhc difficult .
the suppression of the coupling to gauge bosons also means that production at the ilc will be reduced , making this higgs a particularly difficult one to find .
however , it will be essential to measure the higgs couplings with precision to identify a warped extra dimension as the correct theory of new physics , if indeed this is what is realized in nature .
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the proper - motion observations of pulsars show that the pulsars had the kick velocity in the formation stage .
the young pulsars have proper velocity of @xmath4 @xcite .
the physical mechanism of such kick velocity may be due to the harrison
tademaru mechanism @xcite , anisotropic emission of neutrinos , anisotropic explosion and so on ( see lorimer @xcite for the review ) .
therefore , it is also reasonable to assume the existence of the proper motion of the pulsars in the formation process of pop iii nss , although there is no direct evidence since no pop iii star or pulsar is observed . while , repetto et al .
@xcite suggest that bhs also have a natal kick velocity comparable to pulsars from the galactic latitude distribution of the low mass x - ray binaries in our galaxy .
but , first , this is not the direct observation of proper motion of bhs , and second , since the mass of pop iii bhs is larger than pop i and pop ii bhs , their kick velocity might be so small that it can be neglected .
therefore , we take into account the natal kick for pop iii nss but not for pop iii bhs in this paper .
the kick speed @xmath5 obeys a maxwellian distribution as @xmath6 \,,\ ] ] where @xmath7 is the dispersion .
the details of the method how to calculate the natal kick are shown in ref .
@xcite . in this paper
, we perform population synthesis monte carlo simulations of pop iii binary stars .
we calculate the pop iii ns - bh and pop i and ii ns - bh for comparison .
pop i and pop ii stars mean solar metal stars and metal poor stars whose metallicity is less than 10% of solar metallicity , respectively . in this paper , we consider five metallicity cases of @xmath8 ( pop iii ) , @xmath9 and @xmath10 ( pop i ) .
there are important differences between pop iii and pop i and ii .
pop iii stars are ( 1 ) more massive , @xmath11 , ( 2 ) smaller stellar radius compared with that of pop i and ii , and ( 3 ) no stellar wind mass loss . these properties play key roles in binary interactions . in order to estimate the event rate of ns - bh mergers and the properties of ns - bh , we use the binary population synthesis method @xcite which is the monte calro simulation of binary evolution .
first , we choose the binary initial conditions such as the primary mass @xmath12 , the mass ratio @xmath13 , the separation @xmath14 , and the eccentricity @xmath15 when the binary is born .
these binary initial conditions are chosen by the monte calro method and the initial distribution functions such as the initial mass function ( imf ) , the initial mass ratio function ( imrf ) , the initial separation function ( isf ) , and the initial eccentricity distribution function ( ief ) .
we adopt these distribution functions for pop iii stars and pop i and ii stars as table [ idf ] . [ cols="^,^,^",options="header " , ]
this work was supported by mext grant - in - aid for scientific research on innovative areas , `` new developments in astrophysics through multi - messenger observations of gravitational wave sources '' , no .
24103006 ( tn , hn ) , by the grant - in - aid from the ministry of education , culture , sports , science and technology ( mext ) of japan no .
15h02087 ( tn ) , and jsps grant - in - aid for scientific research ( c ) , no .
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the reason is that pop iii stars have no metal so that no mass loss is expected .
then , in the final supernova explosion to ns , much mass is lost so that the semi major axis becomes too large for pop iii ns - bh binaries to merge within @xmath1 .
however it is almost established that the kick velocity of the order of @xmath2 exists for ns from the observation of the proper motion of the pulsar .
therefore , the semi major axis of the half of ns - bh binaries can be smaller than that of the previous argument for pop iii ns - bh binaries to decrease the merging time .
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this suggests that there is a good chance of the detection of pop iii ns - bh mergers in o2 of advanced ligo and advanced virgo from this autumn . |
i am grateful to alekos kechris for informing me of t.dyck/ ; the proof given seems to be due to alain louveau .
i thank norm levenberg for references .
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we illustrate these with some important examples . we pose several general questions and conjectures .
primary 60k99 , 60g55 ; secondary 42c30 , 37a15 , 37a35 , 37a50 , 68u99 .
random matrices , eigenvalues , orthogonal projections , positive contractions , exterior algebra , stochastic domination , negative association , point processes , mixtures , spanning trees , orthogonal polynomials , completeness , bernoulli processes .
determinantal point processes were originally defined by macchi @xcite in physics . starting in the 1990s ,
determinantal probability began to flourish as examples appeared in numerous parts of mathematics @xcite .
recently , applications to machine learning have appeared @xcite .
a discrete determinantal probability measure is one whose elementary cylinder probabilities are given by determinants . more specifically ,
suppose that @xmath0 is a finite or countable set and that @xmath1 is an @xmath2 matrix .
for a subset @xmath3 , let @xmath4 denote the submatrix of @xmath1 whose rows and columns are indexed by @xmath5 .
if @xmath6 is a random subset of @xmath0 with the property that for all finite @xmath7 , we have e.dpm = ( qa ) , then we call @xmath8 a . the inclusion - exclusion principle in combination with yields the probability of each elementary cylinder event .
therefore , for every @xmath1 , there is at most one probability measure , to be denoted @xmath9 , on subsets of @xmath0 that satisfies .
conversely , it is known ( see , e.g. , b.lyons:det/ ) that there is a determinantal probability measure corresponding to @xmath1 if @xmath1 is the matrix of a positive contraction on @xmath10 ( in the standard orthonormal basis ) .
technicalities are required even to define the corresponding concept of determinantal point process for @xmath0 being euclidean space or a more general space .
we present a virtually complete development of their basic properties in a way that minimizes such technicalities by adapting the approach of b.lyons:det/ from the discrete case .
in addition , we use an idea of goldman b.goldman/ to deduce properties of the general case from corresponding properties in the discrete case .
space limitations prevent mention of most of what is known in determinantal probability theory , which pertains largely to the analysis of specific examples .
we focus instead on some of the basic properties that hold for all determinantal processes and on some intriguing open questions .
let @xmath0 be a denumerable set .
we identify a subset of @xmath0 with an element of @xmath11 in the usual way .
there are several approaches to prove the basic existence results and identities for determinantal probability measures .
we sketch the one used by b.lyons : det/. this depends on understanding first the case where @xmath1 is the matrix of an orthogonal projection .
it also relies on exterior algebra so that the existence becomes immediate .
any unit vector @xmath12 in a hilbert space with orthonormal basis @xmath0 gives a probability measure @xmath13 on @xmath0 , namely , @xmath14 associated to orthogonal projections @xmath15 .
we refer to b.lyons:det/ for details not given here .
identify @xmath0 with the standard orthonormal basis of the real or complex hilbert space @xmath10 . for @xmath16 ,
let @xmath17 denote a collection of ordered @xmath18-element subsets of @xmath0 such that each @xmath18-element subset of @xmath0 appears exactly once in @xmath17 in some ordering .
define @xmath19 if @xmath20 , then @xmath21 and @xmath22 .
we also define @xmath23 to be the scalar field , @xmath24 or @xmath25 .
the elements of @xmath26 are called of @xmath18 , or for short .
we then define the ( or ) of multivectors in the usual alternating multilinear way : @xmath27 for any permutation @xmath28 , and @xmath29 for any scalars @xmath30 ( @xmath31,\ ; e \in e'$ ] ) and any finite @xmath32 .
( thus , @xmath33 unless all @xmath34 are distinct . ) the inner product on @xmath26 satisfies e.ipdet = _ i , j when @xmath35 and @xmath36 are 1-vectors .
( this also shows that the inner product on @xmath26 does not depend on the choice of orthonormal basis of @xmath37 . )
we then define the ( or ) @xmath38 , where the summands are declared orthogonal , making it into a hilbert space .
( throughout the paper , @xmath39 is used to indicate the sum of orthogonal summands , or , if there are an infinite number of orthogonal summands , the closure of their sum . )
vectors @xmath40 are linearly independent iff @xmath41 . for a @xmath18-element subset @xmath3 with ordering @xmath42 in @xmath17 , write @xmath43 .
we also write @xmath44 for any function @xmath45 .
although there is an isometric isomorphism @xmath46 for @xmath47 , this does not simplify matters in the discrete case
. it will be very useful in the continuous case later , however .
if @xmath48 is a closed linear subspace of @xmath37 , written @xmath49 , then we identify @xmath50 with its inclusion in @xmath51 .
that is , @xmath52 is the closure of the linear span of the @xmath18-vectors @xmath53 . in particular ,
if @xmath54 , then @xmath55 is a 1-dimensional subspace of @xmath51 ; denote by @xmath56 a unit multivector in this subspace .
note that @xmath56 is unique up to a scalar factor of modulus 1 ; which scalar is chosen will not affect the definitions below .
we denote by @xmath15 the orthogonal projection onto @xmath48 for any @xmath49 or , more generally , @xmath57 .
l.projection for every closed subspace @xmath49 , every @xmath16 , and every @xmath58 , we have @xmath59 write @xmath60 and expand the product .
all terms but @xmath61 have a factor of @xmath62 in them , making them orthogonal to @xmath50 by e.ipdet/. a multivector is called or if it is the wedge product of 1-vectors .
b.whitney:book/ , p. 49 , shows that e.whitney .
we shall use the defined by duality : @xmath63 in particular , if @xmath64 and @xmath65 is a multivector that does not contain any term with @xmath66 in it ( that is , @xmath67 ) , then @xmath68 and @xmath69 . more generally , if @xmath70 with @xmath71 and @xmath72 , then @xmath73 and @xmath74 .
note that the interior product is sesquilinear , not bilinear , over @xmath25 .
for @xmath70 , write @xmath75 $ ] for the subspace of scalar multiples of @xmath12 in @xmath37 . if @xmath48 is a finite - dimensional subspace of @xmath37 and @xmath76 , then e.hwedge _ h
e = p_h^e_h + [ e ] ( up to signum ) . to see this ,
let @xmath77 be an orthonormal basis of @xmath48 , where @xmath78 .
put @xmath79 .
then @xmath80 is an orthonormal basis of @xmath81 $ ] , whence @xmath82 } = u_1 \wedge u_2 \wedge \cdots \wedge u_r \wedge v = \mv_h \wedge v = \mv_h \wedge e/\|p_h^\perp e\|\ ] ] since @xmath83 .
this shows e.hwedge/. similarly , if @xmath84 , then e.hvee _ h e = p_h e_h e^ ( up to signum ) .
indeed , put @xmath85 .
let @xmath86 be an orthonormal basis of @xmath48 with @xmath87 .
then @xmath88 ( up to signum ) , as desired .
finally , we claim that e.reverse = .
indeed , @xmath89 , so this is equivalent to @xmath90 thus , it suffices to show that @xmath91 by sesquilinearity , it suffices to show this for @xmath92 members of an orthonormal basis of @xmath48 .
but then it is obvious . for a more detailed presentation of exterior algebra ,
see b.whitney : book/. let @xmath48 be a subspace of @xmath37 of dimension @xmath93 . define the probability measure @xmath94 on subsets @xmath95 by e.xihpr ^h(\{b } ) : = ||^2 .
note that this is non-0 only for @xmath96 .
also , by l.projection/ , @xmath97 for @xmath96 , which is non-0 iff @xmath98 are linearly independent .
that is , @xmath99 iff the projections of the elements of @xmath100 form a basis of @xmath48
. let @xmath101 be any basis of @xmath48 .
if we use e.ipdet/ and the fact that @xmath102 for some scalar @xmath103 , then we obtain another formula for @xmath94 : we use @xmath104 to denote a random subset of @xmath0 arising from a probability measure @xmath94 . to see that e.dpm/ holds for the matrix of @xmath15 , observe that for @xmath96 , @xmath105 = \bigip{p_{\ext(h ) } \theta_b , \theta_b } = \bigip{\bigwedge_{e \in b } p_h e , \bigwedge_{e \in b } e } = \det [ \ip{p_h e , f}]_{e , f \in b}\ ] ] by e.ipdet/.
this shows that e.dpm/ holds for @xmath106 since @xmath107 @xmath94-a.s .
the general case is a consequence of multilinearity , which gives the following extension of e.dpm/. we use the convention that @xmath108 and @xmath109 for any multivector @xmath65 .
t.genprs if @xmath110 and @xmath111 are ( possibly empty ) subsets of a finite set @xmath0 , then e.genprs ^h[a_1 , a_2 = ] = . in particular , for every @xmath3
, we have e.included ^h[a ] = p_(h ) _ a^2 .
c.dualrep if @xmath0 is finite , then for every subspace @xmath49 , we have e.dualrep ^h^(\{e b } ) = ^h(\{b } ) .
these extend to infinite @xmath0 . in order to define @xmath94
when @xmath48 is infinite dimensional , we proceed by finite approximation .
let @xmath112 be infinite .
consider first a finite - dimensional subspace @xmath48 of @xmath37 .
define @xmath113 as the image of the orthogonal projection of @xmath48 onto the span of @xmath114 . by considering a basis of @xmath48 , we see that @xmath115 in the weak operator topology ( wot ) , i.e. , matrix - entrywise , as @xmath116 .
it is also easy to see that if @xmath117 , then @xmath118 for all large @xmath18 and , in fact , @xmath119 in the usual norm topology .
it follows that e.genprs/ holds for this subspace @xmath48 and for every finite @xmath120 .
now let @xmath48 be an infinite - dimensional closed subspace of @xmath37 .
choose finite - dimensional subspaces @xmath121 .
it is well known that @xmath115 ( wot ) . then e.detgenprs a ( p_h_k a ) ( p_h a ) , whence @xmath122 has a weak@xmath123 limit that we denote @xmath94 and that satisfies e.genprs/. we also note that for _ any _ sequence of subspaces @xmath113 , if @xmath124 ( wot ) , then @xmath125 weak@xmath123 because e.detgenprs/ then holds .
we call @xmath1 a if @xmath1 is a self - adjoint operator on @xmath37 such that for all @xmath126 , we have @xmath127 . a of @xmath1 is an orthogonal projection @xmath15 onto a closed subspace @xmath128 for some @xmath129 such that for all @xmath126 , we have @xmath130 , where we regard @xmath131 as the orthogonal sum @xmath132 . in this case , @xmath1 is also called the of @xmath15 to @xmath37 .
choose such a dilation ( see e.vecdilate/ or e.dilate/ ) and define @xmath9 as the law of @xmath133 when @xmath104 has the law @xmath94 .
then e.dpm/ for @xmath1 is a special case of e.dpm/ for @xmath15 .
of course , when @xmath1 is the orthogonal projection onto a subspace @xmath48 , then @xmath134 .
basic properties of @xmath9 follow from those for orthogonal projections , such as : t.q if @xmath1 is a positive contraction , then for all finite @xmath135 , e.qgenprs ^q= .
if e.dpm/ is given , then e.qgenprs/ can be deduced from e.dpm/ without using our general theory and , in fact , without assuming that the matrix @xmath1 is self - adjoint . indeed , suppose that @xmath136 is any diagonal matrix .
denote its @xmath137-entry by @xmath138 . comparing coefficients of @xmath138
shows that e.dpm/ implies , for finite @xmath3 , e.xe = ( ( q + x ) a ) . replacing @xmath5 by @xmath139 and
choosing @xmath140 gives e.qgenprs/. on the other hand , if we substitute @xmath141 , then we may rewrite e.xe/ as e.ze = ( ( q z + i - q ) a ) , where @xmath142 is the diagonal matrix of the variables @xmath143 .
let @xmath0 be finite .
write @xmath144 for @xmath3
. then e.ze/ is equivalent to e.affine _ a e ^q[= a ] z^a = ( i - q+qz ) .
this is the same as the laplace transform of @xmath9 after a trivial change of variables .
when @xmath145 , we can write @xmath146 with @xmath147 . thus , for all @xmath3 , we have a probability measure @xmath8 on @xmath148 is called if its generating polynomial @xmath149 z^a$ ] satisfies the inequality for all @xmath150 and all real @xmath151 .
this property is satisfied by every determinantal probability measure , as was shown by b.bbl:rayleigh/ , who demonstrated its usefulness in showing other properties , such as negative associations and preservation under symmetric exclusion processes . for a set @xmath152 ,
denote by @xmath153 the @xmath154-field of events that are measurable with respect to the events @xmath155 for @xmath156 .
define the @xmath154-field to be the intersection of @xmath157 over all finite @xmath158 .
we say that a measure @xmath8 on @xmath148 has if every event in the tail @xmath154-field has measure either 0 or 1 .
t.tail b.lyons:det/ if @xmath1 is a positive contraction , then @xmath9 has trivial tail . for finite @xmath0 and a positive contraction @xmath1 ,
define the of @xmath9 to be @xmath159 numerical calculation supports the following conjecture b.lyons:det/ : g.concave for all positive contractions @xmath160 and
@xmath161 , we have e.concave ( ( q_1+q_2)/2 ) ( ( q_1 ) + ( q_2))/2 . let @xmath0 be denumerable .
a function @xmath162 is called if for all @xmath163 and all @xmath164 , we have @xmath165 . an event is called increasing or if its indicator is increasing . given two probability measures @xmath166 , @xmath167 on @xmath148 , we say that and write @xmath168 if for all increasing events @xmath169 , we have @xmath170 .
this is equivalent to @xmath171 for all bounded increasing @xmath172 .
a of two probability measures @xmath166 , @xmath167 on @xmath148 is a probability measure @xmath173 on @xmath174 whose coordinate projections are @xmath166 , @xmath167 ; it is if @xmath175 by strassen s theorem @xcite , stochastic domination @xmath176 is equivalent to the existence of a monotone coupling of @xmath166 and @xmath167 .
t.dominate-infinite b.lyons:det/ if @xmath177 , then @xmath178
. it would be very interesting to find a natural or explicit monotone coupling .
a coupling @xmath173 has @xmath8 if for all events @xmath179 , we have @xmath180 .
q.unioncoupling @xcite given @xmath181 , is there a coupling of @xmath182 and @xmath183 with union marginal @xmath94 ? a positive answer is supported by some numerical calculation .
it is easily seen to hold when @xmath184 by c.dualrep/. in the sequel , we write @xmath185 if @xmath186 for all @xmath126 .
t.dominate @xcite if @xmath187 , then @xmath188 . by t.dominate-infinite/ , it suffices that there exist orthogonal projections @xmath189 and @xmath190 that are dilations of @xmath160 and @xmath161 such that @xmath191 .
this follows from namark s dilation theorem @xcite , which says that any measure whose values are positive operators , whose total mass is @xmath192 , and which is countably additive in the weak operator topology dilates to a spectral measure .
the measure in our case is defined on a 3-point space , with masses @xmath160 , @xmath193 , and @xmath194 , respectively . if we denote the respective dilations by @xmath195 , @xmath196 , and @xmath197 , then we set @xmath198 and @xmath199
. a positive answer in general to q.unioncoupling/ would give the following more general result by compression : if @xmath160 , @xmath161 and @xmath200 are positive contractions on @xmath37 , then there is a coupling of @xmath201 and @xmath202 with union marginal @xmath203
. it would be very useful to have additional sufficient conditions for stochastic domination : see the end of s.orthogpoly/ and g.fkdom/. for examples where more is known , see t.gmdom/. we shall say that the events in @xmath153 are @xmath158 and likewise for functions that are measurable with respect to @xmath153 .
we say that @xmath8 has if for every pair @xmath204 , @xmath205 of increasing functions that are measurable with respect to complementary subsets of @xmath0 , e.negass .
@xcite if @xmath206 , then @xmath9 has negative associations .
the details for finite @xmath0 were given in b.lyons : det/. for infinite @xmath0 , let @xmath204 and @xmath205 be increasing bounded functions measurable with respect to @xmath207 and @xmath208 , respectively . choose finite @xmath209 .
the conditional expectations @xmath210 $ ] and @xmath211 $ ] are increasing functions to which e.negass/ applies ( because restriction to @xmath212 corresponds to a compression of @xmath1 , which is a positive contraction ) and which , being martingales , converge to @xmath204 and @xmath205 in @xmath213 .
write @xmath214 for the distribution of a bernoulli random variable with expectation @xmath215 . for @xmath216 $ ] ,
let @xmath217 be the distribution of a sum of independent @xmath218 random variables . recall that @xmath75 $ ] is the set of scalar multiples of @xmath12 .
t.eigmix @xcite ; lemma 3.4 of @xcite ; ( 2.38 ) of @xcite ; @xcite let @xmath1 be a positive contraction with spectral decomposition @xmath219}$ ] , where @xmath220 are orthonormal .
let @xmath221 be independent .
let @xmath222 $ ] ; thus , @xmath223 . then @xmath224 .
hence , if @xmath225 , then @xmath226 . by t.dominate/
, it suffices to prove it when only finitely many @xmath227 . then by t.q/
, we have @xmath228 = \bigip{\bigwedge_{e \in a } q e , \theta_a } $ ] for all @xmath3 . now
@xmath229 } e & = \sum_{j \colon a \to \bbn } \prod_{e \in a } \lambda_{j(e ) } \bigwedge_{e \in a } p_{[v_{j(e ) } ] } e \\ & = \sum_{j \colon a \rightarrowtail \bbn } \prod_{e \in a } \lambda_{j(e ) } \bigwedge_{e \in a } p_{[v_{j(e ) } ] } e\end{aligned}\ ] ] because @xmath230 and @xmath231 } e$ ] is a multiple of @xmath12 , so none of the terms where @xmath232 is not injective contribute .
thus , @xmath233 } e = \ebig{\sum_{j \colon a \rightarrowtail \bbn } \prod_{e \in a } i_{j(e ) } \bigwedge_{e \in a } p_{[v_{j(e ) } ] } e } \\ & = \ebig{\sum_{j \colon a \to \bbn } \prod_{e \in a } i_{j(e ) } \bigwedge_{e \in a } p_{[v_{j(e ) } ] } e } = \be\bigwedge_{e \in a } \sum_k i_k p_{[v_k ] } e = \be \bigwedge_{e \in a } p_{\rh } e \,.\end{aligned}\ ] ] we conclude that @xmath234 = \be \leftip{\bigwedge_{e \in a } p_{\rh } e , \theta_a } = \ebig { \bp^{\rh}\left [ a \subseteq \ba \right ] } $ ] by e.qgenprs/. we sketch another proof : let @xmath235 be disjoint from @xmath0 with the same cardinality .
choose an orthonormal sequence @xmath236 in @xmath131 .
define then @xmath1 is the compression of @xmath15 to @xmath37 . expanding @xmath237 in the obvious way into orthogonal pieces and restricting to @xmath0 , we obtain the desired equation from e.xihpr/. the first proof shows more generally the following : let @xmath238 be a positive contraction .
let @xmath220 be ( not necessarily orthogonal ) vectors such that @xmath239 } \lloew i$ ] .
let @xmath240 be independent bernoulli random variables with @xmath241 .
write @xmath242}$ ]
. then @xmath243 .
this was observed by ghosh and krishnapur ( personal communication , 2014 )
. note that in the mixture of t.eigmix/ , the distribution of @xmath244 is determinantal corresponding to the diagonal matrix with diagonal @xmath245 .
thus , it is natural to wonder whether @xmath246 can be taken to be a general determinantal measure .
if such a mixture is not necessarily determinantal , must it be strongly rayleigh or at least have negative correlations ? here
, we say that a probability measure @xmath8 on @xmath148 has if for every pair @xmath5 , @xmath100 of finite disjoint subsets of @xmath0 , we have @xmath247 \le \bp [ a \subseteq \qba ] \bp [ b \subseteq \qba ] $ ] .
note that negative associations is stronger than negative correlations .
the most well - known example of a ( nontrivial discrete ) determinantal probability measure is that where @xmath6 is a uniformly chosen random spanning tree of a finite connected graph @xmath248 with @xmath249 . here ,
we regard a spanning tree as a set of edges .
the fact that holds for the uniform spanning tree is due to b.burpem/ and is called the transfer current theorem .
the case with @xmath250 was shown much earlier by b.kirchhoff/ , while the case with @xmath251 was first shown by b.bsst/. write @xmath252 for the uniform spanning tree measure on @xmath253 . to see that @xmath252 is indeed determinantal , consider the vertex - edge incidence matrix @xmath254 of @xmath253 , where each edge is oriented ( arbitrarily ) and the @xmath255-entry of @xmath254 equals 1 if @xmath256 is the head of @xmath66 , @xmath257 if @xmath256 is the tail of @xmath66 , and 0 otherwise .
identifying an edge with its corresponding column of @xmath254 , we find that a spanning tree is the same as a basis of the column space of @xmath254 .
given @xmath258 , define the at @xmath256 to be the @xmath256-row of @xmath254 , regarded as a vector @xmath259 in the row space , @xmath260 .
it is easy that the row - rank of @xmath254 is @xmath261 .
let @xmath262 and let @xmath65 be the wedge product ( in some order ) of the stars at all the vertices other than @xmath263 .
thus , @xmath264 for some @xmath265 .
since spanning trees are bases of the column space of @xmath254 , we have @xmath266 iff @xmath5 is a spanning tree .
that is , the only non - zero coefficients of @xmath65 are those in which choosing one edge in each @xmath259 for @xmath267 yields a spanning tree ; moreover , each spanning tree occurs exactly once since there is exactly one way to choose an edge incident to each @xmath267 to get a given spanning tree .
this means that its coefficient is @xmath268 .
hence , @xmath269 is indeed uniform on spanning trees .
simultaneously , this proves the matrix tree theorem that the number of spanning trees equals @xmath270_{x , y \ne x_0}$ ] , since this determinant is @xmath271
. one can define analogues of @xmath252 on infinite connected graphs @xcite by weak limits . for brevity ,
we simply define them here as determinantal probability measures .
again , all edges of @xmath253 are oriented arbitrarily .
we define @xmath272 as the closure of the linear span of the stars .
an element of @xmath273 that is finitely supported and orthogonal to @xmath272 is called a ; the closed linear span of the cycles is @xmath274 .
the is @xmath275 , while the is @xmath276 .
our discussion of the continuous " case includes the discrete case , but the discrete case has the more elementary formulations given earlier .
let @xmath0 be a measurable space .
as before , @xmath0 will play the role of the underlying set on which a point process forms a counting measure . while before we implicitly used counting measure on @xmath0 itself , now we shall have an arbitrary measure @xmath173 ; it need not be a probability measure . the case of lebesgue measure on euclidean space is a common one .
the hilbert spaces of interest will be @xmath277
. there may be no natural order in @xmath0 , so to define , e.g. , a probability measure on @xmath278 points of @xmath0 , it is natural to use a probability measure on @xmath279 that is symmetric under coordinate changes and that vanishes on the diagonal @xmath280 .
likewise , for exterior algebra , it is more convenient to identify @xmath281 with @xmath282 for @xmath283 .
thus , @xmath284 is identified with the function @xmath285_{i , j \in \{1 , \ldots , n\}}/\sqrt{n ! } $ ] .
note that @xmath286 \det [ { v_i(x_j ) } ] = \det [ u_i(x_j ) ] \det [ { v_i(x_j)}]^t \nonumber \\ & = \det [ u_i(x_j)][{v_i(x_j)}]^t = \det [ k(x_i , x_j)]_{i , j \in \{1 , \ldots , n\}}\end{aligned}\ ] ] with @xmath287 .
here , @xmath288 denotes transpose .
suppose from now on that @xmath0 is a locally compact polish space ( equivalently , a locally compact second countable hausdorff space ) .
let @xmath173 be a radon measure on @xmath0 , i.e. , a borel measure that is finite on compact sets .
let @xmath289 be the set of radon measures on @xmath0 with values in @xmath290 .
we give @xmath289 the vague topology generated by the maps @xmath291 for continuous @xmath172 with compact support ; then @xmath289 is polish .
the corresponding borel @xmath154-field of @xmath289 is generated by the maps @xmath292 for borel @xmath3 .
let @xmath293 be a simple point process on @xmath0 , i.e. , a random variable with values in @xmath289 such that @xmath294 for all @xmath295 .
the power @xmath296 lies in @xmath297 .
thus , @xmath298 $ ] is a borel measure on @xmath299 ; the part of it that is concentrated on @xmath300 is called the of @xmath293 .
if the intensity measure is absolutely continuous with respect to @xmath301 , then its radon - nikodym derivative @xmath302 is called the or the : since the intensity measure vanishes on the diagonal @xmath303 , we take @xmath302 to vanish on @xmath303
. we also take @xmath302 to be symmetric under permutations of coordinates .
intensity functions are the continuous analogue of the elementary probabilities e.dpm/. since the sets @xmath304 generate the @xmath154-field on @xmath300 for pairwise disjoint borel @xmath305 , a measurable function @xmath306 is the " @xmath18-point intensity function iff since @xmath293 is simple , @xmath307 , where @xmath308 . since @xmath302 vanishes on the diagonal , it follows from e.rn/ that for disjoint @xmath309 and non - negative @xmath310 summing to @xmath18 , again , this characterizes @xmath302 , even if we use only @xmath311 . in the special case that @xmath312 a.s .
for some @xmath313 , then the definition e.rn/ shows that a random ordering of the @xmath278 points of @xmath293 has density @xmath314 .
more generally , e.rn/ shows that for all @xmath315 , whence in this case , we call @xmath293 if for some measurable @xmath316 and all @xmath16 , @xmath317 @xmath301-a.e . here
, @xmath318 is the matrix @xmath319_{i , j \le k}$ ] . in this case
, we denote the law of @xmath293 by @xmath320 .
we consider only @xmath158 that are locally square integrable ( i.e. , @xmath321 is radon ) , are hermitian ( i.e. , @xmath322 for all @xmath323 ) , and are positive semidefinite ( i.e. , @xmath324 is positive semidefinite for all finite @xmath325 , written @xmath326 ) . in this case , @xmath158 defines a positive semidefinite integral operator @xmath327 on functions @xmath328 with compact support . for every borel @xmath3 , we denote by @xmath329 the measure @xmath173 restricted to borel subsets of @xmath5 and by @xmath330 the compression of @xmath158 to @xmath5 , i.e. , @xmath331 for @xmath332 .
the operator @xmath158 is locally trace - class , i.e. , for every compact @xmath3 , the compression @xmath330 is trace class , having a spectral decomposition @xmath333 , where @xmath334 are orthonormal eigenfunctions of @xmath330 with positive summable eigenvalues @xmath335 . if @xmath110 is the set where @xmath336 , then @xmath337 and @xmath338 converges on @xmath339 , with sum @xmath340-a.e .
equal to @xmath158 .
we normally redefine @xmath158 on a set of measure 0 to equal this sum .
such a @xmath158 defines a determinantal point process iff the integral operator @xmath158 extends to all of @xmath341 as a positive contraction @xcite .
the joint intensities determine uniquely the law of the point process ( * ? ? ?
* lemma 4.2.6 ) .
poisson processes are not determinantal processes , but when @xmath173 is continuous , they are distributional limits of determinantal processes . to see that a positive contraction defines a determinantal point process , we first consider @xmath158 that defines an orthogonal projection onto a finite - dimensional subspace , @xmath48
. then @xmath342 for every orthonormal basis @xmath343 of @xmath48 and @xmath344 is a unit multivector in the notation of s.ext/. because of e.prodtensor/ , we have i.e. , @xmath345/n!$ ] is a density with respect to @xmath346 .
although in the discrete case , the absolute squared coefficients of @xmath347 give the elementary probabilities , now coefficients are replaced by a function whose absolute square gives a probability density .
as noted already , e.firstdensity/ means that @xmath348 is the @xmath278-point intensity function . in order to show that this density gives a determinantal process with kernel @xmath158
, we use the cauchy - binet formula , which may be stated as follows : for @xmath349 matrices @xmath350 $ ] and @xmath351 $ ] with @xmath352_{\substack{i \le k \\ j \in j}}$ ] , we have @xmath353 [ b_{i , j}]^t\big ) = \sum_{|j| = k } \det a^j \cdot \det b^j = \sum _ { \substack{\sigma , \tau \in \sym(k , n ) \\
\operatorname{im}(\sigma ) = \operatorname{im}(\tau ) } } ( -1)^\sigma ( -1)^\tau \prod_{i=1}^k a_{i , \sigma(i ) } b_{i , \tau(i ) } \,,\ ] ] where @xmath354 denotes the image of @xmath154 and the sums extend over all pairs of injections @xmath355 here , the sign @xmath356 of @xmath154 is defined in the usual way by the parity of the number of pairs @xmath357 for which @xmath358 .
we have @xmath359 \,d\mu^{n - k}(x_{k+1 } , \ldots , x_n ) \nonumber \\ & = \frac{1}{(n - k ) ! }
\int_{e^{n - k } } \sum_{\sigma \in \sym(n ) } ( -1)^\sigma \prod_{i=1}^n \phi_{\sigma(i)}(x_i ) \cdot { } \nonumber \\
\noalign{$\displaystyle \hfill \cdot \sum_{\tau \in \sym(n ) } ( -1)^\tau \prod_{i=1}^n \overline{\phi_{\tau(i)}(x_i ) } \,d\mu^{n - k}(x_{k+1 } , \ldots , x_n ) $ } & = \sum_{\substack{\sigma , \tau \in \sym(k , n ) \\
\operatorname{im}(\sigma ) = \operatorname{im}(\tau ) } } ( -1)^\sigma ( -1)^\tau \prod_{i=1}^k \phi_{\sigma(i)}(x_i ) \overline{\phi_{\tau(i)}(x_i ) } \nonumber \\ & = \det \big(k \restrict ( x_1 , \ldots , x_k)\big ) \,.\end{aligned}\ ] ] here , the first equality uses e.integrate/ , the second equality uses e.prodtensor/ , the third equality uses the fact that @xmath360 is 1 or 0 according as @xmath361 or not , and the fourth equality uses cauchy - binet .
note that a factor of @xmath362 arises because for every pair of injections @xmath363 with equal image , there are @xmath362 extensions of them to permutations @xmath364 with @xmath361 for all @xmath365 ; in this case , @xmath366 .
we write @xmath94 for the law of the associated point process on @xmath0 .
l.weaklimit let @xmath367 with @xmath368 for some @xmath369 .
then @xmath370 is tight and every weak limit point of @xmath371 is simple . by using the kernel @xmath372 with respect to the measure @xmath373 , we may assume that @xmath374 .
tightness follows from @xmath375 \le \be[\sx_n(a ) ] = \int_a k_n(x , x ) \,d\mu(x)\,.\ ] ] for the rest , we may assume that @xmath0 is compact and @xmath376 .
let @xmath293 be a limit point of @xmath371 .
let @xmath377 be the atomic part of @xmath173 and @xmath378 .
choose @xmath379 and partition @xmath0 into sets @xmath380 with @xmath381 .
let @xmath5 be such that @xmath382 and @xmath383 .
let @xmath384 be open such that @xmath385 and @xmath386 .
then @xmath387 & \le \limsup_n \big(\bp[\sx_n(u \setminus a ) \ge 1 ] + \bp[\texists i \sx_n(a_i ) \ge 2]\big ) \\ & \le \limsup_n \big(\be[\sx_n(u \setminus a ) ] + \sum_i \be[(\sx_n(a_i))_2]\big ) \\ & \le \muc(u ) + \sum_i \mu(a_i)^2 < 2/m \ , .
\tag*{\qedhere}\end{aligned}\ ] ] now , given any locally trace - class orthogonal projection @xmath158 onto @xmath48 , choose finite - dimensional subspaces @xmath388 with corresponding projections @xmath389 .
clearly @xmath390 @xmath391-a.e.and @xmath392 @xmath173-a.e .
thus , the joint intensity functions converge a.e . by dominated convergence , if @xmath393 is relatively compact and borel , then @xmath394 \to \int_a \det ( k \restrict f ) \,d\mu^k(f)$ ] . by uniform exponential moments of @xmath395 (
* ? ? ?
* proof of lemma 4.2.6 ) , it follows that all weak limit points of @xmath396 are equal , and hence , by l.weaklimit/ , define @xmath94 with kernel @xmath158 .
( in s.cinequalities/ , we shall see that @xmath397 is stochastically increasing . ) finally , let @xmath158 be any locally trace - class positive contraction . define the orthogonal projection on @xmath398 whose block matrix is take an isometric isomorphism of @xmath277 to @xmath131 for some denumerable set @xmath235 and interpret the above as an orthogonal projection @xmath399 on @xmath400 .
then @xmath399 is clearly locally trace - class and @xmath158 is the compression of @xmath399 to @xmath0 .
thus , we define @xmath320 by intersecting samples of @xmath401 with @xmath0 .
we remark that by writing @xmath399 as a limit of increasing finite - rank projections that we then compress , we see that @xmath320 may be defined as a limit of determinantal processes corresponding to increasing finite - rank positive contractions .
g.ctail if @xmath158 is a locally trace - class positive contraction , then @xmath320 has trivial tail in that every event in @xmath402 is trivial . rather than using compressions as in the last paragraph above , an alternative approach to defining @xmath320 uses mixtures and starts from finite - rank projections , as in s.mix/. this approach is due to b.hkpv : survey/. consider first a finite - rank @xmath403 .
let @xmath404 be independent .
let @xmath405 $ ] ; thus , @xmath406 . we claim that @xmath407 is determinantal with kernel @xmath158 .
indeed , it is clearly a simple point process .
write @xmath408 , @xmath409 , and @xmath410 .
let @xmath411 .
combining cauchy - binet with e.prodtensor/ yields @xmath412 .
similarly , the joint intensities of @xmath413 are the expectations of the joint intensities of @xmath414 , which equal @xmath415 essentially the same works for trace - class @xmath416 ; we need merely take , in the last step , a limit in the above equation as @xmath417 for @xmath418 , since all terms are non - negative and @xmath419 a.e .
given this construction of @xmath320 for trace - class @xmath158 , one can then construct @xmath320 for a general locally trace - class positive contraction by defining its restriction to each relatively compact set @xmath5 via the trace - class compression @xmath330 . as noted by b.hkpv:survey/ ,
a consequence of the mixture representation is a clt due originally to b.soshnikov:gauss/ : t.clt let @xmath389 be trace - class positive contractions on spaces @xmath420 .
let @xmath367 and write @xmath421 . if @xmath422 as @xmath417 , then @xmath423 obeys a clt .
in order to simulate @xmath320 when @xmath158 is a trace - class positive contraction , it suffices , by taking a mixture as above , to see how to simulate @xmath424 when @xmath425 . the following algorithm ( * ? ? ? * algo .
18 ) gives a uniform random ordering of @xmath293 as @xmath426 . since @xmath427 , the measure @xmath428/n = n^{-1 } k(x , x)\,d\mu(x)$ ] is a probability measure on @xmath0 .
select a point @xmath429 at random from that measure .
if @xmath430 , then we are done .
if not , then let @xmath431 be the orthogonal complement in @xmath48 of the function @xmath432 , where @xmath343 is an orthonormal basis for @xmath48 .
then @xmath433 and we may repeat the above for @xmath431 to get the next point , @xmath434 , then @xmath435 , etc .
the conditional density of @xmath436 given @xmath437 is @xmath438 by e.densityktuple/ , i.e. , @xmath439 times the squared distance from @xmath440 to the linear span of @xmath441 .
it can help for rejection sampling to note that this is at most @xmath442 .
one can also sample faster by noting that the conditional distribution of @xmath436 is the same as that of @xmath443 , where @xmath444 is a uniformly random vector on the unit sphere of @xmath113 .
note that if @xmath445 are bounded @xmath446-valued random variables , then the function @xmath447 determines the joint distribution of @xmath448 since it gives the derivatives at @xmath449 of the probability generating function @xmath450 .
let us re - examine e.falling/ in the context of a finite - rank @xmath451 .
given disjoint @xmath452 and non - negative @xmath310 summing to @xmath18 , it will be convenient to write @xmath453 for @xmath454 .
we have by cauchy - binet @xmath455 = \int_{\prod_{\ell=1}^r a_\ell^{k_\ell } } \rho_k \,d\mu^k = \int_{\prod_{\ell=1}^r a_\ell^{k_\ell } } \det ( k \restrict ( x_1 , \ldots , x_k ) ) \,\prod_{j=1}^k d\mu(x_j ) \\ & = \int_{\prod_{\ell=1}^r a_\ell^{k_\ell } } \sum_{\substack{\sigma , \tau \in \sym(k , n ) \\
\operatorname{im}(\sigma ) = \operatorname{im}(\tau ) } } ( -1)^\sigma ( -1)^\tau \prod_{j=1}^k \lambda_{\sigma(j ) } \phi_{\sigma(j)}(x_j ) \overline{\phi_{\tau(j)}(x_j ) } \,\prod_{j=1}^k d\mu(x_j ) \\ & = \sum_{\substack{\sigma , \tau \in \sym(k , n ) \\
\operatorname{im}(\sigma ) = \operatorname{im}(\tau ) } } ( -1)^\sigma ( -1)^\tau \prod_{j=1}^k \int_{a_{\kappa(j ) } } \lambda_{\sigma(j ) } \phi_{\sigma(j)}(x_j ) \overline{\phi_{\tau(j)}(x_j ) } \,d\mu(x_j ) \\ & = \sum_{\substack{\sigma , \tau \in \sym(k , n ) \\
\operatorname{im}(\sigma ) = \operatorname{im}(\tau ) } } ( -1)^\sigma ( -1)^\tau \lambda^{\operatorname{im}(\sigma ) } \prod_{j=1}^k \bigip{\boi{a_{\kappa(j ) } } \phi_{\sigma(j ) } , \overline{\phi_{\tau(j ) } } } \\ & = \sum_{\sigma \in \sym(k , n ) } ( -1)^\sigma \lambda^{\operatorname{im}(\sigma ) } \det \big [ \bigip{\boi{a_{\kappa(j ) } } \phi_{\sigma(j ) } , \overline{\phi_\ell } } \big]_{\substack{j \le k \hfill \\ \ell
\in \operatorname{im}(\sigma ) } } \,.\end{aligned}\ ] ] as an immediate consequence of this formula , we obtain the following important principle of goldman ( * ? ? ?
* proposition 12 ) that allows one to infer properties of continuous determinantal point processes from corresponding properties of discrete determinantal probability measures : t.transfer let @xmath456 and @xmath457 be two radon measure spaces on locally compact polish sets .
let @xmath458 be pairwise disjoint borel subsets of @xmath0 and @xmath459 be pairwise disjoint borel subsets of @xmath325 .
let @xmath460 $ ] with @xmath461 .
let @xmath462 be orthonormal in @xmath277 and @xmath463 be orthonormal in @xmath464 .
let @xmath465 and @xmath466 . if @xmath467 for all @xmath468 , then the @xmath320-distribution of @xmath469 equals the @xmath470-distribution of @xmath471 .
when only finitely many @xmath227 , this follows from our previous calculation .
the general case follows from weak convergence of the processes corresponding to the partial sums , as in the paragraph following l.weaklimit/. this permits us to compare to discrete measures via ( * ? ? ?
* lemma 16 ) : l.compare let @xmath173 be a radon measure on a locally compact polish space , @xmath0 .
let @xmath458 be pairwise disjoint borel subsets of @xmath0 .
let @xmath472 for @xmath16 .
then there exists a denumerable set @xmath325 , pairwise disjoint subsets @xmath459 of @xmath325 , and @xmath473 such that @xmath474 and @xmath475 for all @xmath468 . without loss of generality
, we may assume that @xmath476 .
for each @xmath477 , fix an orthonormal basis @xmath478 for the subspace of @xmath277 spanned by @xmath479 . here ,
@xmath480 .
define @xmath481 and @xmath482 .
let @xmath483 be the isometric isomorphism from the span of @xmath484 to @xmath485 that sends @xmath486 to @xmath487 .
defining @xmath488 yields the desired vectors .
we now show how the discrete models of s.transf/ allow us to obtain the analogues of the stochastic inequalities known to hold for discrete determinantal probability measures . for a borel set @xmath7 , let @xmath207 denote the @xmath154-field on @xmath289 generated by the functions @xmath489 for borel @xmath490 .
we say that a function that is measurable with respect to @xmath207 is , more simply , measurable with respect to @xmath5 .
the obvious partial order on @xmath289 allows us to define what it means for a function @xmath491 to be . as in the discrete case
, we say that @xmath8 has if @xmath492 \le \be[f_1 ] \be[f_2 ] $ ] for every pair @xmath204 , @xmath205 of bounded increasing functions that are measurable with respect to complementary subsets of @xmath0 .
an event is increasing if its indicator is increasing .
then @xmath8 has negative associations iff for every pair @xmath493 , @xmath494 of increasing events that are measurable with respect to complementary subsets of @xmath0 .
we also say that and write @xmath495 if @xmath496 for every increasing event @xmath169 .
call an event if it has the form @xmath497 , where @xmath100 is a relatively compact borel set and @xmath498 .
write @xmath499 for the closure under finite unions and intersections of the collection of elementary increasing events with @xmath500 ; the notation @xmath501 is chosen for upwardly closed " .
note that every event in @xmath499 is measurable with respect to some finite collection of functions @xmath502 for pairwise _ disjoint _ relatively compact borel @xmath503 .
write @xmath504 for the closure of @xmath499 under monotone limits , i.e. , under unions of increasing sequences and under intersections of decreasing sequences ; these events are also increasing .
this is the same as the closure of @xmath499 under countable unions and intersections .
l.approxincr let @xmath5 be a borel subset of a locally compact polish space , @xmath0 .
then @xmath504 is exactly the class of increasing borel sets in @xmath207 .
we give a proof at the end of this subsection .
first , we derive two consequences . a weaker version ( negative correlations of elementary increasing events ) of the initial one is due to b.ghosh/. t.cfm let @xmath173 be a radon measure on a locally compact polish space , @xmath0 .
let @xmath158 be a locally trace - class positive contraction on @xmath277 .
then @xmath320 has negative associations .
let @xmath505 be borel .
let @xmath506 and @xmath507 .
then @xmath508 for some compact @xmath100 by definition of @xmath509 .
we claim that e.cnegass/ holds for @xmath493 , @xmath494 , and @xmath510 , i.e. , for @xmath511 .
now @xmath493 is measurable with respect to a finite number of count functions @xmath502 for some disjoint @xmath512 ( @xmath513 ) and likewise @xmath494 is measurable with respect to a finite number of functions @xmath514 for some disjoint @xmath515 ( @xmath513 ) .
thus , there are functions @xmath516 and @xmath517 such that @xmath518 and @xmath519 . by t.transfer/ and l.compare/
, there is some discrete determinantal probability measure @xmath9 on some denumerable set @xmath325 and pairwise disjoint sets @xmath520 such that the joint @xmath521-distribution of all @xmath522 and @xmath523 is equal to the joint @xmath9-distribution of all @xmath524 and @xmath525 .
define the corresponding events @xmath526 by @xmath527 and @xmath528 .
since @xmath526 depend on disjoint subsets of @xmath325 , t.fm/ gives that @xmath529 .
this is the same as e.cnegass/ by t.transfer/. the same e.cnegass/ clearly then holds in the less restrictive setting @xmath530 by taking monotone limits .
l.approxincr/ completes the proof .
t.cdom theorem 3 of b.goldman/ suppose that @xmath531 and @xmath532 are two locally trace - class positive contractions such that @xmath533
. then @xmath534 .
it suffices to show that @xmath535 for every @xmath536 .
again , it suffices to assume that @xmath537 are trace class .
l.compare/ applied to all eigenfunctions of @xmath531 and @xmath532 yields a denumerable @xmath325 and two positive contractions @xmath538 on @xmath485 , together with an event @xmath539 , such that @xmath540 for @xmath541 .
furthermore , by construction , every function in @xmath485 is the image of a function in @xmath542 under the isometric isomorphism @xmath483 used to prove l.compare/ , whence @xmath543 .
therefore t.dominate/ yields @xmath544 , as desired .
again , it would be very interesting to have a natural monotone coupling of @xmath545 with @xmath546 .
for some examples where this would be desirable , see s.orthogpoly/. l.approxincr/ will follow from this folklore variant of a theorem of dyck b.dyck/ : t.dyck let @xmath136 be a polish space on which @xmath547 is a partial ordering that is closed in @xmath548 . let @xmath501 be a collection of open increasing sets that generates the borel subsets of @xmath136 .
let @xmath549 be the closure of @xmath501 under countable intersections and countable unions .
suppose that for all @xmath550 , either @xmath551 or there is @xmath552 and an open set @xmath553 such that @xmath554 , @xmath555 , and @xmath556 . then @xmath549 equals the class of increasing borel sets .
obviously every set in @xmath549 is borel and increasing . to show the converse
, we prove a variant of lusin s separation theorem .
namely , we show that if @xmath557 is increasing and analytic ( with respect to the paving of closed sets , as usual ) and if @xmath558 is analytic with @xmath559 , then there exists @xmath560 such that @xmath561 and @xmath562 . taking @xmath563 to be borel and @xmath564 forces @xmath565 and gives the desired conclusion . to prove this separation property , we first show a stronger conclusion in a special case
: suppose that @xmath566 are compact such that @xmath110 is contained in an increasing set @xmath563 that is disjoint from @xmath111 ; then there exists an open @xmath560 and an open @xmath567 such that @xmath568 , @xmath569 , and @xmath556 .
indeed , since @xmath563 is increasing , for every @xmath570 , we do _ not _ have that @xmath551 , whence by hypothesis , there exist @xmath571 and an open @xmath572 with @xmath573 , @xmath574 , and @xmath575 . because @xmath111 is compact , for each @xmath576 , we may choose @xmath577 such that @xmath578 .
define @xmath579 .
then @xmath580 is open , contains @xmath256 , and is disjoint from @xmath581 , whence compactness of @xmath110 ensures the existence of @xmath582 with @xmath583 .
then @xmath584 is open , contains @xmath111 , and is disjoint from @xmath384 , as desired . to prove the general case ,
let @xmath585 and @xmath586 be the two coordinate projections on @xmath587 .
define @xmath588 for @xmath589 to be 0 if there exists @xmath560 such that @xmath590 and @xmath591 ; and to be 1 otherwise .
we claim that @xmath192 is a capacity in the sense of ( * ? ? ?
* ( 30.1 ) ) .
it is obvious that @xmath592 if @xmath593 and it is simple to check that if @xmath594 , then @xmath595 .
suppose for the final property that @xmath5 is compact and @xmath596 ; we must find an open @xmath597 for which @xmath598 .
there exists some @xmath599 with @xmath600 and @xmath601 .
then the result of the second paragraph yields sets @xmath384 and @xmath567 that give @xmath602 as desired
. now let @xmath563 and @xmath603 be as in the first paragraph .
if @xmath604 is compact , then setting @xmath605 and applying the second paragraph shows that @xmath596 .
thus , by the choquet capacitability theorem ( * ? ? ?
* ( 30.13 ) ) , @xmath606 .
l.approxincr/ clearly every set in @xmath504 is increasing and in @xmath207 .
for the converse , endow @xmath5 with a metric so that it becomes locally compact polish while preserving its class of relatively compact sets and its borel @xmath154-field : choose a denumerable partition of @xmath5 into relatively compact sets @xmath607 and make each one compact and of diameter at most 1 ; make the distance between @xmath256 and @xmath608 be 1 if @xmath256 and @xmath608 belong to different @xmath607 .
let @xmath609 with the vague topology and let @xmath501 be the class of elementary increasing events defined with respect to ( relatively compact ) sets @xmath500 that are open for this new metric .
apply t.dyck/. since @xmath610 , the result follows .
natural examples of determinantal point processes arise from orthogonal polynomials with respect to a probability measure @xmath173 on @xmath25 .
assume that @xmath173 has infinite support and finite moments of all orders .
let @xmath389 denote the orthogonal projection of @xmath611 onto the linear span @xmath612 of the functions @xmath613 .
there exist unique ( up to signum ) polynomials @xmath614 of degree @xmath18 such that for every @xmath278 , @xmath615 is an orthonormal basis of @xmath612 . by elementary row operations
, we see that for variables @xmath616 , the map @xmath617_{i , j \le n}$ ] is a vandermonde polynomial up to a constant factor , whence @xmath618 [ \phi_i(z_j)]^ * = c_n \prod_{1 \le i < j \le n } |z_i - z_j|^2\ ] ] for some constant @xmath619 . therefore , the density of @xmath620 ( with points randomly ordered ) with respect to @xmath346 is given by @xmath621 times the square of a vandermonde determinant .
classical examples include the following : 1
. if @xmath173 is gaussian measure on @xmath24 , i.e. , @xmath622 , then @xmath614 are the hermite polynomials , @xmath623 , and @xmath620 is the law of the , which is the set of eigenvalues of @xmath624 , where @xmath625 is an @xmath626 matrix whose entries are independent standard complex gaussian .
( a standard complex gaussian random variable is the same as a standard gaussian vector in @xmath627 divided by @xmath628 in order that the complex variance equal 1 .
its density is @xmath629 with respect to lebesgue measure on @xmath25 . )
this is due to wigner ; see b.mehta/. 2 .
if @xmath173 is unit lebesgue measure on the unit circle @xmath630 , then @xmath631 , so @xmath632 , and @xmath620 is the law of the , which is the set of eigenvalues of a random matrix whose distribution is haar measure on the set of @xmath626 unitary matrices .
this ensemble was introduced by dyson , but the law of the eigenvalues is due to weyl ; see b.hkpv : book/. 3 .
if @xmath173 is standard gaussian measure on @xmath25 , then @xmath633 , @xmath623 , and @xmath620 is the law of the , which is the set of eigenvalues of an @xmath626 matrix whose entries are independent standard complex gaussian .
this is due to ginibre ; see b.hkpv : book/. 4 .
if @xmath173 is unit lebesgue measure on the unit disk @xmath634 , then @xmath635 , so @xmath636 , and the limit of @xmath620 is the law of the zero set of the random power series whose coefficients are independent standard complex gaussian , which converges in the unit disk a.s .
this is due to peres and virg b.peresvirag/. 5 .
if @xmath173 has density @xmath637 with respect to lebesgue measure on @xmath25 , then @xmath638 for @xmath315 , so @xmath639 , and @xmath620 is the law of the , which is the set of eigenvalues of @xmath640 when @xmath641 are independent @xmath626 matrices whose entries are independent standard complex gaussian .
( here , we are limited to @xmath612 since the larger spaces do not lie in @xmath341 . )
this is due to krishnapur b.krishnapur:thesis/ ; see b.hkpv : book/. the process was studied earlier by b.caillol/ and b.fjm/ , but without observing the connection to eigenvalues .
inverting stereographic projection , we identify this process with one whose density with respect to lebesgue measure on the unit sphere in @xmath642 is proportional to @xmath643 . for additional information on such processes ,
see @xcite . for an extension to complex manifolds ,
see @xcite . by t.cdom/ ,
the processes @xmath620 stochastically increase in @xmath278 for each of the examples above except the last
. it would be interesting to see natural monotone couplings .
perhaps the last example also increases stochastically in @xmath278 .
the is the limit of the @xmath278th ginibre processes as @xmath417 ; it has the kernel @xmath644 with respect to standard gaussian measure on @xmath25 .
this process is invariant under all isometries of @xmath25 . for each of the plane , sphere , and hyperbolic disk ,
there is only a 1-parameter family of determinantal point processes having a kernel @xmath645 that is holomorphic in @xmath646 and in @xmath647 and whose law is isometry invariant ( * ? ? ?
* theorem 3.0.5 ) . for the sphere , that family
has already been given above ; the parameter is a positive integer . for the other two families ,
the parameter is a positive real number , @xmath648 . in the case of the plane ,
the processes are related simply by homotheties , @xmath649 .
the push - forward of the ginibre process with respect to @xmath650 has kernel @xmath651 with respect to the measure @xmath652 , where @xmath173 is lebesgue measure on @xmath25 .
do these processes increase stochastically in @xmath648 , like poisson processes do ? in the hyperbolic disk , the processes have kernel @xmath653 with respect to the measure @xmath654 , where @xmath173 is lebesgue measure on @xmath655 .
( we fix a branch of @xmath656 for @xmath657 . )
these give orthogonal projections onto the generalized bergman spaces .
the case @xmath658 is that of the limiting ope4 above .
do these processes stochastically increase in @xmath648 ?
recall that when @xmath48 is a finite - dimensional subspace of @xmath37 , the measure @xmath94 is supported by those subsets @xmath95 that project to a basis of @xmath48 under @xmath15 .
similarly , when @xmath158 is the kernel of a finite - rank orthogonal projection onto @xmath659 , define the functions @xmath660 .
then the measure @xmath320 is supported by those @xmath661 such that @xmath662 is a basis of @xmath48 , since @xmath663 .
here , @xmath664 means that @xmath665 .
the question of extending this to infinite - dimensional @xmath48 turns out to be very interesting .
a basis of a finite - dimensional vector space is a minimal spanning set .
although @xmath666 is @xmath94-a.s .
linearly independent , minimality does not hold in general , even for the wired spanning forest of a tree , as shown by the examples in b.heicklenlyons/. see also c.ell2min/. however , the other half of being a basis does hold in the discrete case and is open in the continuous case .
let @xmath667 $ ] be the closed linear span of @xmath668 .
t.basis b.lyons:det/ for every @xmath49 , we have @xmath669 = h$ ] @xmath94-a.s .
we give an application of t.basis/ for @xmath670 , but it has an analogous statement for every countable abelian group . let @xmath671 be the unit circle equipped with unit lebesgue measure
. for a measurable function @xmath672 and @xmath673 , the of @xmath172 at @xmath278 is @xmath674 .
let @xmath675 denote the restriction of @xmath676 to @xmath677 .
if @xmath678 is measurable , we say @xmath679 is @xmath5 if the set @xmath680 is dense in @xmath681 , where we identify @xmath681 with the set of functions in @xmath682 that vanish outside @xmath5 .
the case where @xmath5 is an interval is quite classical ; see b.redheffer/ for a review . a crucial role in that case is played by the following notion of density of @xmath677 .
d.bm for an interval @xmath683 \subset \bbr \setminus \ { 0 \}$ ] , define its @xmath684\big ) : = \max \big\ { |a| , |b| \big\}/ \min \big\ { |a| , |b| \big\ } \,.\ ] ] for a discrete @xmath685 , the of @xmath677 , denoted @xmath686 , is the supremum of those @xmath687 for which there exist disjoint nonempty intervals @xmath688 with @xmath689 for all @xmath278 and @xmath690 ^ 2 = \infty$ ] .
a simpler form of the beurling - malliavin density was provided by b.red:two/ , who showed that e.bmred ( s ) = \ { c : s _ k s | - | < } .
c.seqdual b.lyons:det/ let @xmath691 be lebesgue measurable with measure @xmath692 .
then there is a set of beurling - malliavin density @xmath692 in @xmath693 that is complete for @xmath5 .
indeed , let @xmath694 be the determinantal probability measure on @xmath695 corresponding to the toeplitz matrix @xmath696
. then @xmath694-a.e .
@xmath697 is complete for @xmath5 and has @xmath698 .
when @xmath5 is an interval , the celebrated theorem of beurling and malliavin b.bm/ says that if @xmath677 is complete for @xmath5 , then @xmath699 , and that if @xmath700 , then @xmath677 is complete for @xmath5 .
( this holds for @xmath677 that are not necessarily sets of integers , but we are concerned in this subsection only with @xmath679 . )
c.seqdual/ can be compared ( take @xmath701 and @xmath702 ) to a theorem of bourgain and tzafriri b.btz/ , according to which there is a set @xmath697 of ( schnirelman ) density at least @xmath703 such that if @xmath704 and @xmath676 vanishes off @xmath677 , then @xmath705 it would be interesting to find a quantitative strengthening of c.seqdual/ that would encompass this theorem of @xcite .
the following theorem is equivalent to t.basis/ by duality : t.morris b.lyons:det/ for every @xmath49 , we have @xmath706 } h } = [ \ba]$ ] @xmath94-a.s . as an example , consider the wired spanning forest of a graph , @xmath253 . here , @xmath707 .
in this case , @xmath708 } \star(g ) } = \star(b)$ ] for @xmath709 .
thus , the conclusion of t.morris/ is that @xmath710 , which equals @xmath711 , is concentrated on the singleton @xmath712 for @xmath713-a.e .
@xmath714 .
this was a conjecture of , established by b.morris/. c.ell2min for every @xmath49 , @xmath94-a.s . the maps @xmath715 \to h$ ] and @xmath716 } \colon h \to [ \ba]$ ] are injective with dense image .
both statements are equivalent to @xmath717 \cap h^\perp = \{0\ } = h \cap \ba^\perp$ ] , and these are the contents of theorems [ thm : basis ] and [ thm : morris ] . proved that on any network @xmath718 ( where @xmath253 is the underlying graph and @xmath719 is the function assigning conductances , or weights , to the edges ) , for @xmath720-a.e .
forest @xmath714 and for every component tree @xmath483 of @xmath714 , the @xmath721 of @xmath722 equals @xmath483 a.s .
this suggested b.lyons:det/ the following extension .
given a subspace @xmath48 of @xmath37 and a set @xmath95 , the subspace of @xmath723 $ ] most like " or closest to " @xmath48 is the closure of the image of @xmath48 under the orthogonal projection @xmath724}$ ] ; we denote this subspace by @xmath725 .
for example , if @xmath726 , then @xmath727 since for each @xmath728 , we have @xmath724 } ( \star_x^g ) = \star_x^b$ ] .
to say that @xmath729 is concentrated on @xmath730 is the same as to say that @xmath731 $ ] .
this motivated the following theorem and shows how it is an extension of morris s theorem .
if @xmath158 is a locally trace - class orthogonal projection onto @xmath48 , then for @xmath732 , we have @xmath733 in other words , @xmath158 is a reproducing kernel for @xmath48 .
a subset @xmath677 of @xmath48 is called if the closed linear span of @xmath677 equals @xmath48 ; equivalently , the only element of @xmath48 that is orthogonal to @xmath677 is 0 .
an analogue of t.basis/ was conjectured by lyons and peres in 2010 : g.cbasis if @xmath158 is a locally trace - class orthogonal projection onto @xmath48 , then for @xmath320-a.e .
@xmath293 , @xmath734 = h$ ] , i.e. , if @xmath735 and @xmath736 , then @xmath737 .
just as in the discrete case , this appears to be on the critical border for many special instances , as we illustrate for several processes where @xmath738 : 1 .
let @xmath173 be lebesgue measure on @xmath24 and @xmath739 , the .
denote the fourier transform on @xmath24 by @xmath740 for @xmath741 , and , by isometric extension , for @xmath742 .
write @xmath743}$ ] . since @xmath744 , we have @xmath745 , where @xmath746 is the inverse fourier transform of @xmath172 .
therefore , the induced operator @xmath158 arises from the orthogonal projection onto the paley - wiener space @xmath747 .
the sine - kernel process arises frequently ; e.g. , it is various scaling limits of the @xmath278th gaussian unitary ensemble in the bulk " as @xmath417 .
( a related scaling limit of the gue is wigner s semicircle distribution . )
we may more easily interpret g.cbasis/ for fourier transforms of functions in @xmath748 $ ] : it says that for @xmath320-a.e .
@xmath293 , the only @xmath749 $ ] such that @xmath750 is @xmath751 .
although the beurling - malliavin theorem applies , no information can be deduced because @xmath752 a.s .
however , ghosh b.ghosh/ has proved this case .
2 . let @xmath173 be standard gaussian measure on @xmath25 and @xmath753 .
this is the ginibre process .
it corresponds to orthogonal projection onto the @xmath754 consisting of the entire functions that lie in @xmath611 ; this is the space of power series @xmath755 such that @xmath756 .
completeness of a set of elements @xmath757 in @xmath754 is equivalent to completeness in @xmath758 ( with lebesgue measure ) of the gabor system of windowed complex exponentials @xmath759 \st \lambda \in \sqrt{2}\lambda\big\ } \,,\ ] ] which is used in time - frequency analysis of non - band - limited signals
. the equivalence is proved using the bargmann transform @xmath760 \,dt \big ) \,,\ ] ] which is an isometry from @xmath758 to @xmath754 . that the critical density is 1 was shown in various senses going back to von neumann ; see b.clp/. this case has also been proved by ghosh b.ghosh/. 3 .
let @xmath173 be unit lebesgue measure on the unit disk @xmath761 and @xmath762 .
this process is the limiting ope4 in s.orthogpoly/. it corresponds to orthogonal projection onto the @xmath763 consisting of the analytic functions that lie in @xmath764 .
what is known about the zero sets of functions in the bergman space b.duren/ is insufficient to settle g.cbasis/ in this case and it remains open .
the two instances above that have been proved by ghosh b.ghosh/ follow from his more general result that g.cbasis/ holds whenever @xmath173 is continuous and @xmath320 is , which means that @xmath765 is measurable with respect to the @xmath320-completion of @xmath766 for every ball @xmath767 .
the limiting process ope4 is not rigid b.hs : tolerance/. ghosh and krishnapur ( personal communication , 2014 ) have shown that @xmath320 is rigid only if @xmath158 is an orthogonal projection .
it is not sufficient that @xmath158 be a projection , as the example of the bergman space shows .
a necessary and sufficient condition to be rigid is not known .
let @xmath158 be a locally trace - class orthogonal projection onto @xmath768 .
for a function @xmath172 , write @xmath769 for the function @xmath770
. let @xmath771 .
clearly @xmath772 for a.e .
@xmath293 . also , for @xmath773
, the function @xmath774 is bounded .
a conjecture analogous to c.ell2min/ is that @xmath293 is a sort of set of interpolation for @xmath48 in the sense that given any countable dense set @xmath775 , for a.e .
@xmath293 , the set @xmath776 is dense in @xmath777 .
one may also ask about completeness for appropriate poisson point processes .
suppose @xmath778 is a group that acts on @xmath0 and that @xmath158 is @xmath778-invariant , i.e. , @xmath779 for all @xmath780 , @xmath295 , and @xmath781 .
( this is equivalent to the operator @xmath158 being @xmath778-equivariant . )
then the probability measure @xmath320 is @xmath778-invariant .
this contact with ergodic theory and other areas of mathematics suggests many interesting questions .
lack of space prevents us from considering more than just a few aspects of the case where @xmath0 is discrete and from giving all definitions .
let @xmath782 . in this case
, @xmath158 is invariant iff @xmath783 for some @xmath784 $ ] , where @xmath785 .
we write @xmath786 in place of @xmath320 . some results and questions from b.ls:dyn/
follow .
t.bern for all @xmath172 , the process @xmath786 is isomorphic to a bernoulli process .
this was shown in dimension 1 by b.shitak:ii/ for those @xmath172 such that @xmath787 by showing that those @xmath786 are weak bernoulli ( wb ) , also called @xmath788-mixing " and absolutely regular " . despite its name
, it is known that wb is strictly stronger than bernoullicity . the precise class of @xmath172 for which @xmath786 is wb
is not known . as usual ,
the of a nonnegative function @xmath172 is @xmath789 .
t.gmdom for all @xmath172 , the process @xmath786 stochastically dominates product measure @xmath790 and is stochastically dominated by product measure @xmath791 .
these bounds are optimal .
we conjecture that ( kolmogorov - sinai ) entropy is concave , as would follow from g.concave/. g.invconcave for all @xmath172 and @xmath792 , we have @xmath793 .
q.block let @xmath794 $ ] be a trigonometric polynomial of degree @xmath795 .
then @xmath786 is @xmath795-dependent , as are all @xmath796-block factors of independent processes .
is @xmath797 an @xmath796-block factor of an i.i.d .
process ?
this is known when @xmath798 b.broman/. let @xmath778 be a sofic group , a class of groups that includes all finitely generated amenable groups and all finitely generated residually amenable groups .
no finitely generated group is known not to be sofic .
let @xmath0 be @xmath778 or , more generally , a set acted on by @xmath778 with finitely many orbits , such as the edges of a cayley graph of @xmath778 .
the following theorems are from b.lyonsthom/. t.sbern for every @xmath778-equivariant positive contraction @xmath1 on @xmath37 , the process @xmath9 is a @xmath799-limit of finitely dependent ( invariant ) processes . if @xmath778 is amenable and @xmath800 , then @xmath9 is isomorphic to a bernoulli process . even if @xmath166 and @xmath167 are @xmath778-invariant probability measures on @xmath801 with @xmath168 , there need not be a @xmath778-invariant monotone coupling of @xmath166 and @xmath167 b.mester : mono/. the proof of the preceding theorem depends on the next one : t.monojoin if @xmath160 and @xmath161 are two @xmath778-equivariant positive contractions on @xmath37 with @xmath185 , then there exists a @xmath778-invariant monotone coupling of @xmath201 and @xmath202 .
the proof of t.sbern/ also uses the inequality @xmath802 for equivariant positive contractions , @xmath1 and @xmath803 , where @xmath804 is the schatten 1-norm .
when @xmath1 and @xmath803 commute , one can improve this bound to @xmath805 we do not know whether this inequality always holds .
write @xmath806 for the fuglede - kadison determinant of @xmath1 when @xmath1 is a @xmath778-equivariant operator
. the following would extend t.gmdom/. it is open even for finite groups .
g.fkdom for all @xmath778-equivariant positive contractions @xmath1 on @xmath807 , the process @xmath9 stochastically dominates product measure @xmath808 and is stochastically dominated by product measure @xmath809 , and these bounds are optimal .
it turns out that the expected degree of a vertex in the free uniform spanning forest of a cayley graph depends only on the group , via its first @xmath810-betti number , @xmath811 , and not on the generating set used to define the cayley graph b.lyons:betti/ : t.betti in every cayley graph @xmath253 of a group @xmath778 , we have @xmath812 = 2 \beta_1(\gp ) + 2 \,.\ ] ] this is proved using the representation of @xmath813 as a determinantal probability measure .
it can be used to give a uniform bound on expansion constants b.lpv/ : t.lpv for every finite symmetric generating set @xmath677 of a group @xmath778 , we have @xmath814 for all finite non - empty @xmath815 .
there are extensions of these results to higher - dimensional cw - complexes and higher @xmath810-betti numbers b.lyons : betti/. in unpublished work with d. gaboriau @xcite , we have shown the following : t.damien let @xmath253 be a cayley graph of a finitely generated group @xmath778 and @xmath816 . then there exists a @xmath778-invariant finitely dependent determinantal probability measure @xmath9 on @xmath817 that stochastically dominates @xmath818 and such that @xmath819 \le \be_\fsf\big[\deg_\fo(\bp)\big ] + \epsilon \,.\ ] ] in addition , if @xmath778 is sofic , then @xmath820 .
if it could be shown that @xmath9 , or indeed every invariant finitely dependent probability measure that dominates @xmath813 , yields a connected subgraph a.s . , then it would follow that @xmath821 is equal to the cost of @xmath778 , a major open problem of b.gaboriau : invar/. |
the study of the high - redshift progenitors of today s massive galaxies can provide us with invaluable insights into the key mechanisms that shape the evolution of galaxies in the high - mass regime .
the latest generation of galaxy formation models are now able to explain the number densities and ages of massive galaxies at high redshift . however , this is only part of the challenge , as recent studies have posed new questions about how the morphologies of massive galaxies evolve with redshift .
in addition to the basic question of how high - redshift galaxies evolve in size , there is also still much debate about how these massive galaxies evolve in terms of their fundamental morphological type .
extensive studies of the local universe have revealed a bimodality in the colour - morphology plane , with spheroidal galaxies typically inhabiting the red sequence and disk galaxies making up the blue cloud ( e.g. ( * ? ? ?
* baldry et al . 2004 ) ) .
however , recent studies at both low ( e.g. ( * ? ? ?
* bamford et al . 2009 ) ) and high redshift ( e.g. ( * ? ? ? * van der wel et al . 2011 ) ) have uncovered a significant population of passive disk - dominated galaxies , providing evidence that the physical processes which quench star - formation may be distinct from those responsible for driving morphological transformations .
this result is particularly interesting in light of the latest morphological studies of high - redshift massive galaxies by and ( * ? ? ?
* van der wel et al . ( 2011 ) ) who find that , in contrast to the local population of massive galaxies ( which is dominated by bulge morphologies ) , by @xmath6 massive galaxies are predominantly disk - dominated systems . in this work
we attempt to provide significantly improved clarity on these issues .
the candels ( ( * ? ? ?
* grogin et al . 2011 ) , ( * ? ? ?
* koekemoer et al . 2011 ) ) near - infrared f160w data provides the necessary combination of depth , angular resolution , and area to enable the most detailed study to date of the rest - frame optical morphologies of massive ( @xmath1 ) galaxies at @xmath2 in the ukidss ultra deep survey ( ( * ? ? ?
* lawrence et al . 2007 ) ) .
for this study we have constructed a sample based on photometric redshifts and stellar mass estimates which were determined using the stellar population synthesis models of ( * ? ? ?
* bruzual & charlot ( 2003 ) ) assuming a chabrier initial mass function ( see ( * ? ? ?
* bruce et al .
2012 ) for full details ) .
this provides us with a total mass - complete sample of @xmath7 galaxies .
we have employed the galfit ( ( * ? ? ?
* peng et al . 2002 ) ) morphology fitting code to determine the morphological properties for all the objects in our sample . to conduct the double component fitting we define three components : a srsic index fixed at @xmath8 bulge , an @xmath9 fixed disk and a centrally concentrated psf component to account for any agn or nuclear starbursts within our galaxies .
these three components are combined to generate six alternative multiple component model fits , of varying complexity , for every object in the sample .
these models are formally nested , and thus @xmath10 statistics can be used to determine the `` best '' model given the appropriate number of model parameters .
armed with this unparalleled morphological information on massive galaxies at high redshift we can consider how the relative number density of galaxies of different morphological type changes during the key epoch in cosmic history probed here . in fig .
1 we illustrate this by binning our sample into four redshift bins of width @xmath11 , and consider three alternative cuts in morphological classification as measured by @xmath12 from our bulge - disk decompositions . in the left - hand panel of fig . 1 we have simply split the sample into two categories : bulge - dominated ( @xmath13 ) and disk - dominated ( @xmath14 ) . in the central panel we have separated the sample into three categories , with any object for which @xmath15 classed as `` intermediate '' .
finally , in the right - hand panel we have expanded this intermediate category to encompass all objects for which @xmath16 . and using three alternative cuts in morphological classification ( both to try to provide a complete picture , and to facilitate comparison with different categorisations in the literature).,width=528 ] from these panels it can be seen that @xmath6 marks a key transition phase , above which massive galaxies are predominantly disk - dominated systems and below which they become increasingly mixed bulge+disk systems .
we also note that at the lowest redshifts probed by this study ( @xmath17 ) it is seen that , while bulge - dominated objects are on the rise , pure - bulge galaxies ( i.e. objects comparable to present - day giant ellipticals ) have yet to emerge in significant numbers , with @xmath18% of these high - mass galaxies still retaining a significant disk component .
this is compared with @xmath19 of the local @xmath1 galaxy population , which would be classified as pure - bulges from our definition ( @xmath20 , corresponding to @xmath21 ) from the sample of ( * ? ? ?
* buitrago et al . ( 2013 ) ) .
thus , our results further challenge theoretical models of galaxy formation to account for the relatively rapid demise of massive star - forming disks , but the relatively gradual emergence of genuinely bulge - dominated morphologies .
in addition to our morphological decompositions we also make use of the sed fitting already employed in the sample selection to explore the relationship between star - formation activity and morphological type .
2 shows specific star - formation rate ( @xmath22 ) versus morphological type for the massive galaxies in our sample , where morphology is quantified by single srsic index in the left - hand panel , and by bulge - to - total @xmath23-band flux ratio ( @xmath12 ) in the right - hand panel .
the values of @xmath22 plotted are derived from the original optical - infrared sed fits employed in the sample selection , and include correction for dust extinction as assessed from the best fitting value of @xmath24 derived during the sed fitting . as a check of the potential failure of this approach to correctly identify reddened dusty star - forming galaxies , we have also searched for 24@xmath25 m counterparts in the _ spitzer _ spuds mips imaging of the uds , and have highlighted in blue stars those objects which yielded a mips counterpart within a search radius of @xmath26arcsec . to first order ,
our results show that the well - documented bimodality in the colour - morphology plane seen at low redshift , where spheroidal galaxies inhabit the red sequence , while disk galaxies occupy the blue cloud is at least partly already in place by @xmath6 .
nonetheless , the sample also undoubtedly contains star - forming bulge - dominated galaxies and , perhaps more interestingly , a significant population of apparently quiescent disk - dominated objects . to highlight and quantify this population
we have indicated by a box on both the panels the region occupied by objects with disk - dominated morphologies and @xmath27 . in the left - hand panel ,
disk - dominated is defined as @xmath28 , and @xmath29% of the quiescent galaxies lie within this box ( if we exclude the 24@xmath25 m detections ) , while in the right - hand panel , disk - dominated is defined by @xmath14 , in which case @xmath30% of the quiescent objects lie within this region .
the presence of a significant population of passive disks among the massive galaxy population at these redshifts indicates that star - formation activity can cease without a disk galaxy being turned directly into a disk - free spheroid , as generally previously expected if the process that quenches star formation is a major merger .
one possible mechanism for this arises from the latest generation of hydrodynamical simulations ( e.g. ( * ? ? ?
* kere et al . 2005 ) , ( * ? ? ?
* dekel et al . 2009a ) ) and analytic theories ( e.g. ( * ? ? ?
* birnboim & dekel 2003 ) ) , which suggest a formation scenario whereby at high redshift star - formation is fed through inflows of cold gas .
another scenario which can account for star - formation quenching , whilst still being consistent with the existence of passive disks , is the model of violent disk instabilities ( e.g. ( * ? ? ?
* dekel et al . 2009b ) ) , coupled with
morphology quenching " ( ( * ? ? ?
* martig et al . 2009 ) ) . | we have used high - resolution , hst wfc3/ir , near - infrared imaging to conduct a detailed bulge - disk decomposition of the morphologies of @xmath0 of the most massive ( @xmath1 ) galaxies at @xmath2 in the candels - uds field .
we find that , while such massive galaxies at low redshift are generally bulge - dominated , at redshifts @xmath3 they are predominantly mixed bulge+disk systems , and by @xmath4 they are mostly disk - dominated .
interestingly , we find that while most of the quiescent galaxies are bulge - dominated , a significant fraction ( @xmath5% ) of the most quiescent galaxies , have disk - dominated morphologies
. thus , our results suggest that the physical mechanisms which quench star - formation activity are not simply connected to those responsible for the morphological transformation of massive galaxies . |
natural hamiltonian systems are the mathematical models of those physical systems for which the energy is constant , for example harmonic oscillators or the kepler system .
often , as in the previous two examples , more quantities are constants of the motion ( or _ first integrals _ ) : angular momentum , laplace - runge - lentz vector , etc . usually , these constants are expressed by quadratic polynomials in the momenta or , for quantum systems , by second - order differential operators .
hamiltonian systems with constants of the motion of degree higher than two are less common , nevertheless , some of them are of great interest , as for instance the three - body jacobi - calogero and wolfes systems .
these systems represent the dynamics of three point - masses on a line under forces determined by the potential functions @xmath4 respectively ( we do not consider here the harmonic oscillator terms ) and they have essentially the same dynamics @xcite . both the resulting natural hamiltonians in @xmath5 admit one linear and one quadratic in the momenta constants of the motion , making the systems liouville - integrable and solvable by separation of variables ( see @xcite and references therein ) .
other two independent constants of the motion do exist , one quadratic , due to the multiseparability of the hamiltonian , and one cubic .
the systems are then maximally superintegrable ( ms ) , having a number of functionally independent constants of the motion equal to twice the degrees of freedom , minus one ( for quantum systems , the same number of algebraically independent symmetry operators ) .
ms systems are of the greatest importance in mathematical physics , harmonic oscillators and kepler are ms and this makes them to satisfy bertrand s theorem . indeed , maximal superintegrability manifests itself , for classical systems , in the fact that all finite orbits of ms systems are closed while , for quantum systems , in the fact that the energy levels are totally degenerate @xcite .
in recent years , several techniques made possible the construction of classical and quantum hamiltonian systems , ms and not , with first integrals of arbitrarily high degree @xcite whose study , still in development , produced remarkable results in special functions , quantum algebras , canonical quantization theories @xcite . in this note it is shortly introduced the work on the topic done by claudia chanu , luca degiovanni and the author ( in short cdr ) in several joint articles . in few words ,
the extension procedure ( theorem [ teo0 ] ) adds one degree of freedom to some suitable hamiltonian @xmath6 in such a way an extra non trivial first integral , polynomial of degree @xmath7 , of the new hamiltonian do exist .
the following theorem , stated in @xcite , defines and characterizes what we intend for `` extensions '' in the particular case of natural hamiltonians on cotangent bundles of riemannian manifolds ; for a more general definition , see @xcite .
given an @xmath8-dimensional natural hamiltonian @xmath6 on the cotangent bundle of a ( pseudo)-riemannian manifold @xmath9 , let be @xmath10 and @xmath11 where @xmath12 is the hamiltonian vector field of @xmath6 , then [ teo0 ] let @xmath9 be a @xmath8-dimensional ( pseudo-)riemannian manifold with metric tensor @xmath13 . the natural hamiltonian @xmath14 on @xmath15 with canonical coordinates @xmath16 admits an extension @xmath17 in the form ( [ hamext ] ) with a first integral @xmath18 with @xmath19 given by ( [ u ] ) and @xmath20 , if and only if the following conditions hold : 1 . the functions @xmath21 and @xmath22 satisfy @xmath23 @xmath24 where @xmath25 is the hessian tensor of @xmath21 .
2 . for @xmath26 the extended hamiltonian @xmath17 and
the first integral @xmath27 are @xmath28 for @xmath29 the extended hamiltonian @xmath17 and the first integral @xmath27 are @xmath30 with @xmath31 , @xmath32 , @xmath33 and @xmath34 in @xcite it is proved that @xmath35 is functionally independent from @xmath17 , @xmath6 and any other first integral of @xmath6 in @xmath36 .
the integrability conditions of ( [ hessteo ] ) are discussed in @xcite and it is found that their complete integrability requires @xmath37 , where @xmath31 is the constant curvature of @xmath9 . then , the function @xmath20 can depend linearly on up to @xmath38 parameters and the maximal number of parameters is attained on constant curvature manifolds only .
however , non complete solutions can be found in non - constant curvature manifolds ( cdr to appear ) . from equation ( [ vteo ] ) , the expressions of the admissible potentials @xmath22 can be computed .
several examples are given in @xcite .
the particular form of @xmath19 makes possible to explicit any @xmath35 by expanding the @xmath39-th power of a binomial , obtaining @xcite @xmath40 with @xmath41}{\left ( \begin{matrix } m \cr 2k \end{matrix } \right ) \gamma^{2k}p_u^{m-2k}\left(-2m(cl+l_0)\right)^k},\ ] ] @xmath42}{\left ( \begin{matrix } m \cr 2k+1 \end{matrix } \right ) \gamma^{2k+1}p_u^{m-2k-1}\left(-2m(cl+l_0)\right)^k } , \quad m>1,\ ] ] where @xmath43 $ ] denotes the integer part and @xmath44 .
we remark that first integrals of high degree obtained in other ways than by the extension procedure @xcite can be explicitly expressed only thanks to the fact that the dynamical equations are in these cases separated in some coordinate system . as a first example of the extension procedure we consider the one - dimensional hamiltonian @xcite @xmath45 the geodesic term of the extended hamiltonian @xmath17 is @xmath46 where @xmath31 is here the constant curvature of the extended configuration manifold .
the solutions of equations ( [ hessteo ] ) and ( [ vteo ] ) are @xmath47 where @xmath48 . when @xmath49 and @xmath50 , the configuration manifold of @xmath17 is the euclidean plane , the sphere @xmath51 and the pseudosphere @xmath52 respectively , while for @xmath53 and @xmath50 , the minkowski plane , the desitter and anti - desitter manifolds , respectively . after a rescaling of the coordinate @xmath54 , the parameter @xmath39 in @xmath17 passes into @xmath6 and @xmath55
this makes evident that the extension procedure introduces some discrete symmetry into @xmath17 , in this case a dihedral symmetry of order @xmath56 , somehow connected with the extra first integral @xmath35 . in the euclidean plane ( i.e. @xmath57 ) with @xmath58 and @xmath59 ,
@xmath22 is associated with the jacobi - calogero potential or , equivalently , with the wolfes potential @xcite . indeed , in cylindrical coordinates of @xmath5 , @xmath60 , with axis @xmath61 parallel to @xmath62 w.r .
to cartesian coordinates @xmath63 , we have @xmath64 the procedure of extension provides two new functionally independent first integrals to the extended hamiltonian @xmath17 : @xmath17 itself and @xmath27 .
this fact is particularly relevant when the hamiltonian @xmath6 is ms . in this case , @xmath17 is ms too , admitting @xmath65 functionally independent first integrals . in @xcite this property of extended hamiltonians
is studied in several cases .
for example , let us consider @xmath66 that is a particular case of the generalized tremblay - turbiner - winternitz system ( ttw ) @xcite for @xmath67 and @xmath68 defined on constant - curvature manifolds of curvature @xmath69 .
this system is ms for any rational parameter @xmath70 and admits polynomial first integrals of degree related to @xmath70 @xcite . in @xcite
it is shown that @xmath6 always admits extensions of the form @xmath71 with @xmath72 , creating in this way new ms systems .
similarly , harmonic oscillators in @xmath73 , isotropic or not , can be extended into harmonic oscillators in @xmath74 @xcite .
the assumption @xmath20 can be generalized to @xmath75 .
this leads to important generalizations , introduced in @xcite , that will be developed in a paper in preparation ( cdr ) .
the extension procedure can be in this case applied with @xmath39 substituted by any positive rational @xmath76 after a suitable definition of @xmath77 , so that the generalized ttw system of above , with @xmath78 , can be written as an extension for any rational @xmath70 . to classical extended hamiltonians and their first integrals
can be associated quantum hamiltonians and symmetry operators by some procedure of quantization , usually in form of laplace - beltrami operators .
when the curvature of @xmath9 is not constant , the quantization requires additional terms ( quantum corrections ) in order to keep integrability or superintegrability . the quantum correction
is then determined by the scalar curvature and by the weyl tensor @xcite . at least in the case
@xmath79 , the simultaneous quantization of @xmath17 and @xmath80 is possible , allowing the preservation of maximal superintegrability of ms classical extended systems to the quantum limit .
this will be shown in a paper in preparation ( cdr ) . | given an n - dimensional natural hamiltonian l on a riemannian or pseudo - riemannian manifold , we call `` extension '' of l the n+1 dimensional hamiltonian @xmath0 with new canonically conjugated coordinates @xmath1 . for suitable l ,
the functions @xmath2 and @xmath3 can be chosen depending on any natural number m such that h admits an extra polynomial first integral in the momenta of degree m , explicitly determined in the form of the m - th power of a differential operator applied to a certain function of coordinates and momenta .
in particular , if l is maximally superintegrable ( ms ) then h is ms also .
therefore , the extension procedure allows the creation of new superintegrable systems from old ones . for m=2 , the extra first integral generated by the extension procedure
determines a second - order symmetry operator of a laplace - beltrami quantization of h , modified by taking in account the curvature of the configuration manifold .
the extension procedure can be applied to several hamiltonian systems , including the three - body calogero and wolfes systems ( without harmonic term ) , the tremblay - turbiner - winternitz system and n - dimensional anisotropic harmonic oscillators .
we propose here a short review of the known results of the theory and some previews of new ones . |
the effect of temperature and angular momentum on pairing properties is an interesting subject in the study of nuclear structure . because of its simplicity
, the bcs theory is often used , which offers a good description of pairing correlation in the macroscopic systems such as metallic superconductors .
it predicts a collapse of the pairing gap at @xmath0 , which signals the sharp superfluid - normal ( sn ) phase transition at finite temperature .
the bcs theory , however , ignores quantal and thermal fluctuations , which are significant in finite small systems .
therefore , it needs to be corrected for the application to finite nuclei .
various theoretical approaches have been proposed to study the effects of fluctuations on nuclear pairing @xcite .
their results show that , at zero angular momentum , thermal fluctuations smear out the sharp sn phase transition , resulting in a pairing gap , which does not collapse at finite temperature . in rotating nuclei ,
a phenomenon of temperature induced pair correlations , which reflects the strong fluctuations of the order parameter in small systems , has also been predicted @xcite .
the recent microscopic approach , called the modified bcs ( mbcs ) theory @xcite has shown , for the fist time , that the microscopic source causing the non - collapsing pairing gap is the quasiparticle - number fluctuation ( qnf ) .
recently , we proposed the self - consistent quasiparticle random - phase approximation ( scqrpa ) @xcite , which includes the qnf as well as the quantal fluctuations due to dynamic coupling to pair vibrations .
the purpose of present work is to extend this approach to finite temperature and finite angular momentum .
the pairing hamiltonian is considered , which describes a system of @xmath1 particles interacting via a pairing force with the parameter @xmath2 and rotating with angular velocity @xmath3 and a fixed angular momentum projection @xmath4 on the laboratory ( or body ) fixed @xmath5 axis : @xmath6 where @xmath7 ( @xmath8 ) is the operator that creates ( annihilates ) a particle with angular momentum @xmath9 , spin projection @xmath10 or @xmath11 , and energy @xmath12 . for simplicity , the subscripts @xmath9 label the single - particle states @xmath13 with @xmath14 0 ,
whereas @xmath15 denote the time - reversal states @xmath16 .
the particle number operator @xmath17 is defined as @xmath18 , whereas @xmath19 is the @xmath20-projection of total angular momentum .
the variational procedure is applied to minimize the expectation value of this hamiltonian in the grand canonical ensemble .
the result yields the final equations for the pairing gap , particle number and total angular momentum , which include the effect of qnf in the form @xmath21 @xmath22~ , \hspace{5 mm } m = \sum_k m_k(n_k^{+ } - n_k^{-})~ , \label{nm}\ ] ] where the quasiparticle energy @xmath23 and renormalized single - particle energy @xmath24 are given as @xmath25 @xmath26 with @xmath27 , and @xmath28 .
the expectation values @xmath29 and @xmath30 are evaluated by solving a set of coupled equations , which contain the scqrpa @xmath31 and @xmath32 amplitudes .
the qnf is given as @xmath33 , where the quasiparticle occupation numbers @xmath34 are found from the integral equations @xmath35^{2}+[\gamma_{k}^{\pm}(\omega)]^2}d\omega~ , \label{nkcoupling}\ ] ] with the mass operators @xmath36 obtained by solving the set of equations for double - time quasiparticle green s functions and those of a quasiparticle coupled with scqrpa pair vibrations .
the quasiparticle dampings are given as @xmath37 $ ] .
the proposed approach is called the ftbcs1+scqrpa theory . neglecting the coupling to scqrpa , i.e. the factors @xmath29 and @xmath30
, it becomes the ftbcs1 theory , which is different from the conventional ftbcs theory by the presence of the qnf .
the violation of particle number at zero angular momentum is approximately removed by applying the lipkin - nogami ( ln ) method .
the corresponding approaches are called the ftln1+scqrpa and ftln1 .
the numerical calculations are carried out within the @xmath38 doubly degenerate equidistant model with the number @xmath38 of levels equal to that of particles , @xmath1 , as well as for @xmath39o , @xmath40ca , @xmath41fe , and @xmath42sn .
the results obtained show that , at zero angular momentum , under the effect of qnf within the ftbcs1 ( ftln1 ) , the sharp sn phase transition predicted by the ftbcs theory is smoothed out . as the result ,
the pairing gap does not collapse at @xmath43 , but has a tail , which extends to high @xmath44 .
the dynamic coupling to the scqrpa vibrations significantly improves the agreement with the exact results for the total energies and heat capacities obtained for @xmath45 as well as those obtained @xmath41fe within the finite - temperature quantum monte carlo method @xcite [ figs .
[ fig ] ( a ) [ fig ] ( c ) ] .
however , for heavy nuclei such as @xmath42sn , the scqrpa corrections are found to be negligible in comparison with the ftbcs1 ( ftln1 ) results . for @xmath39o and @xmath40ca , the ftbcs1 pairing gaps , obtained at different @xmath4 , decreases as @xmath44 increases and do not collapses at high @xmath44 .
at @xmath4 higher than the critical value @xmath46 , where the ftbcs gap for @xmath47 disappears , there appear thermally assisted pairing correlations , in which the ftbcs1 gap reappears at a given @xmath48 , and remains finite at @xmath49 [ fig .
[ fig ] ( d ) ] .
this phenomenon is caused by the qnf within the ftbcs1 theory . at @xmath47 ,
the qnf is zero , so the ftbcs and ftbcs1 gaps are the same as functions of @xmath4 ( or @xmath3 ) , and both collapse at @xmath50 . however , with increasing @xmath44 , the ftbcs1 gaps , which are obtained at different @xmath44 , collapse at @xmath51 , and remain finite even at very high @xmath44 , whereas those given by the conventional ftbcs theory vanish at @xmath52 and @xmath53 [ figs .
( e ) and [ fig ] ( f ) ] .
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c * 58 * , 3295 ( 1998 ) . | an approach is proposed to nuclear pairing at finite temperature and angular momentum , which includes the effects of the quasiparticle - number fluctuation and dynamic coupling to pair vibrations within the self - consistent quasiparticle random - phase approximation .
the numerical calculations of pairing gaps , total energies , and heat capacities are carried out within a doubly folded multilevel model as well as several realistic nuclei .
the results obtained show that , in the region of moderate and strong couplings , the sharp transition between the superconducting and normal phases is smoothed out , causing a thermal pairing gap , which does not collapse at a critical temperature predicted by the conventional bardeen - cooper - schrieffer s ( bcs ) theory , but has a tail extended to high temperatures .
the theory also predicts the appearance of a thermally assisted pairing in hot rotating nuclei . |
* the anomalous x - ray pulsars ( axps ) * are a group of x - ray pulsars whose spin periods fall in a narrow range ( @xmath0 s ) , whose x - ray spectra are very soft , and which show no evidence that they accrete from a binary companion ( see mereghetti 1999 for a recent review ) . these objects may be isolated neutron stars with extremely strong ( @xmath1 g ) surface magnetic fields , or they may be accreting from a `` fallback '' accretion disk .
optical measurements could potentially help discriminate between these models .
an optical counterpart to one axp , 4u 0142 + 61 , has recently been identified and shown to have peculiar optical colors ( hulleman et al .
* the radio - quiet neutron stars ( rqnss ) * are a group of compact x - ray sources found near the center of young supernova remnants .
their x - ray spectra are roughly consistent with young , cooling neutron stars , but they show no evidence for the non - thermal emission associated with `` classical '' young pulsars like the crab ( see brazier & johnston 1999 for a review )
. the x - ray spectral properties of the rqnss and the axps are similar ( see , e.g. , chakrabarty et al .
below in table 1 , the general properties of the three rqnss as our targets in the southern sky are listed .
clcccc & & @xmath2 & age & @xmath3 & + source & snr & ( kpc ) & ( @xmath4 yr ) & ( kev ) & refs + 1e 08204247 & pup a & 2.0 & 3.7 & 0.28 & 1 - 3 + 1e 16145055 & rcw 103 & 3.3 & 1 - 3 & 0.56 & 4 - 6 + 1e 12075209 & pks 120952 & 1.5 & 7 & 0.25 & 7 - 9 + + + +
our observations were made using the magellan instant camera ( magic ) on the magellan-1/walter baade 6.5-meter telescope at las campanas observatory , chile .
magic is a ccd filter photometer built by mit and cfa for the @xmath5 focus of the baade telescope .
the current detector is a 2048@xmath62048 site ccd with a 69 mas / pixel scale and a 142@xmath6142 arcsec field of view .
we used the sloan filter set , which have the following central wavelengths ( fukugita et al .
1996 ) : @xmath7=3540 ; @xmath8=4770 ; @xmath9=6230 ; @xmath10=7620 ; and @xmath11=9130 .
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the observations were carried out with the new mit / cfa magic camera on the magellan - i 6.5 m telescope in chile .
we present deep multiband optical images of the x - ray error circles for each of these targets and discuss the resulting candidates and limits .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
active galactic nuclei ( agn ) involve the most powerful , steady sources of luminosity in the universe .
it is believed that the center core of agn consist of super massive black hole ( smbh ) surrounded by an accretion disk . in some cases
powerful collimated jets are found in agn , perpendicular to the plane of accretion disk .
the origin of jets are still unclear .
agns whose jets are viewed at a small angle to its axis are called blazars . the overall ( radio to @xmath4-ray ) spectral energy distribution ( sed ) of blazars shows two broad non - thermal continuum peaks .
the low - energy peak is thought to arise from electron synchrotron emission .
the leptonic model suggests that the second peak forms due to inverse compton emission .
this can be due to upscattering , by the same non - thermal population of electrons responsible for the synchrotron radiation , and synchrotron photons ( synchrotron self compton : ssc ) @xcite .
blazars often show violent flux variability , that may or may not appear correlated in the different energy bands .
simultaneous observation are then crucial to understand the physics behind variability .
in this section we discuss the code that we have used to obtain an estimation of the characteristic parameters of the ssc model .
the ssc model assumes a spectrum for the accelerated electron density @xmath5 , which is a broken power law with exponents @xmath6 and @xmath7 . the minimum , maximum and break lorentz factors for the electrons are usually called @xmath8 , @xmath9 and @xmath10 respectively .
the emitting region is considered to be a blob of radius @xmath11 moving with doppler factor @xmath3 with respect to the observer in a magnetic field of intensity @xmath1 .
the model is thus characterized by nine free parameters . ' '' '' @xmath12 ' '' '' in the present work we have kept @xmath8 fixed and equal to unit , which is a satisfactory approximation already used in the literature .
the determination of the remaining eight parameters has been performed by finding their best values and uncertainties from a @xmath13 minimization in which multi - frequency experimental points have been fitted to the ssc spectrum modelled as in @xcite .
minimization has been performed using the levenberg - marquardt method @xcite , which is an efficient standard for non - linear least - squares minimization that smoothly interpolates between two different minimization approaches , namely the inverse hessian method and the steepest descent method . for completeness
, we briefly present the pseudo - code for the algorithm in table i. a crucial point in our implementation is that from @xcite we can only obtain a numerical approximation to the ssc spectrum , in the form of a sampled sed . on the other hand , from table i
, we understand that at each step the calculation of the @xmath14 requires the evaluation of the sed for all the observed frequencies .
although an observed point will likely not be one of the sampled points coming from @xcite , it will fall between two sampled points , so that interpolation can be used to approximate the value of the sed .
at the same time , the levenberg - marquardt method requires the calculation of the partial derivatives of @xmath14 with respect to the ssc parameters .
these derivatives have also been obtained numerically by evaluating the incremental ratio of the @xmath14 with respect to a sufficiently small , dynamically adjusted increment of each parameter .
this method could have introduced a potential inefficiency in the computation , due to the recurrent need to evaluate the sed at many , slightly different points in parameter space , this being the most demanding operation in terms of cpu time .
for this reason we set up the algorithm to minimize the number of calls to @xcite across different iterations .
the @xmath0 fit during different iterations are shown in fig.1 .
.data sets used in this study .
the observation period of each state can be found at fig.2 . [ cols="<,^,^,^",options="header " , ] [ l2ea4-t1 ]
in order to study the behavior of parameters with source activity , we choose mrk421 ( table ii ) , considering the larger availability of mwl data sets and the lower redshift , hence less uncertainty after ebl correction of vhe data .
the @xmath0 fitted seds are shown in fig.2 .
in addition to the @xmath0 test , we also checked the goodness of the fit using the kolmogorov - smirnov ( ks ) test . considering the occurrence of different physical processes ( synchrotron and inverse compton , at substantially different energies ) , and the different quality of low- and high - energy data
, we used a _
piecewise ks test _ , _ i.e. _ we applied the ks test separately to low- and high - energy data .
then the ks test always confirms that the fit residuals are normal at 5% confidence level .
our results suggest that in mkn421 , @xmath1 decreases with source activity whereas @xmath15 and @xmath3 increase ( fig.3 top ) .
this can be interpreted in a frame where the synchrotron power and peak frequency remain constant with varying source activity by decreasing magnetic field and increasing the number of low energy electrons .
this mechanism results in an increased electron - photon scattering efficiency and hence in an increased compton power .
other emission parameters appear uncorrelated with source activity . in fig.3 ( bottom ) , the @xmath1-@xmath15 anti - correlation results from a roughly constant synchrotron peak frequency .
the @xmath1-@xmath3 correlation suggests that the compton emission of mkn421 is always in the thomson limit .
the @xmath3-@xmath15 correlation is an effect of the constant synchrotron and compton frequencies of the radiation emitted by a plasma in bulk relativistic motion towards the observer . | here we report our recent study on the spectral energy distribution ( sed ) of the high frequency bllac object mrk421 in different luminosity states .
we used a full - fledged @xmath0-minimization procedure instead of more commonly used `` eyeball '' fit to model the observed flux of the source ( from optical to very high energy ) , with a synchrotron - self - compton ( ssc ) emission mechanism .
our study shows that the synchrotron power and peak frequency remain constant with varying source activity , and the magnetic field ( @xmath1 ) decreases with the source activity while the break energy of electron spectrum ( @xmath2 ) and the doppler factor ( @xmath3 ) increase .
since a lower magnetic field and higher density of electrons result in increased electron - photon scattering efficiency , the compton power increases , so does the total emission . |
classification problem is one of the most important tasks in time series data mining . a well - known 1-nearest neighbor ( 1-nn ) with dynamic time warping ( dtw )
distance is one of the best classifier to classify time series data , among other approaches , such as support vector machine ( svm ) @xcite , artificial neural network ( ann ) @xcite , and decision tree @xcite . for the 1-nn classification ,
selecting an appropriate distance measure is very crucial ; however , the selection criteria still depends largely on the nature of data itself , especially in time series data .
though the euclidean distance is commonly used to measure the dissimilarity between two time series , it has been shown that dtw distance is more appropriate and produces more accurate results .
sakoe - chiba band ( s - c band ) @xcite originally speeds up the dtw calculation and later has been introduced to be used as a dtw global constraint .
in addition , the s - c band was first implemented for the speech community , and the width of the global constraint was fixed to be 10% of time series length .
however , recent work @xcite reveals that the classification accuracy depends solely on this global constraint ; the size of the constraint depends on the properties of the data at hands . to determine a suitable size , all possible widths of the global constraint
are tested , and the band with the maximum training accuracy is selected . ratanamahatana - keogh band ( r - k band ) @xcite has been introduced to generalize the global constraint model represented by a one - dimensional array .
the size of the array and the maximum constraint value is limited to the length of the time series .
and the main feature of the r - k band is the multi bands , where each band is representing each class of data . unlike the single s - c band
, this multi r - k bands can be adjusted as needed according to its own class warping path .
although the r - k band allows great flexibility to adjust the global constraint , a learning algorithm is needed to discover the best multi r - k bands . in the original work of r - k band ,
a hill climbing search algorithm with two heuristic functions ( accuracy and distance metrics ) is proposed .
the search algorithm climbs though a space by trying to increase / decrease specific parts of the bands until terminal conditions are met .
however , this learning algorithm still suffers from an overfitting phenomenon since an accuracy metric is used as a heuristic function to guide the search . to solve this problem ,
we propose two new learning algorithms , i.e. , band boundary extraction and iterative learning .
the band boundary extraction method first obtains a maximum , mean , and mode of the paths positions on the dtw distance matrix , and the iterative learning , band s structures are adjusted in each round of the iteration to a silhouette index @xcite .
we run both algorithms and the band that gives better results . in prediction step ,
the 1-nn using dynamic time warping distance with this discovered band is used to classify unlabeled data .
note that a lower bound , lb_keogh @xcite , is also used to speed up our 1-nn classification .
the rest of this paper is organized as follows .
section 2 gives some important background for our proposed work . in section 3 ,
we introduce our approach , the two novel learning algorithms .
section 4 contains an experimental evaluation including some examples of each dataset .
finally , we conclude this paper in section 5 .
our novel learning algorithms are based on four major fundamental concepts , i.e. , dynamic time warping ( dtw ) distance , sakoe - chiba band ( s - c band ) , ratanamahatana - keogh band ( r - k band ) , and silhouette index , which are briefly described in the following sections .
dynamic time warping ( dtw ) @xcite distance is a well - known similarity measure based on shape .
it uses a dynamic programming technique to find all possible warping paths , and selects the one with the minimum distance between two time series . to calculate the distance
, it first creates a distance matrix , where each element in the matrix is a cumulative distance of the minimum of three surrounding neighbors .
suppose we have two time series , a sequence @xmath0 of length @xmath1 ( @xmath2 ) and a sequence @xmath3 of length @xmath4 ( @xmath5 ) .
first , we create an @xmath1-by-@xmath4 matrix , where every ( @xmath6 ) element of the matrix is the cumulative distance of the distance at ( @xmath6 ) and the minimum of three neighboring elements , where @xmath7 and @xmath8 .
we can define the ( @xmath6 ) element , @xmath9 , of the matrix as : @xmath10 where @xmath11 is the squared distance of @xmath12 and @xmath13 , and @xmath9 is the summation of @xmath14 and the the minimum cumulative distance of three elements surrounding the ( @xmath6 ) element .
then , to find an optimal path , we choose the path that yields a minimum cumulative distance at ( @xmath15 ) , which is defined as : @xmath16 where @xmath17 is a set of all possible warping paths , @xmath18 is ( @xmath6 ) at @xmath19 element of a warping path , and @xmath20 is the length of the warping path . in reality , dtw may not give the best mapping according to our need because it will try its best to find the minimum distance .
it may generate the unwanted path .
for example , in figure [ flo : dtw1 ] @xcite , without global constraint , dtw will find its optimal mapping between the two time series .
however , in many cases , this is probably not what we intend , when the two time series are expected to be of different classes .
we can resolve this problem by limiting the permissible warping paths using a global constraint .
two well - known global constraints , sakoe - chiba band and itakura parallelogram @xcite , and a recent representation , ratanamahatana - keogh band ( r - k band ) , have been proposed , figure [ flo : dtw2 ] @xcite shows an example for each type of the constraints . [
cols="^,^ " , ] [ flo : result ]
in this work , we propose a new efficient time series classification algorithm based on 1-nearest neighbor classification using the dynamic time warping distance with multi r - k bands as a global constraint .
to select the best r - k band , we use our two proposed learning algorithms , i.e. , band boundary extraction algorithm and iterative learning .
silhouette index is used as a heuristic function for selecting the band that yields the best prediction accuracy .
the lb_keogh lower bound is also used in data prediction step to speed up the computation .
we would like to thank the scientific parallel computer engineering ( space ) laboratory , chulalongkorn university for providing a cluster we have used in this contest . 1 fumitada itakura .
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cikm international conference on information and knowledge management ( cikm 2004 ) _ , pages 324333 , washington , dc , usa , november 8 - 13 2004 . | 1-nearest neighbor with the dynamic time warping ( dtw ) distance is one of the most effective classifiers on time series domain .
since the global constraint has been introduced in speech community , many global constraint models have been proposed including sakoe - chiba ( s - c ) band , itakura parallelogram , and ratanamahatana - keogh ( r - k ) band .
the r - k band is a general global constraint model that can represent any global constraints with arbitrary shape and size effectively .
however , we need a good learning algorithm to discover the most suitable set of r - k bands , and the current r - k band learning algorithm still suffers from an overfitting phenomenon . in this paper , we propose two new learning algorithms , i.e. , band boundary extraction algorithm and iterative learning algorithm .
the band boundary extraction is calculated from the bound of all possible warping paths in each class , and the iterative learning is adjusted from the original r - k band learning .
we also use a silhouette index , a well - known clustering validation technique , as a heuristic function , and the lower bound function , lb_keogh , to enhance the prediction speed .
twenty datasets , from the workshop and challenge on time series classification , held in conjunction of the sigkdd 2007 , are used to evaluate our approach . |
believed to be the main origin of the jet quenching phenomena observed @xcite in nucleus
nucleus collisions at rhic energy @xmath2@xmath3 , parton energy loss via gluon - radiation is expected to depend on the properties ( gluon density and volume ) of the ` medium ' formed in the collision and on the properties ( color charge and mass ) of the ` probe ' parton @xcite .
hard gluons would lose more energy than hard quarks due to the stronger color coupling with the medium .
in addition , charm and beauty quarks are qualitatively different probes with respect to light partons , since their energy loss is expected to be reduced , as a consequence of a mass - dependent restriction in the phase - space into which gluon radiation can occur @xcite .
we study quenching effects for heavy quarks by supplementing perturbative qcd calculations of the baseline @xmath4 distributions with in - medium energy loss , included via the bdmps quenching weights .
the quenching weights , computed for light quarks and gluons in @xcite and for heavy quarks in @xcite , depend on the transport coefficient @xmath5 , a measure of the medium density , and on the in - medium path length .
these inputs are evaluated on a parton - by - parton level , using a glauber - model based description of the local @xmath5 profile in the transverse direction @xcite .
the @xmath5 value is chosen in order to reproduce the light - flavor particles nuclear modification factor @xmath6 measured in central collisions at @xmath7 ( fig .
[ fig : rhic ] , left ) : the range favored by the data for the parton - averaged transport coefficient is @xmath8@xmath9 .
[ cols="<,^ " , ] heavy - quark energy loss is presently studied at rhic using measurements of the nuclear modification factor @xmath10 of ` non - photonic ' ( @xmath11-conversion- and @xmath12-dalitz - subtracted ) single electrons .
the most recent data by phenix @xcite and star @xcite , reaching out to 5 and 9 gev , respectively , are shown in fig .
[ fig : rhic ] ( right ) .
since this is an inclusive measurement , with charm decays dominating at low @xmath4 and beauty decays dominating at high @xmath4 , the comparison with mass - dependent energy loss predictions should rely on a solid and data - validated pp baseline .
such baseline is still lacking at the moment , as we explain in the following .
the state - of - the - art perturbative predictions ( fonll ) , that we use as a baseline , indicate that , in pp collisions , charm decays dominate the electron @xmath4 spectrum up to about 5 gev @xcite .
however , there is a large perturbative uncertainty on position in @xmath4 of the @xmath13-decay/@xmath14-decay crossing point : depending on the choice of the factorization and renormalization scales this position can vary from 3 to 9 gev @xcite .
in addition , the calculation tends to underpredict the non - photonic electron spectrum measured in pp collisions @xcite . for our electron @xmath10 results ( fig .
[ fig : rhic ] , right ) , in addition to the uncertainty on the medium density ( curves for @xmath8 , 10 , @xmath9 ) , we also account for the perturbative uncertainty by varying the values of the scales and of the @xmath13 and @xmath14 quark masses ( shaded band associated to the @xmath15 curve ) @xcite .
we find that the nuclear modification factor of single electrons is about 0.2 larger than that of light - flavor hadrons .
thus , electrons are in principle sensitive to the mass hierarchy of parton energy loss . the available data neither allow us to support claims of inconsistency between theory and experiment , nor
do they support yet the expected mass hierarchy .
it is important to note that , in general , the perturbative uncertainty in calculating the partonic baseline spectrum is comparable to the model - intrinsic uncertainty in determining @xmath5 . if future experimental studies at rhic succeeded in disentangling the charm and beauty contributions to single electrons , the sensitivity in the theory - data comparison would be largely improved .
( left ) and @xmath1 ( right ) mesons for the case of realistic heavy - quark masses and for a case study in which the quark mass dependence of parton energy loss is neglected @xcite , scaledwidth=85.0% ] heavy quarks will be produced with large cross sections at lhc energy and the experiments will be equipped with detectors optimized for the separation of charm and beauty decay vertices .
thus , it should be possible to carry out a direct comparison of the attenuation of light - flavor hadrons , @xmath0 mesons , and @xmath1 mesons .
we calculate the expected nuclear modification factors @xmath10 exploring a conservatively - large range in the medium density for central collisions at @xmath16 : @xmath17 .
we use standard nlo perturbative predictions for the @xmath13 and @xmath14 @xmath4-differential cross sections @xcite .
figure [ fig : lhc ] ( thick lines ) shows our results for the heavy - to - light ratios of @xmath0 and @xmath1 mesons @xcite , defined as the ratios of the nuclear modification factors of @xmath18 mesons to that of light - flavor hadrons ( @xmath19 ) : @xmath20 .
we illustrate the effect of the mass by artificially neglecting the mass dependence of parton energy loss ( thin curves ) .
the enhancement above unity that persists in the @xmath21 cases is mainly due to the color - charge dependence of energy loss , since at lhc energy most of the light - flavor hadrons will originate from a gluon parent .
our results indicate that , for @xmath0 mesons , the mass effect is small and limited the region @xmath22 , while for @xmath1 mesons a large enhancement can be expected up to @xmath23 .
therefore , the comparison of the high-@xmath4 suppression for @xmath0 mesons and for light - flavor hadrons will test the color - charge dependence ( quark parent vs. gluon parent ) of parton energy loss , while the comparison for @xmath1 mesons and for light - flavor hadrons will test its mass dependence @xcite . | the attenuation of heavy - flavored particles in nucleus
nucleus collisions tests the microscopic dynamics of medium - induced parton energy loss and , in particular , its expected dependence on the identity ( color charge and mass ) of the parent parton .
we discuss the comparison of theoretical calculations with recent single - electron data from rhic experiments .
then , we present predictions for the heavy - to - light ratios of @xmath0 and @xmath1 mesons at lhc energy . address = universit degli studi di padova and infn , padova , italy address = dep . de fsica de partculas and igfae , universidade de santiago de compostela , spain address = lpthe , universit pierre et marie curie ( paris 6 ) , france address = department of physics , cern , theory division , genve , switzerland address = department of physics and astronomy , university of stony brook , ny , usa |
in our experiment , we begin with an optical characterization of the qds and observe a significantly reduced spectral linewidth of the emitted photons from a resonantly driven single qd compared with incoherent excitation methods including via above - bandgap and p - shell using cw lasers .
figure@xmath3s2(a - c ) present a direct comparison of the spectral linewidth of the emitted photons from a single qd ( qd2 ) neutral exciton for different cw - laser excitation methods . at moderate power regime ( around saturation ) , the cw photoluminescence spectra arising from above band - gap and _ p_-shell excitation yields a linewidth of @xmath52.5ghz ( see fig.@xmath3s2a ) and @xmath51.5ghz ( fig.@xmath3s2b ) , respectively . on the other hand , cw rf photons ( see fig.@xmath3s2c ) exhibit a significantly narrower linewidth of @xmath50.48ghz even at high power regime well above saturation ( 32@xmath46 ) where a mollow triplet arises @xcite .
figure@xmath3s2d shows a series of cw rf spectra at different laser power .
the coherence time @xmath47 fitted ( using the corrected eqn.(1 ) from ref.@xcite ) from the cw rf spectra at @xmath46 is closest to being radiative lifetime limited : @xmath47/@xmath48=0.93(6 ) , where @xmath49 is the exciton lifetime which is measured separately to be of 390(10)ps using time - resolved pulsed rf .
this is consistent with the prediction that the pure _ s_-shell resonant excitation can eliminate dephasings associated with the incoherent excitation methods @xcite .
a high - resolution pulsed rf spectrum from qd2 is shown in fig.@xmath3s3 . for a range of laser power from 0.2@xmath0 to @xmath0 pulse
, we fit the rf spectra with the voigt profile to extract the inhomogeneous ( gaussian ) linewidth ( @xmath50 ) .
as plotted in the inset of fig.@xmath3s3 , the @xmath50 shows a increase at larger excitation power , which is in qualitative agreement with previous investigations of light - induced spectral diffusion @xcite .
figure@xmath3s4a - b show the data of full histogram obtained on qd2 .
clusters of five peaks appear periodically with repetition period of @xmath1112.2 ns . the central cluster shows an overall reduced photon counts compared to the side clusters due to the single - photon nature of the source .
the hom interference are tested with @xmath0 , 0.72@xmath0 and 0.41@xmath0 pulse excitation where the rf counts reach @xmath6@xmath51 , @xmath6@xmath52 and @xmath6@xmath53 saturation level , and show raw visibilities of 0.903(55 ) , 0.912(56 ) and 0.934(39 ) , respectively ( see fig.@xmath34(c - h ) ) .
taking into account of the residual two - photon emission probability for this qd , @xmath54 , and the optical imperfections of our interferometric setup ( same as in the main text ) , we obtain corrected degrees of indistinguishability to be 0.956(58 ) , 0.966(59 ) , 0.989(41 ) for the @xmath0 , 0.72@xmath0 and 0.41@xmath0 pulses , respectively . | single photon sources based on semiconductor quantum dots offer distinct advantages for quantum information , including a scalable solid - state platform , ultrabrightness , and interconnectivity with matter qubits .
a key prerequisite for their use in optical quantum computing and solid - state networks is a high level of efficiency and indistinguishability .
pulsed resonance fluorescence ( rf ) has been anticipated as the optimum condition for the deterministic generation of high - quality photons with vanishing effects of dephasing . here
, we generate pulsed rf single photons on demand from a single , microcavity - embedded quantum dot under _ s_-shell excitation with 3-ps laser pulses .
the @xmath0-pulse excited rf photons have less than 0.3@xmath1 background contributions and a vanishing two - photon emission probability .
non - postselective hong - ou - mandel interference between two successively emitted photons is observed with a visibility of 0.97(2 ) , comparable to trapped atoms and ions .
two single photons are further used to implement a high - fidelity quantum controlled - not gate .
single photons have been proposed as promising quantum bits ( qubits ) for quantum communication @xcite , linear optical quantum computing @xcite and as messengers in quantum networks @xcite .
these proposals primarily rely upon a high degree of indistinguishability between individual photons to obtain the hong - ou - mandel ( hom ) type interference @xcite which is at the heart of photonic controlled logic gates and photon - interference - mediated quantum networking @xcite . among different types of single - photon emitters @xcite , quantum dots ( qds )
are attractive solid - state devices since they can be embedded in high - quality nanostructure cavities and waveguides to generate ultra - bright sources of single and entangled photons @xcite .
qds also provide a light - matter interface @xcite and can in principle be scaled to large quantum networks @xcite .
two - photon hom interference experiments using photons from a single qd @xcite , as well as from independent sources @xcite , have not only demonstrated the potential of qds as single - photon sources , but also revealed the level of dephasing arising from incoherent excitation .
the method of incoherent pumping ( via above band - gap or _
p_-shell excitation ) typically causes reduced photon coherence times due to homogeneous broadening of the excited state @xcite and uncontrolled emission time jitter from the nonradiative high - level to _ s_-shell relaxation @xcite , leading to a decrease of photon indistinguishability . to eliminate these dephasings ,
an increasing effort has been devoted to _ s_-shell resonant optical excitation of qds .
the mollow triplet spectra and photon correlations of the resonance fluorescence ( rf ) have been measured @xcite . under continuous - wave ( cw ) laser excitation ,
a high degree of indistinguishability for continuously generated rf photons has been demonstrated through post - selective hom interference @xcite .
however , in the cw regime , as the emission time of the rf photons is uncontrolled , the hom interference relies on the finite single - photon detection time resolution to discriminate and post - select a small fraction of photons that overlapped on the beam - splitter at the same time @xcite .
therefore , the obtained interference visibility needs to be convoluted with and is thus limited by the realistic detection time response .
this limitation , together with the low efficiency of two - photon interference owing to the unsynchronized photon arrival time , prohibits the direct application of cw rf photons in many quantum information protocols @xcite .
more recent experiments operating on the low excitation regime have showed that the coherent scattering part of the rf could have coherence comparable to the excitation laser @xcite .
however , such a single - photon source would suffer an intrinsically low efficiency .
it has been anticipated @xcite that _ pulsed _ and resonant _
s_-shell excitation could remedy the above problems and be used for deterministic generation of time - tagged , highly indistinguishable single photons .
in addition , the pulsed and transition - selective rf single photons are also a prerequisite for the much sought - after goal of entangling distant qd spins through photon interference @xcite , as well as for the scheme of generating on - demand multi - photon cluster states @xcite .
earlier experiments @xcite have used pulsed resonant excitation to demonstrate rabi oscillation , a hallmark for quantum optics . yet , access to a background - free on - demand single - photon source with near - unity indistinguishability proved elusive @xcite . in this article , by applying resonant _
s_-shell optical excitation with picosecond laser pulses , we generate pulsed rf single photons on demand from a single qd embedded in a planar microcavity .
rabi oscillations are visible from the variation of the rf intensity as a function of pump pulse area . under deterministic @xmath0-pulse excitations ,
the rf photons have less than 0.3@xmath1 background contributions and show an anti - bunching of @xmath2 .
we observe non - postselective hom interference with a raw visibility of 0.91(2 ) and corrected visibility of 0.97(2 ) for two rf photons excited by two successive @xmath0 pulses separated by 2ns .
finally , the highly indistinguishable rf photons are utilized to demonstrate a quantum controlled - not gate .
our experiments are performed on self - assembled ingaas qds which are embedded in a planar microcavity and cooled in a cryogen - free bath cryostat at 4.2k ( see fig.@xmath3s1 ) .
laser excitation of a single qd and collection of the emitted fluorescence are carried out with a confocal microscope .
the excitation laser is pulsed with nominal pulse width of 3ps .
the microscope is operated in a cross - polarization configuration , whereby a polarizer is placed in the collection arm with its polarization perpendicular to the excitation light , extinguishing the scattered laser by a factor exceeding @xmath4 .
the microcavity has a quality factor of @xmath5200 which increases the fluorescence collection efficiency and reduces the laser power required for excitation of the qds .
figure@xmath31a shows the detected rf photon counts as a function of the square root of the excitation laser power .
the oscillation of the rf intensity is due to the well - known rabi rotation between the ground and the excitonic state .
it has been demonstrated previously by quasi - resonant @xcite or resonant driving @xcite .
the rf intensity reaches its first peak at the @xmath0 pulse .
we excite the qd with @xmath0 pulses at a repetition rate of @xmath682mhz and observed @xmath6230,000 photon counts on a single - photon detector ( with an efficiency of 22@xmath1 ) .
the overall rf collection efficiency is @xmath61.3@xmath1 . after correcting for the fibre coupling efficiency ( @xmath645@xmath1 ) , polarizer ( @xmath650@xmath1 ) and beam splitter ( @xmath695@xmath1 )
, we estimate that @xmath66@xmath1 of the photons emitted by the qd are collected into the first lens , which is in good agreement with numerical simulations ( see supplementary information ) . to verify that it is indeed a single - photon source
, figure@xmath31b shows the second - order correlation measurement of the @xmath0-pulse driven rf photons . at zero delay , it shows a clear anti - bunching with a vanishing multi - photon probability of @xmath2 .
thus it can be concluded that one and only one rf photon is generated on demand from every @xmath0-pulse excitation .
however , the photon extraction efficiency needs to be drastically improved for it to become a deterministic single - photon source .
figure@xmath32a shows a linear - log plot of the pulsed rf ( the sharp central line ) together with the residual laser leakage ( the broadband feature fitted by the red line ) monitored on a spectrometer . taking advantage of the huge linewidth mismatch between the rf signal and the laser background , we pass the rf through an etalon which has a bandwidth of @xmath620ghz much wider than that of the rf photons and much narrower than that of the pulsed laser to further suppress the excitation laser background .
this results in a clean rf spectrum as shown in the inset of fig.@xmath32a , with an improvement of the signal to background ( including the detector dark counts ) ratio from 20 to 357 at @xmath0-pulse excitation . for a range of laser powers ,
the signal to background ratio is extracted and plotted in fig.@xmath32b .
-pulse excitation is obtained with reasonable quality .
our current work only focuses on the @xmath0-pulse regime .
( b ) intensity - correlation histogram of the rf emission from the qd under pulsed _
s_-shell excitation obtained using a hanbury brown and twiss - type setup .
the second - order correlation @xmath2 is calculated from the integrated photons counts in the zero time delay peak divided by the average of the adjacent six peaks , and its error ( 0.002 ) which denotes one standard deviation , is deduced from propagated poissonian counting statistics of the raw detection events.,scaledwidth=49.0% ] a typical example of high - resolution spectra of the pulsed rf measured using a fabry - prot scanning cavity is shown in fig.@xmath32c .
it shows a pronounced deviation from the lorentzian lineshape obtained from cw excitation as shown in fig.@xmath3s2 , and can be fitted with a voigt profile with a homogeneous linewidth of 0.4(1)ghz ( corresponding to t@xmath7=0.7(2)ns ) and an inhomogeneous linewidth of 1.0(1)ghz .
the spontaneous emission lifetime for this qd is measured to be t@xmath8=0.41(2)ps ( see fig.@xmath3s3 ) , and we estimate the pure dephasing time t@xmath9=5.7@xmath10ns .
the gaussian component in this voigt profile could potentially be caused by spectral diffusion owing to pulsed - laser - induced charge fluctuations in the vicinity of the qd ( trapping and untrapping of charges in nearby defects and impurities ) @xcite .
the inhomogeneous linewidth varies for different qds and typically shows an increase at larger excitation power ( see fig.@xmath3s3 ) , which is in qualitative agreement with previous investigations of light - induced spectral diffusion @xcite . to perform pulsed two - photon interference
, we adopt a similar experimental configuration ( see fig.@xmath33a ) as in ref.@xmath3@xcite .
each excitation laser pulse , originally separated by @xmath1112.5ns , is further split into two pulses with a 2-ns delay .
thus , every @xmath1112.5ns , the qd is excited twice , generating two successive single rf photons .
the output rf photons are then fed into an unbalanced mach - zehnder interferometer with a 2-ns path - length difference ( fig.@xmath33a ) .
the two outputs of this interferometer are detected by single - mode fiber - coupled single - photon counters , and a record of coincidence events is kept to build up a time - delayed histogram ( for more details see fig.@xmath3s4 ) .
figure@xmath33(b ) and ( c ) show the central cluster of the histogram when the two @xmath0-pulse excited single photons , before recombining in the last beam splitter , are prepared in cross and parallel polarization states respectively .
the five peaks , from left to right , corresponds to the cases where the two photon arrives at the beam splitter with a time delay of -4ns , -2ns , 0ns , 2ns , and 4ns , respectively .
for distinguishable photons with different polarization , the expected peak - area ratio equals 1:2:2:2:1 , which is in good agreement with fig.@xmath33b .
if two perfectly indistinguishable photons are superposed on a beam splitter , they will always exit the beam splitter together through the same output port , leading to a zero coincidence rate
the hom dip @xcite which can not explained by classical optics .
figure@xmath33c shows a strong suppression of the coincidence counts at zero delay when the two incoming photons are prepared in the same polarization state .
quantitative evaluation ( see the caption of fig.@xmath33 for details ) shows that the probability of the two photons to exit the same channel in a 2-photon fock state ( bunching ) is 95.4@xmath1 .
this corresponds to a raw two - photon hom interference visibility of 0.91(2 ) .
taking into account the residual two - photon emission probability @xmath2 , and the optical imperfections of our interferometric setup which are independently measured , @xmath12 and @xmath13 , where @xmath14 , @xmath15 are the reflectivity and transmitivity of the beam splitter and @xmath16 is the first - order interference visibility of the mach - zehnder interferometer tested with a cw laser , we obtain corrected degrees of indistinguishability to be 0.97(2 ) .
the visibility can be further increased slightly by decreasing the excitation laser power . on another qd
, we test the hom interference with @xmath0 , 0.72@xmath0 and 0.41@xmath0 pulse excitation and observe visibilities of 0.96(6 ) , 0.97(6 ) and 0.99(4 ) , respectively ( see the data in fig.@xmath3s4 ) . taken together , these are to date the highest visibilities reported for qd - based single - photon sources .
these results demonstrate that the solid - state pulsed rf single photons in quick succession are highly indistinguishable to a level comparable to the best results from those well - developed systems such as parametric down - conversion @xcite , trapped atoms and ions @xcite .
the high - visibility results indicate a reduction of the fast dephasing and an elimination of the emission time jitter associated with the pulsed rf , compared to the previous incoherent excitation methods .
the pure dephasing time t@xmath9=5.7@xmath17ns is considerably larger than the 2ns and thus should have little effect on the visibility . the spectral diffusion ( as shown in fig.@xmath32c )
should also happen at a time scale much longer than the 2-ns separation , which is consistent with previous experiments @xcite .
we now demonstrate how the on - demand rf single photons can be utilized to implement a quantum controlled - not ( cnot ) gate .
the quantum cnot gate is a fundamental two - qubit logic gate .
if the control qubit is in logic @xmath18 , nothing happens to the target qubit , whereas if the control qubit is in logic @xmath19 , the target qubit will flip ( @xmath20 , @xmath21 ) .
the photonic cnot gate is a basic building block for quantum computing and has been demonstrated many times with down - converted photons @xcite , and very recently , with
_ p_-shell excited single photons from qds @xcite .
we prepare two input qubits encoded in the polarization states of the pulsed rf single photons @xmath22 and @xmath23 , where @xmath24(@xmath25 ) denotes horizontal@xmath3(vertical ) polarization and is used to encode @xmath26 .
the two inputs are then fed into the optical circuit for the cnot operation as shown in fig.@xmath34a .
the key element in this optical network is a partial polarizing beam splitter ( _ p_-pbs ) which has a transmission of 1(1/3 ) and a reflectivity of 0(2/3 ) for the @xmath24(@xmath25 ) photons .
when the two single photons are superimposed on the _ p_-pbs as shown in fig.@xmath34a , and if one and only one photon leaves through each output channel , the composite state of the two output photons can be written as : @xmath27 the first term corresponds to the case in which both input photons are @xmath28 and fully transmitted .
the second and third terms correspond to the cases where one photon is in @xmath28 and fully transmitted while the other photon is in @xmath29 and partially ( 1/3 ) transmitted .
it is most important to note the last term @xmath30 , where the resulting minus sign of the probability amplitude ( @xmath311/3 ) is due to the quantum interference between two indistinguishable paths , both photons are transmitted ( @xmath32 ) or reflected ( @xmath33 ) , which requires the indistinguishability of the single photons .
next , we swap the @xmath24 and @xmath25 polarizations in eqn.[[1 ] ] using half - wave plates and pass the two photons through two other _ p_-pbss to compensate the unbalanced coefficient ( see fig.@xmath34a ) , and we can obtain @xmath34 this effectively realizes a controlled phase - flip gate with a success probability of 1/9 . finally , after applying two additional hadamard rotations , it can be transformed into the cnot gate ( see the caption of fig.@xmath34a and ref .
@xcite for more details ) .
we experimentally evaluate the performance of the quantum cnot gate using an efficient method proposed by hofmann @xcite .
to show the quantum behaviour of the cnot gate , it is tested for different combinations of input - output states using complementary bases , that is , in both the computational basis ( @xmath35 ) and their linear superpositions ( @xmath36 ) , which are refereed to as the @xmath37 and @xmath38 basis using the pauli matrix language respectively . in the @xmath37 basis , the cnot is expected to flip the target qubit if the control qubit is in logic 1 .
interestingly , in the @xmath38 basis , the target and control qubits are reversed : the control qubit will flip if the target qubit is logic 1 .
the measurement results of the input - output probabilities of the cnot gate in the @xmath37 basis and in the @xmath38 basis are shown in fig.@xmath34b and fig.@xmath34c respectively .
the fidelity of the cnot operation , defined as the probability of obtaining the correct output averaged over all four possible inputs , is in the @xmath37 basis : @xmath39 , and in the @xmath38 basis : @xmath40 .
these two complementary fidelities , @xmath41 and @xmath42 , are sufficient to give an upper and a lower bound for the full quantum process fidelity @xmath43 of the gate by @xmath44 .
thus , here we have @xmath45 .
the process fidelity is directly related to the quantum entangling capability of the cnot gate , that is , the cnot gate can produce entangled states from unentangled input states @xcite . here , the @xmath43 well surpasses the the threshold of 0.5 , which is sufficient to confirm the entangling capability of our cnot gate . in this work ,
we have demonstrated the on - demand generation of near background - free ( @xmath1199.7@xmath1 purity ) and highly indistinguishable rf single photons , from a quantum dot in a planar microcavity driven by resonant @xmath0 pulses . using two rf photons emitted in 2-ns succession , non - postselective hom two - photon interference has revealed near - unity visibilities ( @xmath1197% ) , and a quantum cnot gate with entangling capability has been successfully demonstrated .
such a pulsed rf single - photon source may open the way to new interesting experiments in quantum optics and quantum information . with the high degree of indistinguishability of the rf photons shown here
, they can be used to realize various optical quantum computing algorithms @xcite , interference of multiple photons @xcite , and the on - demand generation of photonic cluster state from a single qd @xcite . in parallel ,
the rf spectra of a two - level system under strong pulsed laser excitation which are expected to exhibit novel features beyond the mollow triplet @xcite is in itself a subject worth studying .
a natural extension is to realize non - postselective high - visibility quantum interference between two pulsed rf single photons from separate qds @xcite .
based on this , it is possible to entangle remote , independent qd spins @xcite .
we note that although the relatively slow spectral diffusion and pure dephasing does not affect the two - photon interference in our present work due to the 2-ns time separation of the photons , it will limit the degree of indistinguishability for photons from independent qds . for future experiments ,
gate - controlled qds could be used to reduce the spectral diffusion .
alternatively , spectral filtering at the expense of photon rate may be needed . for quantum information applications ,
the photon extraction efficiency is a critical issue .
so far , we have obtained @xmath0-pulse excited single photons with an overall collection efficiency of 1.3% reaching the single - photon detector .
the photon extraction efficiency can be improved , for example , by embedding the qds in micropillars or photonic crystal cavities @xcite .
large purcell effects from these microcavities can be helpful to efficiently funnel the spontaneous emission into a guided mode , to further mitigate the dephasings @xcite , and increase the pulse repetition rate to tens of ghz .
lastly , it is important to note that in the previous pulsed above - bandgap or _
p_-shell excitation experiment , the photon coherence time had to be much larger than the incoherent carrier relaxation time jitter ( about tens of ps ) in order to obtain a good two - photon interference visibility @xcite , which fundamentally put a limit on the radiative lifetime shortening through the purcell effect .
we emphasize that the true resonant , time - jitter - free , pulsed rf technique developed here has no such limitation and can be fully compatible with large purcell factors to be implemented in the future . 10 [ 1]`#1 ` [ 2][]#2 pan , j .- w .
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_ acknowledgement _ : we thank y. yu , z. xi , j. bowles , k. chen , c. matthiesen , x .-
l .
wang , l .- j .
wang , n. vamivakas , and y. zhao for helpful discussions .
this work was supported by the national natural science foundation of china , the chinese academy of sciences and the national fundamental research program ( under grant no : 2011cb921300 , 2013cb933300 ) , and the state of bavaria .
m.a . acknowledges the cas visiting professorship .
c .-
y.l acknowledges the anhui nsf and youth qianren program . * author contributions
* : m.a .
, c .- y.l . and
j .- w.p . conceived and designed the experiments , c.s .
, s.h . , and m.k
. grew and fabricated the sample , y .- m.h .
, y.h . , y .- j.w . , d.w . , m.a . , and c .- y.l
. carried out the optical experiments , y .- m.h . , s.h . , c .- y.l . , and j .- w.p . analyzed the data , c .- y.l .
wrote the manuscript with input from all authors , s.h .
, c .- y.l . and j .- w.p .
guided the project .
* additional information : * the authors declare no competing financial interests .
correspondence and requests for materials should be addressed to c .- y.l .
( cylu@ustc.edu.cn ) or s.h .
( sven.hoefling@physik.uni-wuerzburg.de ) or j .- w.p .
( pan@ustc.edu.cn ) . |
the identification of the higgs boson(s ) is one of the main goals of the large hadron collider ( lhc ) being built at cern .
there are expectations that there exists a ` light ' higgs boson with mass @xmath3 gev . in this mass range
, its detection at the lhc will be challenging .
there is no obvious perfect detection process , but rather a range of possibilities , none of which is compelling on its own .
some of the processes are listed in table 1 , together with the predicted event rates for the integrated luminosity of 30 fb@xmath4 expected over the first two or three year period of lhc running .
we see that , _ either _ large signals are accompanied by a huge background , _ or _
the processes have comparable signal and background rates for which the number of higgs events is rather small . here
we wish to draw particular attention to process ( c ) , which is often disregarded ; that is the exclusive signal @xmath5 , where the + sign indicates the presence of a rapidity gap .
it is possible to install proton taggers so that the ` missing mass ' can be measured to an accuracy @xmath6 gev @xcite .
then the exclusive process will allow the mass of the higgs to be measured in two independent ways .
first the tagged protons give @xmath7 and second , via the @xmath1 decay , we have @xmath8 , although now the resolution is much poorer with @xmath9 gev .
the existence of matching peaks , centered about @xmath10 , is a unique feature of the exclusive diffractive higgs signal .
besides its obvious value in identifying the higgs , the mass equality also plays a key role in reducing background contributions .
another advantage of the exclusive process @xmath11 , with @xmath1 , is that the leading order @xmath12 background subprocess is suppressed by a @xmath13 selection rule @xcite .
[ cols="<,^,^,^,^ " , ] the radiation associated with the @xmath14 hard subprocess is not the only way to populate and to destroy the rapidity gaps .
there is also the possibility of soft rescattering in which particles from the underlying event populate the gaps .
the probability , @xmath15 , that the gaps survive the soft rescattering was calculated using a two - channel eikonal model , which incorporates high mass diffraction @xcite . including this factor , and the nlo @xmath16 factor ,
the cross section is predicted to be @xcite @xmath17 for the production of a standard model higgs boson of mass 120 gev at the lhc ) at the tevatron , 0.2 fb , is too low to provide a viable signal . ] .
it is estimated that there may be a factor two uncertainty in this prediction @xcite .
the event rate in entry ( c ) of table 1 includes a factor 0.6 for the efficiency associated with proton tagging , 0.6 for @xmath18 and @xmath19 tagging , 0.5 for the @xmath20 jet polar angle cut , @xmath21 , ( necessary to reduce the @xmath2 qcd background ) and 0.67 for the @xmath1 branching fraction @xcite .
hence the original @xmath22 events is reduced to an observable signal of 11 events , as shown in table 1 .
the advantage of the @xmath23 signal is that there exists a @xmath13 selection rule , which requires the leading order @xmath24 background subprocess to vanish in the limit of massless quarks and forward outgoing protons limit , the two born - level diagrams ( figs .
2(a , b ) _ without _ the emission of the gluon ) cancel each other . ] .
however , in practice , lo background contributions remain .
the prolific @xmath25 subprocess may mimic @xmath2 production since we may misidentify the outgoing gluons as @xmath18 and @xmath19 jets .
assuming the expected 1% probability of misidentification , and applying @xmath21 jet cut , gives a background - to - signal ratio @xmath26 .
secondly , there is an admixture of @xmath27 production , arising from non - forward going protons which gives @xmath28 .
thirdly , for a massive quark there is a contribution to the @xmath13 cross section of order @xmath29 , leading to @xmath26 , where @xmath30 is the transverse energy of the @xmath18 and @xmath19 jets .
next , we have the possibility of nlo @xmath31 background contributions . of course
, the extra gluon may be observed experimentally and these background events eliminated . however , there are exceptions .
the extra gluon may go unobserved in the direction of a forward proton .
this background may be effectively eliminated by requiring the equality @xmath32 .
then we may have soft gluon emission .
first , we note that emission from an outgoing @xmath18 or @xmath19 is not a problem , since we retain the cancellation between the crossed and uncrossed graphs .
emission from the virtual @xmath18 line is suppressed by at least a factor of @xmath33 ( in the amplitude ) , where @xmath34 and @xmath35 are the energies of the outgoing soft gluon and an outgoing @xmath18 quark in the @xmath24 centre - of - mass frame .
the potential danger is gluon emission from an incoming gluon , see fig . 2 .
the first two diagrams no longer cancel , as the @xmath2 system is in a colour - octet state .
however , the third diagram has precisely the colour and spin structure to restore the cancellation .
thus soft gluon emissions from the initial colour - singlet @xmath36 state factorize and , due to the overriding @xmath13 selection rule , qcd @xmath2 production is still suppressed .
the remaining danger is large angle hard gluon emission which is collinear with either the @xmath18 or @xmath19 jet , and therefore unobservable .
if the cone angle needed to separate the @xmath37 jet from the @xmath18 ( or @xmath19 ) jet is @xmath38 then the expected background from unresolved three jet events leads to @xmath39 . the nnlo @xmath40 background contributions are found to be negligible ( after requiring @xmath41 ) , as are soft pomeron - pomeron fusion contributions to the background ( and to the signal ) @xcite .
so , in total , double - diffractive higgs production has a signal - to - background ratio of about three , after including the @xmath16 factors .
identifying a ` light ' higgs will be a considerable experimental challenge .
all detection processes should be considered . from table 1
we see that valuable information can be obtained from weak boson fusion , where the higgs and the accompanying jets are produced at high @xmath42 .
for example , process ( d ) is based on the @xmath43 decay for which the background is small @xcite , whereas process ( f ) exploits rapidity gaps so that the larger @xmath1 signal may be isolated @xcite , provided the pile - up problems can be overcome @xcite .
here we have drawn attention to the exclusive @xmath11 signal , process ( c ) .
the process has the advantage that the signal exceeds the background .
the favourable signal - to - background ratio is offset by a low event rate , caused by the necessity to preserve the rapidity gaps so as to ensure an exclusive signal .
nevertheless , entry ( c ) of table 1 shows that the signal has reasonable significance in comparison to the standard @xmath44 and @xmath45 search modes .
moreover , the advantage of the matching higgs peaks , @xmath46 , can not be overemphasized .
spectrum , see process ( a ) of table 1 . ]
we thank albert de roeck , risto orava and andrei shuvaev for valuable discussions , and the eu , pparc and the leverhulme trust for support .
xx d. zeppenfeld et al . , phys . rev .
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j. * c18 * ( 2000 ) 167 . | we show that exclusive double - diffractive higgs production , @xmath0 , followed by the @xmath1 decay , could play an important role in identifying a ` light ' higgs boson at the lhc , provided that the forward outgoing protons are tagged .
we predict the cross sections for the signal and for all possible @xmath2 backgrounds .
ippp/02/41 + dcpt/02/82 + 3 july 2002 * forward proton tagging as a way to identify a light higgs boson at the lhc * a.d .
martin , v.a .
khoze and m.g .
ryskin institute for particle physics phenomenology , + university of durham , dh1 3le , uk |
radio galaxies ( rgs ) represent the largest single objects in the universe .
powered by an active galactic nucleus ( agn ) jets emerge from the central engine , which very likely is a super - massive black hole accreting matter surrounding it .
there is a huge range of linear extent of the rgs : from less than @xmath0 pc gigahertz - peaked spectrum ( gps ) , through @xmath0
@xmath1 pc compact steep spectrum ( css ) , @xmath1
@xmath2 pc normal - size sources , up to greater than 1 mpc
giant radio galaxies ( grg ) .
the three largest grgs , recognized up to now , are shown in fig . 1 .
although giant - size radio sources are very rare among rgs , from many years they have been of a special interest for several reasons .
their very large angular size on the sky give an excellent opportunity for the study of radio source physics .
they are also very useful to study the density and evolution of the intergalactic and intracluster environment .
one of the key issues of the current research is attempt to trace an individual evolution of rgs .
is there a single evolutionary scheme governing the linear extent of radio sources , or do small and large sources evolve in a different way ? to answer this question , in a number of papers , both theoretical and observational , attempts were undertaken to recognize factors which may differentiate giants from normal - size sources .
it seems that there is no a single factor responsible for the size of classical radio sources ; the large size of grgs probably results from a combination of different factors like : age of a source , jet power , density of environment , etc .
still very limited number of well studied grgs is a reason of that uncertainty .
therefore the phenomenon of grg is still open for a further research .
during the iau symposium no . 199 ( december 1999 ) machalski & jamrozy ( 2002 ) presented an evidence that only a very small fraction of expected faint grgs of fanaroff - riley ( 1974 ) type ii ( frii ) was detected at that time . in order to find those missed giant sources we inspected the radio maps available from the large radio surveys : nvss ( condon et al . , 1998 ) and the first part of first ( becker et al . , 1995 ) .
the maps of these surveys , made with two different angular resolution ( 45@xmath3 and 5@xmath3 , respectively ) at the same observing frequency of 1.4 ghz , allowed ( i ) an effective removal of confusing sources , ( ii ) a reliable determination of morphological type of the giant candidate , and ( iii ) a detection of the compact radio core necessary for the proper identification of the source with its parent optical object . as the result we selected a sample of 36 grg candidates ( cf .
machalski et al . , 2001 ) .
in order to identify their host galaxy , to determine its distance and other physical properties , we have carried out several radio and optical observations of the sample sources . in particular
, we already made optical spectroscopy and got redshift for 17 out of 36 galaxies ( spectroscopic redshifts of 5 sample galaxies were available prior our research ) . out of 22 galaxies , 19 host giant radio sources . in the meantime ,
similar efforts have been undertaken by schoenmakers et al .
( 2001 ) and lara et al .
owing to the above studies , the statistics of giant radio galaxies is enlarged .
the numbers of frii - type grgs , expected from our population analysis ( machalski & jamrozy 2002 ) , are recalled in table 1 and compared with the observed numbers .
the observed numbers denoted by an asterisk refer to the data available in 1999 , while other are from the beginning of the year 2003 .
lccc & @xmath4 mjy & @xmath5 jy & @xmath6 jy + observed & 64/11@xmath7 & 31/26@xmath7 & 11/9@xmath7 + expected & 350 & 45.7 & 8.8 + obs / expected & 18%/3%@xmath7 & 68%/57%@xmath7 & 122%/100%@xmath7 + two examples of grgs from our sample are shown in fig . 2 .
j1343 + 3758 with the linear size of 3.14 mpc has appeared to be the third largest source in the universe ( machalski & jamrozy 2000 ) , while j1604 + 3438 represents a very rare type of agn a so - called double - double rg ( cf .
schoenmakers et al .
2000 ) which shows two pairs of lobes likely originating from an old and a new cycle of activity .
low - resolution optical spectra of host galaxies of these two giant radio sources are shown in fig .
3 . some of the above data are used to constrain the existing analytical models of a dynamical evolution of frii - type radio sources ( machalski et al .
2003 ; chyy et al .
our investigations of the new giant radio sources are in progress .
however , we would like to extend them on grgs on the southern sky .
there are several scientific reasons for such a project , and the main of them are : * all of the recent systematic search for new giants ( lara et al .
2001 , machalski et al .
2001 , schoenmakers et al .
2001 ) were performed on the northern sky .
furthermore , only about 17% of the presently known grgs have negative declinations , and gross of them are high flux density ( @xmath80.5 jy ) nearby objects . therefore , one can expect a large number of undetected yet grgs on the southern hemisphere very useful for a further enlargement of their still unsatisfactory statistics . *
the development of astronomical high - technology facilities i.e. the existing and planned large optical telescopes on the south ( vlt , salt ) is very rapid .
therefore , it should be easy to attain the redshift of new grg hosting galaxies which is the crucial observational parameter for determination of all physical parameters of the radio sources like their distance , projected linear size , volume of their lobes or cocoon , luminosity , etc .
the above needs low - resolution spectroscopic observations of usually faint optical counterparts ( which in many cases have very low apparent magnitudes @xmath9 ) in a reasonably short time .
* there is a high probability that the planned powerful radio interferometer the square kilometer area ( ska ) will be located in the south ( there are two southern site candidates for its possible location , i.e. australia or south africa )
. it would give the opportunity to detect and study low surface - brightness grgs with a very high angular resolution and sensitivity in the future .
this , in turn , would allow to recognize a very last stage of the dynamical evolution of classical double radio galaxies and learn a typical lifetime and end of that physical process .
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1995 , , 450 , 559 chyy , k. , jamrozy , m. , kleinman , s.j . ,
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& riley , j.m .
1974 , mnras , 167 , 31 lara , l. , cotton , w.d . ,
feretti , l. , giovannini , g. , marcaide , j.m . , marquez , i. , & venturi , t. 2001 , , 370 , 409 machalski , j. , chyy , k. , & jamrozy , m. 2003 , submitted for mnras , ( astro - ph/0210546 ) machalski , j. , & jamrozy , m. 2002 , in iau symposium 199 , the universe at low radio frequencies , ed .
a. p. rao , g. swarup , & gopal - krishna ( san francisco : asp ) , 203 machalski , j. , jamrozy , m. , & zola , s. 2001 , , 371 , 445 machalski , j. , & jamrozy , m. 2000 , , 363 , l17 schoenmakers , a.p .
, de bruyn , a.g . , rttgering , h.j.a . , &
van der laan , h. 2001 , , 374 , 861 schoenmakers , a.p .
, de bruyn , a.g . , rttgering , h.j.a . , van der laan , h. , & kaiser , c.r .
2000 , , 315 , 371 | an extensive search for distant giant radio galaxies on the southern hemisphere is justified .
we emphasize the crucial role of optical spectroscopy in determination of their basic physical parameters , i.e. the distance , projected linear size , volume of their lobes or cocoon , luminosity , etc . , and argue that salt will be the best instrument for such a task .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
the long - time dynamics of biological evolution have recently attracted considerable interest among statistical physicists @xcite , who find in this field new and challenging interacting nonequilibrium systems .
an example is the bak - sneppen model @xcite , in which interacting species are the basic units , and less fit " species change by mutations " that trigger avalanches that may lead to a self - organized critical state .
however , in reality both mutations and natural selection act on _ individual organisms _ , and it is desirable to develop and study models in which this is the case .
one such model was recently introduced by hall , christensen , and coworkers @xcite . to enable very long monte carlo ( mc ) simulations of the evolutionary behavior
, we have developed a simplified version of this model , for which we here present preliminary results .
the model consists of a population of individuals with a haploid genome of @xmath1 binary genes @xcite , so that the total number of potential genomes is @xmath2 .
the short genomes we have been able to study numerically ( here , @xmath3 ) should be seen as coarse - grained representations of the full genome .
we thus consider each different bit string as a separate species " in the rather loose sense that this term is used about haploid organisms . in our simplified model
the population evolves asexually in discrete , nonoverlapping generations , and the population of species @xmath4 in generation @xmath5 is @xmath6 .
the total population is @xmath7 . in each generation , the probability that an individual of species @xmath4 has @xmath8 offspring before it dies is @xmath9 , while it dies without offspring with probability @xmath10 .
the reproduction probability @xmath11 is given by @xmath12 } \;. \label{eq : p}\ ] ] the verhulst factor @xmath13 @xcite , which prevents @xmath14 from diverging , represents an environmental `` carrying capacity '' due to limited shared resources . the time - independent interaction matrix @xmath15 expresses pair interactions between different species such that the element @xmath16 gives the effect of the population density of species @xmath17 on species @xmath4
. elements @xmath16 and @xmath18 both positive represent symbiosis or mutualism , @xmath16 and @xmath18 both negative represent competition , while @xmath16 and @xmath18 of opposite signs represent predator - prey relationships . to concentrate on the effects of interspecies interactions , we follow @xcite in taking @xmath19 . as in @xcite , the offdiagonal elements of @xmath16 are randomly and uniformly distributed on @xmath20 $ ] . in each generation , the genomes of the individual offspring organisms undergo mutation with probability @xmath21 per gene and individual .
mc simulations were performed with the following parameters : mutation rate @xmath22 per individual , carrying capacity @xmath23 , fecundity @xmath24 , and genome length @xmath3 . for a system with @xmath25 or only a single species and @xmath26 ,
the steady - state total population is found by linear stability analysis @xcite to be @xmath27 . in this regime both
the number of populated species and the total population @xmath28 are smaller than the number of possible species , @xmath29 .
this appears biologically reasonable in view of the enormous number of different possible genomes in nature .
an important quantity is the diversity of the population , which is defined as the number of species with significant populations .
operationally we define it as @xmath30 $ ] , where @xmath31 is the information - theoretical entropy ( known in ecology as the shannon - weaver index @xcite ) , @xmath32 \ln \left [ { n_i(t)}/{n_{\rm tot}(t ) } \right ] $ ] .
results for a run of @xmath33 generations are shown in fig .
[ fig : fig1 ] . in fig .
[ fig : fig1](*a * ) are shown time series of @xmath34 and @xmath28 .
we see relatively quiet periods ( quasi - steady states , qss ) punctuated by periods of high activity . during the active periods
the diversity fluctuates wildly , while the total population falls below its typical qss value . a corresponding picture of the species index ( the decimal representation of the binary genome ) is shown in fig .
[ fig : fig1](*b * ) , with grayscale indicating @xmath6 .
comparison of the two parts of fig .
[ fig : fig1 ] show that the qss correspond to periods during which the population is dominated by a relatively small number of species , while the active periods correspond to transitions during which the system is searching for " a new qss . closer inspection of fig .
[ fig : fig1 ] suggests that there are shorter qss within some of the periods of high activity .
this led us to consider the power - spectral densities ( psd ) of the diversity and total population , measured in very long simulations of @xmath35 generations .
the psd of the diversity is shown in fig .
[ fig : fig2 ] and indicates that the model exhibits flicker noise with a spectrum near @xmath0 @xcite over at least four to five decades in frequency .
it has been much discussed in evolutionary biology whether species evolve gradually or in a succession of qss , punctuated by periods of rapid change . the latter mode has been termed punctuated equilibria " by gould and eldredge @xcite .
there is also some indication that flicker noise is found in the fossil record of extinctions , but due to the sparseness of the fossil evidence this is a contested issue @xcite .
the model discussed here can at best be applied to the evolution of asexual , haploid organisms such as bacteria , and one should also note that no specific , biologically relevant information has been included in the interaction matrix . nevertheless , we find it encouraging that such a simple model of macroevolution with individual - based births , deaths , and mutations can produce punctuated equilibria and flicker noise reminiscent of current theories of biological macroevolution .
we thank b. schmittmann and u. tuber for useful discussions , and p.a.r .
thanks the department of physics , virginia polytechnic institute and state university , for its hospitality .
this research was supported by u.s .
national science foundation grant nos .
dmr-9981815 , dmr-0088451 , dmr-0120310 , and dmr-0240078 , and by florida state university through the school of computational science and information technology and the center for materials research and technology .
generations with the parameters given in the text .
( * a * ) time series showing the diversity , @xmath34 ( _ black _ ) , and the normalized total population , @xmath36 $ ] ( _ red _ ) . ( * b * ) species index @xmath4 vs time .
the symbols indicate @xmath37 ( _ black _ ) , @xmath38 $ ] ( _ blue _ ) , @xmath39 $ ] ( _ red _ ) , @xmath40 $ ] ( _ green _ ) , and @xmath41 ( _ yellow _ ) .
, title="fig : " ] generations with the parameters given in the text .
( * a * ) time series showing the diversity , @xmath34 ( _ black _ ) , and the normalized total population , @xmath36 $ ] ( _ red _ ) . ( * b * ) species index @xmath4 vs time .
the symbols indicate @xmath37 ( _ black _ ) , @xmath38 $ ] ( _ blue _ ) , @xmath39 $ ] ( _ red _ ) , @xmath40 $ ] ( _ green _ ) , and @xmath41 ( _ yellow _ ) .
, title="fig : " ] generations each .
the model parameters are those given in the text and used in fig .
[ fig : fig1 ] .
the @xmath0 like spectrum is indicative of very long - time correlations and a wide distribution of qss lifetimes . ] | we present long monte carlo simulations of a simple model of biological macroevolution in which births , deaths , and mutational changes in the genome take place at the level of individual organisms .
the model displays punctuated equilibria and flicker noise with a @xmath0-like power spectrum , consistent with some current theories of evolutionary dynamics . |
generally , the observed radio spectra of most pulsars can be modelled as a power law with negative spectral indices of about -1.8 ( @xcite ) .
if a pulsar can be observed at frequencies low enough ( i.e. ) , it may also show a low - frequency turnover in its spectrum ( @xcite ; @xcite ) .
on the other hand , lorimer ( 1995 ) mentioned three pulsars which have positive spectral indices in the frequency range 300 - 1600 mhz .
later , maron ( 2000 ) re - examined spectra of these pulsars taking into account the data obtained at higher frequencies ( above 1.6 ghz ) and consequently were the first to demonstrate a possible existence of spectra with turnover at high frequencies , about 1 ghz .
kijak ( 2011a ) provided a definite evidence for a new type of pulsar radio spectra .
these spectra show the maximum flux above 1 ghz , while at higher frequencies the spectra look like a typical pulsar spectrum . at lower frequencies ( below 1 ghz ) ,
the observed flux decreases , showing a positive spectral index ( @xcite ) .
they called these objects the gigahertz - peaked spectra ( gps ) pulsars .
a frequency at which such a spectrum shows the maximum flux was called the peak frequency .
kijak et al .
( 2011a ) also indicated that the gps pulsars are relatively young objects , and they usually adjoin such interesting environments as hii regions or compact pulsar wind nebulae .
additionally , some of them seem to be coincident with the known but sometimes unidentified x - ray sources from third egret catalogue or hess observations .
we can assume that the gps appearance owes to the environmental conditions around the neutron stars rather than to the radio emission mechanism .
psr b1259 - 63 was also listed by lorimer ( 1995 ) as a pulsar with positive spectral index .
therefore , it seems a natural candidate to be classified as the gps pulsar .
this pulsar is in an unique binary with a massive main - sequence be star . has a short period of 48 ms and a characteristic age of 330 kyr .
its average dispersion measure ( dm ) is about 147 pc @xmath0 and the corresponding distance is about 2.75 kpc .
the companion star ls 2883 is a 10-mag massive be star with a mass of about 10m@xmath1 and a radius of 6r@xmath1 .
be stars are generally believed to have a hot tenuous polar wind and a cooler high - density equatorial disc .
the psr b1259 - 63/ls 2883 emits unpulsed non - thermal emission over a wide range of frequencies ranging between radio and @xmath2rays , and its flux varies with orbital phase . [ cols="^,^ " , ] the flux at the given frequency apparently changes with orbital phases .
when the pulsar is close to periastron , the flux generally decreases at all observed frequencies and the most drastic decrease is observed at the lowest frequency .
moreover , we noticed all types of radio pulsar spectra . psr b1259 - 63 is a object with relatively high dispersion measure which means that its transition frequency is very high
this implies that we definitely have to take into consideration both refractive ( riss ) and diffractive ( diss ) scintillations when analysing spectra for a given day .
we used diffractive bandwidth @xmath3 and timescale @xmath4 from scintillation observations of the pulsar made far from periastron at 4.8 ghz and 8.4 ghz ( @xcite ) to estimate values of these parameters at 1.4 ghz and 2.4 ghz assuming @xmath5 , where @xmath6 and @xmath7 denote frequency and distance respectively .
we estimated the values of @xmath4 to be ranging from 40 s at 1.4 ghz to 360 s at 8.4 ghz which suggests that diffractive scintillations should not affect the average flux measurements ( observing sessions was usually 4 hours long ) .
roughly estimated refractive timescales vary from 12 hours at 8.4 ghz to more than 20 days at 1.4 ghz . however
, for lower frequencies the modulation index is relatively small which means lower uncertainty estimates when measuring flux .
high frequency observations will be affected by refractive scintillations what leads to conclusion that flux values should be averaged over epochs and/or orbital phase intervals to be more reliable .
close to the periastron point the spectra of b1259 - 63 resemble those of the gps pulsars .
the spectrum for the orbital epochs further from the periastron point are more consistent with typical pulsar spectra ( i.e. power - law and broken ) . moreover , detailed study of psr b1259 - 63 spectra revealed the appearance of all types of spectral shapes , including a flat spectrum ( see fig .
[ detailed ] ) .
we believe that the case of b1259 - 63 can be treated as a key factor to our understanding of not only the gps phenomenon ( observed for the solitary pulsars with interesting environments ) but also other types of untypical spectra as well ( e.g. flat or broken spectra ) .
this in turn would suggest , that the appearance of various non - standard spectra shapes in the general population of pulsars can be caused by peculiar environmental conditions .
md is a scholar within sub - measure 8.2.2 regional innovation strategies , measure 8.2 transfer of knowledge , priority viii regional human resources for the economy human capital operational programme co - financed by european social fund and state budget .
, t. w. , johnston , s. , manchester , r. n. & mcconnell , d. 2002 , _ mnras _ , 336 , 1201 , s. , manchester , r. n. , mcconnell , d. & campbell - wilson , d. , 1999 , _ mnras _ , 302 , 277 , s. , ball , l. , wang , n. & manchester , r. n. , 2005 , _ mnras _ , 358 , 1069 , j. , lewandowski , w. , maron , o. , gupta , y. & jessner , a. , 2011a , _
a&a _ , 531 , a16 , j. , dembska , m. , lewandowski , w. , melikidze , g. & sendyk , m. , 2011b , _ mnras _ , 418 , l114 , d. r. , yates , j. a. , lyne , a. g. & gould , d. m. , 1995 , _ mnras _ , 273 , 411 , v. m. , gil , j. a. , jessner , a. , et al .
1994 , _ a&a _ , 285 , 201 , o. , kijak , j. , kramer , m. & wielebinski , r. , 2000 , _
a&a s _ , 147 , 195 , n. m. , johnston , s. , stinebring , d. r. & nicastro , l. , _ apj _ , 1998 , 492 , l49 , w. , 1973 , _
a&a _ , 28 , 237 | we studied the radio spectrum of psr b1259 - 63 in an unique binary with be star ls 2883 and showed that the shape of the spectrum depends on the orbital phase .
we proposed a qualitative model which explains this evolution .
we considered two mechanisms that might influence the observed radio emission : free - free absorption and cyclotron resonance .
recently published results have revealed a new aspect in pulsar radio spectra . there were found objects with turnover at high frequencies in spectra , called gigahertz - peaked spectra ( gps ) pulsars .
most of them adjoin such interesting environments as hii regions or compact pulsar wind nebulae ( pwn ) .
thus , it is suggested that the turnover phenomenon is associated with the environment than being related intrinsically to the radio emission mechanism .
having noticed the apparent resemblance between the b1259 - 63 spectrum and the gps , we suggest that the same mechanisms should be responsible for both cases . therefore , the case of b1259 - 63 can be treated as a key factor to explain the gps phenomenon observed for the solitary pulsars with interesting environments and also another types of spectra ( e.g. with break ) . |
let @xmath8 and @xmath1 be the space of @xmath2-frames in @xmath3 ( i.e. the space of @xmath2-tuples of linearly independent vectors in @xmath3 ) , @xmath9 .
the group @xmath10 acts on this space as follows : @xmath11 the action is transitive for @xmath12 . let @xmath5 be a lattice in @xmath10 ; that is , a discrete subgroup in @xmath10 such that the factor space @xmath13 has finite volume ( e.g. @xmath14 ) . the main result of this paper concerns distribution of @xmath5-orbits in @xmath1 . when @xmath15 , every orbit of @xmath5 is discrete
the situation becomes much more interesting for @xmath12 .
let us recall known results : * ( dani , raghavan @xcite ) * [ th_dr ] let @xmath14 , and @xmath16 be an @xmath2-frame in @xmath3 , @xmath4 . then the orbit @xmath17 is dense in @xmath1 iff the space spanned by @xmath18 contains no nonzero rational vectors . *
( veech @xcite ) * [ th_ve ] if @xmath5 is a cocompact lattice in @xmath10 , then every orbit of @xmath5 in @xmath1 , @xmath4 , is dense .
theorems [ th_dr ] and [ th_ve ] provide examples of dense @xmath5-orbits in @xmath1 . here
we show that dense @xmath5-orbits are uniformly distributed with respect to an explicitly described measure on @xmath1 .
this measure is @xmath19 , where @xmath20 is the lebesgue measure on @xmath21 , and @xmath22 is the @xmath2-dimensional volume of the frame @xmath23 .
note that the measure @xmath20 is @xmath10-invariant , and it is unique up to a constant .
however , orbits of @xmath5 are equidistributed with respect to the measure @xmath19 , which is not @xmath10-invariant
. this phenomenon was already observed by ledrappier @xcite .
define a norm on @xmath24 by @xmath25 for @xmath26 , @xmath27 , @xmath28 , put @xmath29 we determine asymptotic behavior of @xmath30 as @xmath31 .
this result gives a quantitative strengthening of theorems [ th_dr ] and [ th_ve ] , and it can be interpreted as uniform distribution of dense orbits of @xmath5 in @xmath1 .
[ th_frames00 ] let @xmath5 be a lattice in @xmath32 .
let @xmath33 be an @xmath2-frame in @xmath3 such that @xmath34 is dense in @xmath35 .
let @xmath36 be a relatively compact borel subset of @xmath35 such that @xmath37 .
then @xmath38 where @xmath39 is a constant ( which is computed in ( [ eq_anl ] ) below ) , and @xmath40 is a @xmath10-invariant measure on @xmath13 ( which is defined in ( [ eq_mubar ] ) below ) .
the term @xmath41 in ( [ eq_f_main00 ] ) comes from the asymptotics of the volume of the set @xmath42 in the stabilizer @xmath43 of @xmath44 with respect to the measure on @xmath43 which is determined by the choice of the haar measures on @xmath10 and @xmath45 ( see section [ sec_ttt ] ) . for @xmath46 and @xmath47 ,
this theorem was proved by ledrappier @xcite for general @xmath5 and by nogueira @xcite for @xmath48 and @xmath49-norm using different methods .
combining theorems [ th_dr ] and [ th_frames00 ] , we get : [ th_frames ] let @xmath14 .
let @xmath50 be an @xmath2-frame in @xmath3 such that the space @xmath51 contains no nonzero rational vectors .
let @xmath36 be a relatively compact borel subset of @xmath35 such that @xmath37 .
then @xmath52 where @xmath53 is a constant ( which is computed in ( [ eq_bnl ] ) below ) .
figure [ pic1 ] shows a part of the the orbit @xmath54 for @xmath55 . by the result of ledrappier
, this orbit is uniformly distributed in @xmath56 with respect to the measure @xmath57 .
[ pic1 ] dani and raghavan also considered orbits of frames under @xmath58 . denote @xmath59 j= ( [ cols="^,^",options="header " , ] ) , @xmath59 and @xmath60 is a continuous function depending only on the @xmath61-components of @xmath62 .
we can use proposition [ pro_assym ] with @xmath63 , @xmath64 , and @xmath65 .
since @xmath34 is dense in @xmath66 , @xmath67 is dense in @xmath10 . by ( [ eq_last ] )
, the condition ( [ eq_h1 ] ) holds for @xmath63 . since @xmath68 is unipotent , the condition ( [ eq_h2 ] ) for @xmath63 holds too @xcite . applying proposition [ pro_assym ] , we get @xmath69 as @xmath31 , where @xmath70 is defined in ( [ eq_dh ] ) .
thus , by ( [ eq_last ] ) , @xmath71 where @xmath72
to find the constant @xmath73 , we calculate measures of the set @xmath74 denote by @xmath75 the lebesgue measure of a @xmath76-dimensional unit ball . recall that @xmath77 clearly , @xmath78 for @xmath79 , @xmath80 , and @xmath81 , @xmath82 iff @xmath83 for @xmath84 .
we have @xmath85 let as introduce new coordinates on @xmath86 : @xmath87 , @xmath88 .
the haar measure on @xmath86 ( [ eq_da ] ) is given by @xmath89 . by ( [ eq_nnn ] ) , the set of @xmath90 such that @xmath91 is described by conditions : @xmath92 thus , @xmath93 in the last step , we have used ( [ eq_vball ] ) and the well - known identity for @xmath5-function and @xmath61-function .
finally , by ( [ eq_vol1 ] ) and ( [ eq_vol2 ] ) , @xmath94 let @xmath95 for @xmath96 , and @xmath97 for @xmath98 , define @xmath99 note that @xmath100 .
thus , it is enough to compute asymptotics of the function @xmath101 as @xmath102 . by tauberian theorem (
v , theorem 4.3 ) , it can be deduced from asymptotics of the function @xmath103 as @xmath104 .
it is more convenient to work with the function @xmath105 let @xmath106 .
one can check that @xmath107 for @xmath108 .
( in fact , each of the integral defines a right haar measure on @xmath109 . )
consider mellin transform of the function @xmath110 : @xmath111 using that @xmath112 , we get @xmath113 making substitution @xmath114 , we get @xmath115 by mellin inversion formula , for sufficiently large @xmath116 , @xmath117 since @xmath5-function decays fast on vertical strips , we can shift the line of integration to the left . by ( [ eq_fz ] )
, the first pole of @xmath118 occurs at @xmath119 .
therefore , it follows from ( [ eq_fff ] ) that @xmath120 by ( [ eq_psi2 ] ) , @xmath121 finally , the asymptotic estimate for @xmath122 as @xmath102 follows from tauberian theorem ( * ? ? ? * ch .
v , theorem 4.3 ) .
we have @xmath123 this proves the lemma .
note that @xmath127 we use the formula ( [ eq_rho_l ] ) for @xmath128 and make the change of variables @xmath129 for @xmath130 .
the formula ( [ eq_rbtc ] ) follows from the fact that the volume of a unit ball in @xmath131 is @xmath132 . for @xmath133 ,
put @xmath134 we claim that @xmath135 as @xmath31 .
if @xmath136 , then @xmath137 for every @xmath138 . then as in lemma [ lem_btc ] , @xmath139 now the claim follows from ( [ eq_btasy ] ) .
since @xmath140 we have @xmath141 therefore , @xmath142 as @xmath31 . by theorem [ th_dr ] , @xmath143 is dense in @xmath1 . by theorem [ th_frames00 ] , ( [ eq_ntasy ] ) holds .
the volume of @xmath13 was computed by minkowski . for the measure @xmath144
, we have @xmath145 ( see ( * ? ? ?
* theorem 5.6 ) ) .
30 s. g. dani , g. a. margulis , _ limit distributions of orbits of unipotent flows and values of quadratic forms_. i. m. gelfand seminar , 91137 , adv .
soviet math .
, 16 , part 1 , ams , providence , ri , 1993 . | we study distribution of orbits of a lattice @xmath0 in the the space @xmath1 of @xmath2-frames in @xmath3 ( @xmath4 ) .
examples of dense @xmath5-orbits are known from the work of dani , raghavan , and veech .
we show that dense orbits of @xmath5 are uniformly distributed in @xmath1 with respect to an explicitly described measure .
we also establish analogous result for lattices in @xmath6 that act on the space of isotropic @xmath7-frames . |
investigations of sheath formation in front of a floating plate have hitherto been restricted to fluid studies on the ion time scale [ 1 ] . by contrast , the response of the plasma in the very early stages of sheath formation is not well known . in this paper , we present pic simulations of the plasma dynamics over just a few electron plasma periods after the beginning of the process .
these simulations have been performed by means of the bit1 code [ 2 ] , developed on the basis of the xpdp1 code from u. c. berkeley [ 3 ] .
a floating plate is placed in contact with a uniform , quasi - neutral plasma , which is assumed to be infinitely extended on one side . due to the higher thermal velocity of the electrons ,
the plate starts charging up negatively , so that electrons are gradually repelled , ions are attracted , and a positive - space - charge sheath begins to form .
an electron plasma wave is observed the properties of which strongly depend on the plasma characteristics ( electron and ion temperatures , plasma density , etc . ) .
our pic simulations are performed with different numerical set - ups and plasma characteristics .
a full set of simulation diagnostics is used to measure the properties of the electron waves .
we consider a one - dimensional system .
the planar conducting plate and the ( artificial ) right - hand boundary of the systems are placed at positions @xmath5 and @xmath6 , respectively .
the length @xmath7 is to be chosen large enough for this system to reasonably approximate a semi - infinite plasma ( @xmath8 , with @xmath9 the electron debye length ) . in order to have adequate resolution in space ,
the length of the grid cells has been selected as @xmath10 . at the initial time @xmath11 the electron and ion densities are equal @xmath12 , the distribution functions of both particle species are fully maxwellian , and the electric potential is zero @xmath13 everywhere in the system , including the plate surface . throughout the entire simulation , the following boundary conditions are applied to the particles : at the plate , all particles impinging are absorbed and no particles are injected into the plasma . at the right - hand boundary , on the other hand , all particles impinging are absorbed but new particles with half maxwellian distribution functions are injected at a constant rate .
the system is floating , i.e. , the sum of particle plus displacement currents equals zero . according to these conditions we observe the following behavior . in the unperturbed plasma region (
i.e. , for @xmath14 ) the electron velocity distribution function will not change appreciably ( so that @xmath15 ) , whereas at the plate it will acquire a cut - off form .
this is because the negative - velocity electrons are absorbed by the plate and charge it negatively ; during this process , the ions can be considered to be at rest . with increasing negative surface charge , the negative potential drop in the region close to
the plate becomes higher and more and more electrons are reflected towards the plasma . after some time this perturbation propagates into the system .
the shape of the distribution function essentially depends on the potential drop at the plate . due to the loss of particles by absorption at the plate ,
the total number of particles in the system is dropping all the time .
however , this aspect is not of great concern here because the total loss of particles during the entire simulation presented is negligible . in the following tables we present the parameters used for our simulation .
the ( electron and ion ) particle fluxes corresponding to the unperturbed plasma region are : @xmath16 these expressions are used to calculate the particle injection fluxes from the right - hand boundary .
* parameter * & * value * & * remarks * + @xmath17 & @xmath18 & + @xmath19 & @xmath20 & + @xmath21 & @xmath22 & at @xmath23 + @xmath24 & @xmath25 & + @xmath26 & @xmath27 & + @xmath28 & @xmath29 & + @xmath30 & @xmath31 & + @xmath32 & @xmath33 & electron plasma frequency + @xmath34 & @xmath35 & ion plasma frequency + @xmath36 & @xmath37 & proton mass + @xmath9 & @xmath38 & + * parameter * & * value * & * remarks * + @xmath39 & @xmath40 & grid - cell length @xmath41 + @xmath7 & @xmath42 & system lenght + @xmath43 & @xmath44 & plate aria + @xmath45 & @xmath46 & time step + @xmath47 & @xmath48 & total simulation time +
r0.5 figure [ pot_strat_sursa ] shows the potential profile close to the plate at @xmath49 s. the potential drop at the beginning of the sheath evolution is monotonic in space .
after quick acquisition of negative charge , the plate repels the electrons in the form of a pulse leaving behind a positive - space charge region . as a result ,
the potential close to the plate becomes slightly positive . in front of this region ,
the negative space charge produced by the primary - pulse electrons leads to a potential minimum ( `` virtual cathode '' ) , which gradually reflects more and more slower electrons back into the plasma .
these latter electrons spend a long time in the region of the virtual cathode and hence deepen its potential further . according to figures .
[ evol_rho ] and [ cimp_strat ] , this first potential perturbation ( consisting of a potential hill and a potential well ) propagates into the unperturbed plasma , with additional similar wave structures forming behind it .
r0.5 to verify that these waves are physical and not just due to numerical effects , we have performed other simulations with different parameters .
in particular , we concentrated on the electron temperature .
we know that the debye length is proportional to the square root of the electron temperature .
hence , if we increase the temperature by a factor of four , the debye length must increase by a factor of two .
since , in addition , there is a relation between the wavelength of the electron waves and the debye length , the variation of the electron temperature should also have an effect on the wavelength .
this is clearly illustrated in + figure [ comparare ] , where the wavelength is seen to increase with the square root of the electron temperature . and
@xmath50 _ , scaledwidth=70.0% ]
this work represents the beginning of a self - consistent kinetic study of sheath formation , taking into account both electron and ion dynamics . here , during the short simulation time considered , the ions are practically immobile , and only the electrons take part in the process . in the next step
, the effect of ion dynamics on sheath formation will be considered as well .
this work was supported by the austrian science fund ( fwf ) projects p15013-n08 and p16807-n08 , ceepus network a103 , and erasmus / socrates grant 2004 - 2005 .
* [ 1 ] * j.w .
cipolla , jr . , and m. b. silevitch , on the temporal development of a plasma sheath , j. plasma phys . 25 , 373 - 89 ( jun 1981 ) * [ 3 ] * j. p. verboncoeur , m. v. alves , v. vahedi , and c. k. birdsall , simultaneous potential and circuit solution for 1d bounded plasma particle simulation codes , j. comput .
104 ( 2 ) , 321 ( 1993 ) . abstract submittal form | the problem of sheath formation in front of a conductive planar plate inserted into the plasma is formulated .
initially , the plate is assumed to be neutral .
it is shown that the charging - up process of the plate is accompanied by the excitation of electron plasma waves . _
@xmath0 plasma physics department , faculty of physics , al .
i. cuza university , ro-700506 iasi , romania , + @xmath1j .
stefan institute , university of ljubljana , jamova 39 , slo-1000 ljubljana , slovenia , + @xmath2 association euratom - oaw , department of theoretical physics , university of innsbruck , a-6020 innsbruck , austria , + @xmath3 permanent address : institute of physics , georgian academy of sciences , 380077 tbilisi , georgia , + @xmath4association euratom - oaw , department of ion physics , university of innsbruck , a-6020 innsbruck , austria _ |
it is now an established experimental fact that there are events with large rapidity gaps in the hadronic final state in which there is a large momentum transfer across the gap .
such events have been observed at both the tevatron @xcite and hera @xcite in the rapidity gaps between jets process suggested for study by bjorken @xcite .
the issue now for experimentalists and theorists alike is to address the question of what underlying dynamical process is responsible for such striking events .
it is clear that conventional regge phenomenology can not provide an answer , since the soft pomeron contribution has died away at much lower @xmath4 values due to shrinkage .
the two best developed models currently available are the bfkl pomeron @xcite , calculated within the leading logarithmic approximation ( lla ) by mueller and tang @xcite and implemented into the herwig monte carlo @xcite , and the soft colour rearrangement model @xcite .
the recent gaps between jets analysis by the d0 collaboration @xcite favoured the soft colour model to the bfkl pomeron , although conclusions from gaps between jets measurements may be difficult to draw due to the uncertainties in the role of multiple interactions , which are poorly understood theoretically at the present time @xcite .
furthermore , gaps between jets measurements at both hera and the tevatron are limited by the requirement that two jets are observed in the detector , severely restricting the accessible gap size . since the bfkl cross section is predicted to rise exponentially with @xmath5 , whilst soft colour is
not , this is a severe restriction . at hera ,
measurements of high @xmath4 vector meson production @xcite have provided access to larger rapidity gaps in a well defined kinematic range , although the rate is low . with these issues in mind ,
cox and forshaw @xcite suggested the study of the more inclusive double dissociative process @xmath0 at high @xmath4 . in this paper
we report the first measurement of this process , based on h1 data taken during 1996 .
the photon and proton dissociative systems , @xmath1 and @xmath2 respectively , are separated by finding the largest rapidity gap in the event ( the procedure used by the h1 collaboration in previous diffractive measurements @xcite ) .
the process , shown schematically in figure [ diffplot ] , is considered in terms of the kinematic variables @xmath6 @xmath7 where @xmath8 and @xmath2 are the 4-vectors of the photon , proton and x and y systems respectively .
@xmath9 is the @xmath10 center of mass energy and @xmath11 is the four momentum transfer across the rapidity gap . in this study
we present measurements of the differential cross section @xmath12 in the range @xmath13 , @xmath14 , @xmath15 , @xmath16 .
the data for this analysis were collected with the h1 detector during the 1996 running period , when hera collided @xmath17 positrons with @xmath18 protons , with an integrated luminosity of 6.7 @xmath19 .
photoproduction events were selected by detecting the scattered positron in the electron tagger , 33 m down the beam pipe in the scattered electron direction .
this restricts the virtuality of the photon to @xmath20 gev@xmath21 .
the reconstruction of the @xmath1 and @xmath2 system 4-vectors has been optimised by combining tracking and calorimeter information .
techniques are applied to minimise the effects of detector noise .
precise details can be found elsewhere @xcite .
losses in the forward and backward directions are , however , unavoidable , making the measurement of the invariant masses of the systems problematic . for this reason , we introduce the kinematic variables @xmath22 and @xmath23 , reconstructed using the expressions @xmath24 where @xmath25 and @xmath26 are the proton and photon beam energies respectively , and the quantity @xmath27 ( @xmath28 ) is summed over all hadrons reconstructed backward ( forward ) of the largest rapidity gap in the event .
this quantity has the property that it is insensitive to losses down the beam pipe , for which @xmath29 ( @xmath30 ) . in order to ensure that
the systems @xmath1 and @xmath2 are clearly separated , only events with a rapidity gap between the two systems of at least 1.5 units of rapidity are selected .
these events are specified by @xmath31 , and hence our sample is defined in the kinematic range @xmath32 and @xmath15 . and @xmath2 systems must be @xmath33 is not part of the hadron level cross section definition . any losses due to this cut
are included in the acceptance corrections ] the reconstruction of @xmath11 is more problematic .
it is measured as the negative squared transverse momentum of the @xmath1 system , @xmath34 , and is sensitive to losses down the backward beam pipe , particularly for low values of @xmath4 .
for this reason we choose to define our sample for @xmath35 .
the events selected by the criteria described in section 2 are used to determine the cross section @xmath36 in the kinematic range defined in section 1 .
the herwig monte carlo , including bfkl pomeron exchange , is used to correct for losses and migration effects in @xmath22 , @xmath23 and @xmath11 . in the bfkl formalism at leading order
, it does not make sense to run the coupling , and therefore @xmath37 is fixed in the herwig generation at @xmath38 .
this corresponds at leading order to a hard pomeron intercept of @xmath39 , where @xmath40 .
the dominant contribution to the statistical error comes from the limited number of data events in the sample .
systematic uncertainties are calculated on a bin by bin basis , and added in quadrature .
the dominant error is due to the limited number of data events available to calculate the trigger efficiency , contributing a systematic error of approximately @xmath41 in each bin .
the @xmath22 distribution , corrected for detector effects , is shown in figure [ xpom_fixw ] .
the inner error bars are statistical and the outer error bars are the quadratic sum of the statistical and systematic errors .
the solid line is the prediction from the herwig generator for all non - singlet exchange photoproduction processes . a significant excess above the expectation from the standard photoproduction model is observed .
the dashed line shows the herwig prediction with the lla bfkl prediction added .
good agreement is observed in both normalisation and shape .
care must be taken , however , in the interpretation of this result .
there is a large theoretical uncertainty in the overall normalisation of the lla bfkl cross section prediction .
the agreement in normalisation may well therefore be fortuitous .
it should also be noted that the shape of the @xmath22 distribution in this region of phase space is not only determined by the underlying dynamics of the interaction , but also by kinematic effects .
there is a kinematic limit on the lowest possible value of @xmath22 , set by the requirement that @xmath42 and @xmath43 gev , of @xmath44 x @xmath45 ( see equation ( 3 ) ) .
this forces the cross section down in the lowest @xmath22 bin . the good agreement in shape with the bfkl monte carlo prediction , however , implies that the data are consistent with a value of @xmath46 within this model . despite these limitations , however , with higher statistics the outlook for the future is promising .
this measurement demonstrates that it is possible to extend greatly the reach in rapidity allowed by the gaps between jets approach . with the improved statistics already collected in the 1997 hera running period , and higher luminosity in the future , a much more precise determination of the dependence of the cross section on @xmath22 , i.e. the energy dependence , will be possible . s. abachi et al ( d0 collaboration ) , phys .
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c74 ( 1997 ) 221 . | the double dissociation photoproduction cross section for the process @xmath0 , in which the systems @xmath1 and @xmath2 are separated by a large rapidity gap , is measured at large 4-momentum transfer squared @xmath3 by the h1 collaboration at hera .
this measurement provides for the first time a direct measurement of the energy dependence of the gap production process at high @xmath4 . |
finite temperature instantons ( calorons ) have a rich structure if one allows the polyakov loop , @xmath1 in the periodic gauge @xmath2 , to be non - trivial at spatial infinity ( specifying the holonomy ) .
it implies the spontaneous breakdown of gauge symmetry . for a charge one @xmath3 caloron
, the location of the @xmath4 constituent monopoles can be identified through : i. points where two eigenvalues of the polyakov loop coincide , which is where the @xmath5 symmetry is partially restored to @xmath6 .
ii . the centers of mass of the ( spherical ) lumps .
iii . the dirac monopoles ( or rather dyons , due to self - duality ) as the sources of the abelian field lines , extrapolated back to the cores .
if well separated and localised , all these coincide @xcite . here
we study the case of two constituents coming close together for @xmath7 , with an example for @xmath0 .
the eigenvalues of @xmath8 can be ordered by a constant gauge transformation @xmath9 & & -3 mm w_^w_== , + & & -3mm_1
_n_n+11+_1 , with @xmath10 .
the constituent monopoles have masses @xmath11 , where @xmath12 ( using the classical scale invariance to put the extent of the euclidean time direction to one , @xmath13 ) . in the same way we can bring @xmath14 to this form by a _ local _ gauge function , @xmath15 .
we note that @xmath16 ( unique up to a residual abelian gauge rotation ) and @xmath17 will be smooth , except where two ( or more ) eigenvalues coincide .
the ordering shows there are @xmath4 different types of singularities ( called defects @xcite ) , for each of the _ neighbouring _ eigenvalues to coincide .
the first @xmath18 are associated with the basic monopoles ( as part of the inequivalent @xmath19 subgroups related to the generators of the cartan subgroup ) .
the @xmath20 defect arises when the first and the last eigenvalue ( still neighbours on the circle ) coincide .
its magnetic charge ensures charge neutrality of the caloron .
the special status @xcite of this defect also follows from the so - called taubes winding @xcite , supporting the non - zero topological charge @xcite .
to analyse the lump structure when two constituents coincide , we recall the simple formula for the @xmath3 action density @xcite . & & -6mmf_^2(x)=_^2_^2 , + & & -6mm_m(r_m&|y_m -y_m+1| + 0&r_m+1 ) ( c_m&s_m + s_m&c_m ) , with @xmath21 the center of mass location of the @xmath22 constituent monopole .
we defined @xmath23 , @xmath24 , @xmath25 , as well as @xmath26 , @xmath27 .
we are interested in the case where the problem of two coinciding constituents in @xmath3 is mapped to the @xmath28 caloron . for this
we restrict to the case where @xmath29 for some @xmath30 , which for @xmath0 is _ always _ the case when two constituents coincide . since now @xmath31 , one easily verifies that @xmath32 $ ] , describing a _ single _ constituent monopole ( with properly combined mass ) , reducing eq .
( 2 ) to the action density for the @xmath28 caloron , with @xmath33 constituents .
the topological charge can be reduced to surface integrals near the singularities with the use of @xmath34 , where @xmath35 .
if one assumes _ all _ defects are pointlike , this can be used to show that for each of the @xmath4 types the ( net ) number of defects has to equal the topological charge , the type being selected by the branch of the logarithm ( associated with the @xmath4 elements in the center ) @xcite .
one might expect the defects to merge when the constituent monopoles do .
a triple degeneracy of eigenvalues for @xmath0 implies the polyakov loop takes a value in the center .
yet this can be shown _ not _ to occur for the @xmath0 caloron with _ unequal _ masses .
we therefore seem to have ( at least ) one more defect than the number of constituents , when @xmath36 .
we will study in detail a generic example in @xmath0 , with @xmath37 .
we denote by @xmath38 the position associated with the @xmath22 constituent where two eigenvalues of the polyakov loop coincide . in the gauge where @xmath39 ( see eq .
( 1 ) ) , we established numerically @xcite that p_1=p(z_1)=(e^-i_3 , e^-i_3,e^2i_3 ) , + p_2=p(z_2)=(e^2i_1 , e^-i_1,e^-i_1 ) , + p_3=p(z_3)=(-e^-i_2 , e^2i_2,-e^-i_2).this is for _ any _ choice of holonomy and constituent locations ( with the proviso they are well separated , i.e. their cores do not overlap , in which case to a good approximation @xmath40 ) . here
we take @xmath41 , @xmath42 and @xmath43 .
the limit of coinciding constituents is achieved by @xmath44 . with this geometry
it is simplest to follow for changing @xmath45 the location where two eigenvalues coincide . in very good approximation ,
as long as the first two constituents remain well separated from the third constituent ( carrying the taubes winding ) , @xmath46 will be constant in @xmath45 and the @xmath0 gauge field @xcite of the first two constituents will be constant in time ( in the periodic gauge ) .
thus @xmath47 for @xmath48 , greatly simplifying the calculations .
when the cores of the two approaching constituents start to overlap , @xmath49 and @xmath50 are no longer diagonal ( but still block diagonal , mixing the lower @xmath51 components ) . at @xmath52 they are diagonal again , but @xmath50 will be no longer in the fundamental weyl chamber . a weyl reflection maps it back , while for @xmath53 a more general gauge rotation back to the cartan subgroup is required to do so , see fig . 1 .
at @xmath52 , _ each _ @xmath54 ( and @xmath55 ) lies on the dashed line , which is a direct consequence of the reduction to an @xmath19 caloron . to illustrate this more clearly , we give the expressions for @xmath54 ( which we believe to hold for any non - degenerate choice of the @xmath56 ) when @xmath57 : p_1=p(z_1)=(e^2i_2 , e^2i_2,e^-4i_2 ) , + p_2=p(z_2)=(e^-i_2 , e^2i_2,e^-i_2 ) , + p_3=p(z_3)=(-e^-i_2 , e^2i_2,-e^-i_2).these can be factorised as @xmath58 , where @xmath59 describes an overall @xmath60 factor . in terms of @xmath61 , @xmath62 and @xmath63
the @xmath19 embedding in @xmath0 becomes obvious .
it leads for @xmath64 to the trivial and for @xmath65 to the non - trivial element of the center of @xmath19 ( appropriate for the latter , carrying the taubes winding ) . on the other hand
, @xmath66 corresponds to @xmath67 , which for the @xmath19 caloron is not related to coinciding eigenvalues . for @xmath44 , fig .
2 shows that @xmath68 gets `` stuck '' at a _
finite _ distance ( 0.131419 ) from @xmath69 .
the @xmath19 embedding determines the caloron solution for @xmath70 , with constituent locations @xmath71 and @xmath72 , and masses @xmath73 and @xmath74 . the best proof for the spurious nature of the defect is to calculate its location purely in terms of this @xmath19 caloron , by demanding the @xmath19 polyakov loop to equal @xmath75 . for this we can use the analytic expression @xcite of the @xmath19 polyakov loop along the @xmath76-axis .
the location of the spurious defect , @xmath77 , is found by solving @xmath78 $ ] .
for our example , @xmath79 indeed verifies this equation . with the @xmath19 embedded result at hand , we find that only for @xmath80 the defects merge to form a triple degeneracy .
using @xmath81 , this is so for coinciding constituent monopoles of _ equal _ mass . for _ unequal _ masses
the defect is always spurious , but it tends to stay within reach of the non - abelian core of the coinciding constituent monopoles , except when the mass difference approaches its extremal values @xmath82 , see fig . 2 ( bottom ) . at these extremal values
one of the @xmath0 constituents becomes massless and _ delocalised _ , which we excluded for @xmath53 .
however , the limit @xmath44 is singular due to the _ global _ decomposition into @xmath83 at @xmath52 .
gauge rotations @xmath84 in the global @xmath19 subgroup do not affect @xmath59 , and therefore any @xmath85 gives rise to the _ same _ accidental degeneracy .
in particular solving @xmath86 $ ] ( corresponding to the weyl reflection @xmath87 ) yields @xmath88 for @xmath89 ( isolated point in fig . 2 ( top ) ) .
indeed , @xmath90 traces out a ( nearly spherical ) _ shell _ where two eigenvalues of @xmath91 coincide ( note that for @xmath80 this shell collapse to a single point , @xmath92 ) .
a perturbation tends to remove this accidental degeneracy .
abelian projected monopoles are not always what they seem to be , even though required by topology .
_ topology _ can not be localised , no matter how tempting this may seem for smooth fields .
i am grateful to andreas wipf for his provocative question that led to this work .
i thank jan smit , and especially chris ford , for discussions .
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p. romatschke and u. romatschke , arxiv:0706.1522 [ nucl - th ] . | we show that the centrality and system - size dependence of elliptic flow measured at rhic are fully described by a simple model based on eccentricity scaling and incomplete thermalization .
we argue that the elliptic flow is at least 25% below the ( ideal ) `` hydrodynamic limit '' , even for the most central au - au collisions .
this lack of perfect equilibration allows for estimates of the effective parton cross section in the quark - gluon plasma and of its viscosity to entropy density ratio .
we also show how the initial conditions affect the transport coefficients and thermodynamic quantities extracted from the data , in particular the viscosity and the speed of sound .
when two ultrarelativistic nuclei collide at non - zero impact parameter , their overlap area in the transverse plane has a short axis , parallel to the impact parameter , and a long axis perpendicular to it .
this almond shape of the initial profile is converted by the pressure gradient into a momentum asymmetry , so that more particles are emitted along the short axis @xcite .
the magnitude of this effect is characterized by elliptic flow , defined as @xmath0 where @xmath1 is the azimuthal angle of an outgoing particle , @xmath2 is the azimuthal angle of the impact parameter , and angular brackets denote an average over many particles and many events .
the unexpected large magnitude of elliptic flow at rhic @xcite has generated a lot of activity in recent years .
elliptic flow results from the interactions between the produced particles , and can be used to probe local thermodynamic equilibrium . if the produced matter equilibrates , it behaves as an ideal fluid .
hydrodynamics predicts that at a given energy , @xmath3 scales like the eccentricity @xmath4 of the almond @xcite .
it is independent of its transverse size @xmath5 , as a consequence of the scale invariance of ideal - fluid dynamics .
if , on the other hand , equilibration is incomplete , then eccentricity scaling is broken and @xmath6 also depends on the knudsen number @xmath7 , where @xmath8 is the length scale over which a parton is deflected by a large angle . here , we show that the centrality dependence of @xmath6 , for both au+au and cu+cu collisions , can be described by the following simple formula @xcite : @xmath9 @xmath6 is largest in the hydrodynamic limit @xmath10 .
the first order corrections to this limit , corresponding to viscous effects , are linear in @xmath11 . for large mean - free path , far from the hydrodynamic limit , @xmath12 vanishes like the number of collisions per particle .
one expects the transition between these two regimes to occur when @xmath13 , hence that @xmath14 .
a recent transport calculation @xcite in two spatial dimensions indeed obtained @xmath15 .
elliptic flow develops gradually during the early stages of the collision .
due to the strong longitudinal expansion , the thermodynamic properties of the medium depend on the time @xmath16 , of course .
the average particle density , for instance , decreases like @xmath17 ( if their number is approximately conserved , see recent discussion in @xcite ) : @xmath18 where @xmath19 denotes the total ( charged + neutral ) multiplicity per unit rapidity , and @xmath20 is the transverse overlap area between the two nuclei . the quantities that we shall extract from @xmath3 should be intepreted as averages over the transverse area @xmath20 , and over some time interval around @xmath21 , which is the typical time scale for the build - up of @xmath3 in hydrodynamics @xcite .
@xmath22 denotes the velocity of sound . the knudsen number @xmath11 is defined by evaluating the mean free path @xmath23 ( @xmath24 is a partonic cross section ) at @xmath25 .
thus , @xmath26 the purpose of this letter is to show that the centrality and system - size dependence of the data for @xmath3 at rhic is described very well by eqs .
( [ v2k ] ) and ( [ knud ] ) .
this provides three important pieces of information .
first , such a fit allows us to `` measure '' the knudsen number corresponding to a given centrality , which quantifies how close the dense matter produced in heavy - ion collisions at rhic is to perfect fluidity .
second , the extrapolation to @xmath27 allows us to read off the limiting value for @xmath28 extracted from the _ data _ ; this is useful for constraining the equation of state ( eos ) of qcd via hydrodynamic simulations , and we shall also see that it exhibits a rather surprising dependence on the initial conditions . finally , using eq .
( [ knud ] ) , we can convert the knudsen number into the typical partonic cross section @xmath24 ( and viscosity ) in the quark - gluon plasma ( qgp ) .
since only the combination @xmath29 actually appears in eq .
( [ v2k ] ) , uncertainties in @xmath30 or @xmath22 then translate into corresponding uncertainties of @xmath24 . unless mentioned otherwise , our standard choice is @xmath31 ( ideal quark - gluon plasma ) and @xmath32 . letting @xmath33 and @xmath34
instead reduces the estimated @xmath24 by a factor of two ; on the other hand , taking @xmath35 and @xmath36 increases @xmath24 by the same factor . for the elliptic flow , @xmath3 , we use phobos data for au - au @xcite and cu - cu @xcite collisions .
the same analysis could be carried out using data from phenix @xcite or star @xcite .
the initial eccentricity @xmath4 and the transverse density @xmath37 are evaluated using a model of the collision .
two such models will be compared .
the remaining parameters @xmath38 and @xmath24 are fit to the data .
the first step is to plot @xmath6 versus @xmath37 @xcite .
such plots have already been obtained at sps and rhic @xcite , and they are puzzling : while @xmath6 increases with centrality , it shows no hint of the _ saturation _ predicted by eq .
( [ v2k ] ) for @xmath39 , suggesting that the system is far from equilibrium @xcite . on the other hand ,
the value of @xmath3 for central au - au collisions at rhic is about as high as predicted by hydrodynamics , which is widely considered as key evidence that a `` perfect liquid '' has been created at rhic @xcite .
it was understood only recently that the eccentricity of the overlap zone has so far been underestimated , as the result of two effects .
the first effect is fluctuations in initial conditions @xcite : the time scale of the nucleus - nucleus collision at rhic is so short that each nucleus remains in a frozen configuration , with its nucleons distributed according to the nuclear wave function .
fluctuations in the nucleon positions result in fluctuations of the overlap area .
their effect on elliptic flow was first pointed out in ref .
@xcite .
it was later realized by the phobos collaboration @xcite that the orientation of the almond may also fluctuate , so that @xmath2 in eq . ( [ defv2 ] )
is no longer the direction of impact parameter , but the minor axis of the ellipse defined by the positions of the nucleons .
these fluctuations explain both the large magnitude of @xmath3 for small systems , such as cu - cu collisions , as well as the non - zero magnitude of @xmath3 in central collisions , where the eccentricity would otherwise vanish .
they have to be taken into account in order to observe the expected saturation of @xmath6 at high density mentioned above .
the eccentricity is usually estimated from the distribution of participant nucleons in the transverse plane ( glauber model ) .
more precisely , we assume here that the density distribution of produced particles is given by a fixed 80%:20% superposition of participant and binary - collision scaling , respectively @xcite . for au - au collisions ,
this simple model reproduces the centrality dependence of the multiplicity reasonably well ( we assume that charged particles are 2/3 of the total multiplicity , and that @xmath40 at midrapidity ) , while it underestimates it for central cu - cu collisions by about 10% . at high energies a second effect which increases the eccentricity is perturbative gluon saturation , which determines the @xmath41-integrated multiplicity from weak - coupling qcd without additional models for soft particle production .
high - density qcd ( the `` color - glass condensate '' ) predicts a different distribution of produced gluons , @xmath42 , which gives a similar centrality dependence of the multiplicity @xcite but a larger eccentricity @xcite .
when particle production is dominated by transverse momenta below the saturation scale of the denser nucleus , then @xmath43 traces the participant density of the more dilute collision partner , rather than the average as in the glauber model @xcite .
precise figures depend on how the saturation scale is defined @xcite .
naively , the larger initial eccentricity predicted by the gluon saturation approach is expected to require more dissipation in order to reproduce the same experimentally measured @xmath3 .
somewhat surprisingly , we shall find that this expectation is incorrect , which underscores the non - trivial role played by the initial conditions .
both effects , fluctuations and gluon saturation , were recently combined by drescher and nara @xcite . in their approach , the saturation momenta and
the unintegrated gluon distribution functions of the colliding nuclei are determined for each configuration individually .
the finite interaction range of the nucleons is also taken into account .
upon convolution of the projectile and target unintegrated gluon distribution functions and averaging over configurations , the model leads to a very good description of the multiplicity for both au - au as well as cu - cu collisions over the entire available range of centralities .
having determined the density distributions of produced particles from either model as described above , we obtain the eccentricity via @xcite @xmath44 @xmath45 , @xmath46 are the respective root - mean - square widths of the density distributions , and @xmath47 ( a bar denotes a convolution with the density distribution for a given configuration while brackets stand for averages over configurations ) . the overlap area @xmath20
is defined by @xmath48 @xcite .
we find it more appropriate to define these moments via the number density distribution @xmath42 rather than the energy density distribution @xmath49 .
the reason is twofold : first , @xmath3 is extracted experimentally from the azimuthal distribution of particle number , not transverse energy ; second , our cgc approach describes the centrality dependence of the _ measured _ final - state multiplicity very well , which indicates that the ratio of final - state particles to initial - state gluons ( including possible gluon multiplication processes @xcite ) is essentially constant . ) and ( [ knud ] ) .
[ fig : glauber ] ] , using cgc initial conditions .
[ fig : cgc ] ] figs .
[ fig : glauber ] and [ fig : cgc ] display @xmath6 as a function of @xmath37 for au - au and cu - cu collisions at various centralities , within the glauber and cgc approaches , respectively . for both types of initial conditions , cu - cu and au - au collisions at the same
@xmath37 give the same @xmath6 within error bars .
eccentricity fluctuations are crucial for this agreement @xcite .
the figures also show that eqs .
( [ v2k ] ) and ( [ knud ] ) provide a good fit to the data , for both sets of initial conditions .
on the other hand , the values of the fit parameters clearly depend on the initial conditions , which has important consequences for the physics .
the first physical quantity extracted from the fit is the hydrodynamic limit , @xmath50 , obtained by extrapolating to @xmath51 .
the values are @xmath52 with the glauber parameterization , and @xmath53 with cgc initial conditions . comparing these numbers to the experimental data points
one observes that deviations from ideal hydrodynamics are as large as 30% , even for central au - au collisions .
this is our first important result .
so far , a quantitative extraction of the qcd eos from rhic data via hydrodynamic analysis was hampered by the fact that @xmath6 had not been factorized into the perfect - fluid part @xmath50 and the dissipative correction @xmath54 .
for example , huovinen found @xcite that an eos with a rapid cross - over rather than a strong first - order phase transition , as favored by lattice qcd @xcite , overpredicted the flow data .
this finding was rather puzzling , too , as it was widely believed that the rhic data fully saturates the hydrodynamic limit .
our results suggest that ideal hydrodynamics _ should _ in fact overpredict the measured flow . that is , that one should not choose an eos in perfect - fluid simulations that fits the data
rather , the eos could be extracted by comparing ideal hydrodynamics to @xmath50 .
the next result is that cgc initial conditions , which predict a higher initial eccentricity @xmath4 , naturally lead to a lower hydrodynamic limit @xmath50 .
now , close to the ideal - gas limit ( @xmath55 ) , @xmath50 scales approximately like the sound velocity @xmath22 @xcite .
this means that cgc initial conditions imply a lower average speed of sound ( softer equation of state ) than glauber initial conditions , by a factor of @xmath56 .
the second fit parameter is the partonic cross section @xmath24 .
the larger @xmath24 , the faster the saturation of @xmath6 as a function of @xmath37 . for our standard values of @xmath30 and @xmath22
we obtain @xmath57 mb for glauber initial conditions and @xmath58 mb for cgc initial conditions .
these values are significantly smaller than those found in previous transport calculations @xcite , but match the findings of ref .
@xcite .
cgc initial conditions imply a larger value of @xmath24 than glauber initial conditions , that is , a _
lower _ viscosity . this can be easily understood . as already mentioned above
, the cgc predicts a larger eccentricity @xmath4 than the glauber model for semi - central collisions of large nuclei ( when there is a large asymmetry in the local saturation scales of the collision partners , along a path in impact - parameter direction away from the origin @xcite ) .
however , for very peripheral collisions or small nuclei , there is of course very little asymmetry in the saturation scales , and the eccentricity approaches the same value as in the glauber model .
this has been checked numerically in fig .
7 of ref .
@xcite , and can also be clearly seen by comparing our figures : while in fig . [ fig : cgc ] @xmath6 for semi - central au+au collisions is lower than in fig .
[ fig : glauber ] , there is no visible difference for peripheral cu+cu collisions . in all , with cgc initial conditions the scaled flow grows less rapidly with the transverse density , which is the reason for the larger elementary cross - section . the dependence of @xmath24 on the initial conditions is probably even stronger than the numerical values above suggest , for the following reason . as alluded to above , our fit to the data really determines the product @xmath59 , rather than @xmath24 alone .
it appears reasonable to assume that @xmath30 does not depend on the initial conditions .
however , for consistency , the speed of sound @xmath22 entering the knudsen number should match the one underlying the hydrodynamic limit @xmath60 ; hence , if cgc initial conditions require a smaller @xmath22 by a factor @xmath61 , the elementary cross - section obtained above should be rescaled accordingly .
this leads to our final estimate @xmath62 mb .
our numerical results for @xmath24 should be taken as rough estimates rather than precise figures , because of the uncertainties related to the precise values of @xmath30 and @xmath22 .
it is , however , tempting to convert them into estimates of the shear viscosity @xmath63 , which has been of great interest lately .
a universal lower bound @xmath64 ( where @xmath65 is the entropy density ) has been conjectured using a correspondence with black - hole physics @xcite , and it has been argued that the viscosity of qcd might be close to the lower bound .
extrapolations of perturbative estimates to temperatures @xmath66 mev , on the other hand , suggest that the viscosity of qcd could be much larger @xcite . on the microscopic side ,
@xmath63 is related to the scattering cross - section @xmath24 .
following teaney @xcite , the relation for a classical gas of massless particles with isotropic differential cross sections ( which applies , for example , to a boltzmann - transport model ) is @xmath67 @xcite . on the other hand ,
the entropy density of a classical ultrarelativistic cas is @xmath68 , with @xmath69 the particle density , so that @xmath70 the relevant particle density in au - au collisions at rhic , which is estimated at the time when @xmath3 develops @xcite , is 3.9 @xmath71 for both glauber and cgc initial conditions , and @xmath72 mev .
our two estimates @xmath73 mb ( glauber initial conditions ) and @xmath74 mb ( cgc initial conditions ) thus translate into @xmath75 fm , @xmath76 and @xmath77 fm , @xmath78 , respectively .
these values for @xmath79 agree with those from ref .
@xcite if the mean - free path is scaled to our result , and also with estimates of @xmath79 based on the observed energy loss and elliptic flow of heavy quarks @xcite , on transverse momentum correlations @xcite , or bounds on entropy production @xcite .
hence , for our best fit(s ) @xmath79 is slightly larger than the conjectured lower bound , but significantly smaller than extrapolations from perturbative estimates . on the other hand ,
our lower value is close to a recent lattice estimate @xcite for su(3 ) gluodynamics , which gives @xmath80 at @xmath81 .
a complementary approach to incorporate corrections from the ideal - fluid limit is viscous relativistic hydrodynamics . a formulation that is suitable for applications to high - energy heavy - ion collisions
has been developped in recent years @xcite . a first calculation of elliptic flow @xcite shows that for glauber initial conditions and @xmath82
, @xmath3 reaches about @xmath83 of the ideal - fluid value for semi - central au - au collisions .
it is interesting to note that our simple estimates are in good agreement with this finding . using eq .
( [ eta ] ) , @xmath82 corresponds to @xmath84 mb , for which eqs .
( [ v2k ] ) and ( [ knud ] ) give @xmath85 .
the comparison to experimental data in ref .
@xcite , however , appears to favor lower values of @xmath79 because the eos used there underpredicts @xmath86 required for glauber initial conditions .
alternatively , simulations could be performed with cgc initial conditions which require only @xmath87 . in summary
, we have shown that the centrality and system - size dependence of the _ measured _ @xmath3 can be understood as follows : @xmath3 scales like the initial eccentricity @xmath4 ( as predicted by hydrodynamics ) , multiplied by a correction factor due to off - equilibrium ( i.e. , viscous ) effects .
this correction involves the multiplicity density in the overlap area , @xmath37 .
two types of initial conditions have been compared : a glauber - type model , and a color - glass condensate approach .
phobos data can be described with both .
in particular , there is good agreement between cu - cu and au - au data .
the resulting estimates for thermodynamic quantities and transport coefficients , on the other hand , depend significantly on the initial conditions .
color glass condensate - type initial conditions require _ lower _ viscosity and a _
softer _ equation of state ( smaller speed of sound ) .
the scaled flow extrapolated to vanishing mean - free path is lower than for glauber initial conditions by a factor of @xmath88 ; the effective speed of sound should also be lower by about the same factor .
our estimates for the viscosity are @xmath89 for glauber initial conditions , and @xmath90 for cgc initial conditions , but these numbers should be taken only as rough estimates .
we have also shown that the data for the scaled flow indeed _ saturate _ at high densities to a hydrodynamic limit .
in central au - au collisions at rhic , @xmath3 reaches 70% ( resp .
75% ) of the hydrodynamic limit for glauber ( cgc ) initial conditions .
the corrections to ideal hydrodynamics are therefore significant , but reasonably small compared to unity , implying that ( viscous ) hydrodynamics should be a valid approach for understanding flow at rhic .
also , the asymptotic limit of @xmath6 has been isolated and could now be used to test realistic equations of state from lattice - qcd with hydrodynamic simulations of heavy - ion collisions . |
this work was supported by gesellschaft fr schwerionenforschung , darmstadt ( gsi ) and by the loewe initiative of the state of hessen through the helmholtz international center for fair .
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b * 526 * , 309 ( 2002 ) [ arxiv : hep - ph/0006147 ] . | we discuss one of the most prominent features of the very recent preliminary elliptic flow data of @xmath0 meson from the phenix collaboration @xcite . even within the the rather large error bars of the measured data
a negative elliptic flow parameter ( @xmath1 ) for @xmath0 in the range of @xmath2 is visible .
we argue that this negative elliptic flow at intermediate @xmath3 is a clear and qualitative signature for the collectivity of charm quarks produced in nucleus - nucleus reactions at rhic . within a parton recombination approach
we show that a negative elliptic flow puts a lower limit on the collective transverse velocity of heavy quarks . the numerical value of the transverse flow velocity @xmath4 for charm quarks that is necessary to reproduce the data is @xmath5 and therefore compatible with the flow of light quarks . the main goal of the current and past heavy ion programs is the search for a new state of matter called the quark - gluon - plasma ( qgp ) @xcite .
major breakthroughs for the potential discovery @xcite of this new state of matter were the observation of constituent quark number scaling of the elliptic flow @xmath6 , with @xmath7 being the number of constituent quarks in the respective hadron as well as the observation of jet quenching at intermediate transverse momenta @xcite .
together with the standard hydrodynamical interpretation this implies a rapid thermalization and a strong collective flow of the qcd matter created at rhic .
however , open questions remain : how can one obtain a consistent description of the high @xmath3 suppression and the elliptic flow of heavy flavour quarks and hadrons .
i.e. is the collectivity at rhic restricted to light quarks ( up , down , strange ) or do even charm ( bottom ) quarks participate in the collective expansion of the partonic system and reach local kinetic equilibrium ? previously , it was assumed that local equilibrium of ( heavy ) quarks could not be achieved within pqcd transport simulations .
in fact , older studies @xcite based on a parton cascade dynamics restricted to @xmath8 parton interactions seemed to indicate that the opacity needed to achieve local equilibrium would be at least an order of magnitude higher than pqcd estimates .
however , recent state - of - the - art parton cascade calculations ( including @xmath9 parton interactions ) have clearly shown that pqcd cross sections are sufficient to reach local ( gluon ) equilibrium and allow to describe the measured elliptic flow data @xcite .
the aim of the present letter is to investigate whether also the charm quark does locally equilibrate and therefore follows the flow of the light quarks . here
we will focus on the @xmath0 because it reflects the momentum distribution of the charm quarks directly , in addition first experimental data on the @xmath0 elliptic flow just became available .
we will show that the recently measured negative elliptic flow of @xmath0 s provides a unique _ lower _ bound on the charm quark s collective velocity .
under the assumption of local equilibration of light quarks a hydrodynamic parametrization of the freeze - out hyper - surface to parametrize the quark emission function , namely the blast - wave model , can be employed . for the charm quarks ,
the same emission function is used , however , with the transverse collective velocity as a free parameter to be determined by the preliminary phenix data . to calculate @xmath0 s from the charm quark emission function ,
we apply the well known parton recombination approach @xcite . details ( like the exact form of the freeze - out hyper - surface ) of the specific approach employed here can be found in @xcite .
different from there we used a linear increasing transverse flow rapidity instead of a constant one , but the mean value has been preserved .
here we summarize the most important features : in a coalescence process the quarks contribute equally to the hadrons momentum , so it inherits its azimuthal asymmetry directly from its constituents .
therefore in recombination the elliptic flow of @xmath0 s emerges directly from a negative @xmath1 of the charm quark . to incorporate the asymmetry , the transverse expansion rapidity @xmath10 depend on the azimuthal angle @xmath11 and the radial coordinate @xmath12 as @xmath13 with the eccentricity @xmath14 and @xmath15 to model the damping at high @xmath3 . with the factor
@xmath16 we recover @xmath17 as the mean transverse rapidity after integrating over @xmath18 . by applying the definition of the elliptic flow one obtains @xcite @xmath19 k_1 \left[b(\phi,\rho)\right ] \ , d\phi\ , \rho\ , d\rho } { \int i_0 \left[a(\phi,\rho)\right ] k_1\left[b(\phi,\rho)\right ] \ ,
d\phi\ , \rho\ , d\rho}\ ] ] with @xmath20 , @xmath21 and the modified bessel functions @xmath22 and @xmath23 .
for a more general hydrodynamical hypersurface one could assume a dependence of freeze - out time @xmath24 on the radial coordinate @xmath18 .
this would lead to additional terms involving @xmath25 and bessel functions of other order .
we have checked that the modifications are only minor and therefore neglect the contributions in this letter for brevity .
let us investigate the elliptic flow of the @xmath0 at midrapidity as a function of the transverse momentum for various transverse flow velocities as shown in fig .
[ plt : jpsi_flow ] .
the lines from top to bottom indicate calculations with a charm quark mass @xmath26 for different mean expansion velocities @xmath27 , the data by the phenix collaboration are shown as symbols with error bars indicating a negative elliptic flow for @xmath0 s at intermediate transverse momenta .
the calculation shows that with increasing transverse flow a negative @xmath1 at low @xmath3 ( above @xmath28 gev , the elliptic flow values turn positive again ) develops for the @xmath0 , posing a lower bound of @xmath29 for the charm quarks flow .
the best fit to the data is obtained with a mean charm flow velocity of @xmath30 equal to the light quark flow velocity extracted from previous fits within the same model . in fig .
[ plt : compare_flow ] we use @xmath30 and compare the elliptic flow to other heavy mesons and fig .
[ plt : quark_flow ] shows the same for the quarks .
the value for @xmath31 , with a bottom quark mass of @xmath32 , is negativ in the whole range of applicability .
in contrast to @xmath0 , the @xmath1 of @xmath33 stays positiv .
this is due to the positive light quark @xmath1 , which competes with the negative one for the charm quark , and results in nearly zero elliptic flow at low @xmath3 .
while the @xmath34 meson follows the @xmath33 flow for @xmath35 , it is much more suppressed at higher @xmath3 due to the strong negative flow of the bottom quark and approximately zero up to @xmath36 .
data on @xmath37-meson elliptic flow is not yet available .
when comparing it to the non - photonic electron @xmath1 , our calculations fail to predict the data @xcite .
these two observables have been predicted to be similiar @xcite , since the non - photonic electrons are mainly from , @xmath37-meson decays , but with a small contribution of @xmath38-meson decays .
but the electron elliptic flow is no straightforward probe for the @xmath33 @xmath1 . since the electron is not the only decay product , the decay kinematics might smear out the resulting elliptic flow of the electrons . at low @xmath3 ,
the increase of the @xmath33 flow is similiar to the electron data , but shifted to higher transverse momenta . above @xmath39
the electron @xmath1 starts to decrease which might be due to contributions from the @xmath38-mesons or an early onset of the fragmentation regime .
direct measurements on the elliptic flow of heavy mesons will be available in the near future with the heavy - flavor tracker for star , which will allow a better analysis .
therefore the presented results are based only the @xmath0 elliptic flow data . ) of
@xmath0 s for @xmath40 for different mean transverse expansion velocities ( lines ) compared to preliminary data from phenix collaboration @xcite .
while the @xmath1 of @xmath0 s is smaller than for light hadrons , the mean transverse velocity for the best - fit case ( @xmath41 for charm quarks ) is the same as for light quarks . ] ) for @xmath0 , @xmath33 , @xmath31 and @xmath34 at @xmath40 with @xmath41 to data of non - photonic electrons from phenix collaboration @xcite . ] ) of light , charm and bottom quarks at @xmath40 with @xmath41 . ]
these results provide strong evidence for a substantial collectivity and transverse expansion of the charm quarks in nucleus - nucleus reactions at rhic . due to the large error bars this has to be verified when more precise data is available .
note that our present findings are different from previous approaches that assume incomplete thermalization of the charm @xcite .
we also verified our findings within a boltzmann approach to coalescence @xcite using our parametrizations and received similar results .
one should also note that the observation of negative elliptic flow of heavy particles is well known in the literature ( even if not conclusively observed experimentally up to now ) .
it appears due to an interplay between transverse expansion and particle mass , the more flow and the heavier the particle the more negative values does the elliptic flow reach .
e.g. , negative values of the elliptic flow parameter for heavy hadrons has also been found in previous exploratory studies and seem to be a general feature of the blast - wave like flow profile at high transverse velocities @xcite .
it reflects the depletion of the low @xmath3 particle abundance , when the source elements are highly boosted in the transverse direction .
the difference to the present study is that here , @xmath1 is already negative on the quark level .
negative elliptic flow values will even be encountered for light quarks at asymptotically high bombarding energies as discussed in @xcite .
one might argue that this is an artefact of the blast - wave peak and will not survive in more realistic calculations , however also transport model calculations show slightly negative @xmath1 values for heavy particles at low transverse momenta @xcite . in conclusion , we have shown that the recent preliminary phenix data exhibiting a negative elliptic flow at low @xmath3 can be explained within a parton recombination approach using a blast - wave like parametrization .
we point out that studying @xmath42 from @xmath0 offers the possibility to put a lower limit on the charm quark transverse velocity . from the present quantitative analysis we expect the transverse velocity of charm quarks to be above @xmath43 . within the limits of the present model
the best description of the data is obtain for a charm transverse velocity equal to the light quark velocity of @xmath44 .
so if more precise data will still support the negative @xmath1 , we conclude from this observation that charm quarks reach a substantial amount of local kinetic equilibration . |
the magnetosphere of an accreting x - ray pulsar expands as the mass accretion rate decreases .
as it grows beyond the co - rotation radius , centrifugal force prevents material from entering it .
thus , accretion onto the magnetic poles ceases , and , consequently , x ray pulsations cease .
this phenomenon has recently been observed , for the first time , in gx 1 + 4 and gro j1744 - 28 with rxte@xcite .
here , we present further evidence to show that the phenomenon repeated itself for gro j1744 - 28 during the decaying phase of its latest x - ray outburst .
the asm light curve ( as shown in the top panel of fig .
1 ) reveals that there have been two episodes of x - ray outburst in gro j1744 - 28 , separated by roughly one year .
the source has been extensively monitored by the main instruments aboard rxte since its discovery@xcite . for detailed analyses ,
we have selected a number of pca observations , based on the asm light curve , to cover the decay phase of the outbursts .
1 ( bottom panel ) shows the pulsed fraction ( @xmath0 ) measured with each observation . for comparison ,
the published results@xcite for the first outburst are also presented here .
a striking feature is the precipitous drop of the pulsed fraction as the source became `` quiescent '' both times .
gro j1744 - 28 was generally not so quiet after the first outburst .
in previous work@xcite , we happened to catch a brief period ( as indicated in fig .
1 ) when the pulsed emission became very weak or was not detected at all in some observations . following the latest ourburst , the source has shown little activity . its presence ( at about 20 - 30 mcrab ) has , however , been firmly established by the pca slew data .
this provides a good opportunity to verify our previous interpretation of the phenomenon .
we have searched for the known 2.14 hz pulse frequency , employing various techniques including ffts and epoch - folding , but have failed to detect it since the end of june 1997 ( as marked in fig . 1 ) .
the results therefore argue strongly that the centrifugal barrier is active in this source during such faint period , as we have concluded previously@xcite .
the source also shows interesting spectral evolution during the decay .
the observed x - ray spectrum can be characterized by a simple power law with an exponential high - energy cutoff .
as the quiescent state is approached , the spectrum softens significantly : the power - law becomes steeper , and more prominently , the cutoff energy decreases by roughly a factor of 2 ( see fig . 2 ) .
at the end of the first `` quiescent '' period , the spectrum would recover to the bright - state shape .
we have proposed before that the x - ray emission probably consists of two components : the emission from a large portion of the neutron star surface ( thus unpulsed ) , due to the `` leakage between field lines '' @xcite , and that from `` hot spots '' near the poles ( pulsed plus unpulsed ) . when the source was bright , the latter dominated , so the spectrum was hard ( corresponding to a much higher temperature of the hot spots ) . however , as soon as the centrifugal barrier took effect in the quiescent state , the observed x - rays were all due to the surface emission and their spectrum was therefore softer .
it is interesting to note that the pileup of accreting matter on the neutron star surface might also cause unstable thermonuclear burning and produce type i bursts@xcite , like in x - ray bursters .
the lack of such ( or does it ? ) in gro j1744 - 28 may be due to the suppression of this process by a significantly higher field@xcite .
gro j1744 - 28 does produce x - ray bursts@xcite , unlike any other x - ray pulsars .
the bursts are thought to be the product of accretion instability@xcite .
they occurred at a rate of one to two dozen per hour near the peak of the outbursts@xcite , and the rate decreased as the x - ray flux decayed . at the start of the first quiescent period ,
the bursting activity ceased entirely@xcite for weeks before resuming again near the end@xcite .
3 ( the top panel ) shows an example of such activity ( with 7 major bursts ) on mjd 50260 ( @xmath1 26 june 1996 ) .
we have separated the light curve of 26 june 1996 into burst and non - burst intervals .
the x - ray pulsation is detected during the bursts but is _ not _ detected outside of them ( see fig . 3 ) .
this is again consistent with the presence of the centrifugal barrier in gro j1744 - 28 .
a sudden surge in the mass accretion rate that produces a burst would also momentarily push the magnetosphere inside the co - rotation radius and thus , the accretion to the poles would resume to produce the pulsed emission . as the system relaxes following a burst ,
the magnetosphere expands again ; the inhibition of accretion by the centrifugal barrier again suppresses the pulsation .
we conclude by summarizing the main results as follows : * the results support our previous conclusion that the cessation of pulsed emission when the source becomes faint is a manifestation of the centrifugal barrier . * for gro j1744 - 28 ,
the x - ray emission in the quiescent state ( unpulsed ) likely comes from a large portion of the neutron star surface , due to the penetration of accretion flows through the magnetosphere .
* accretion instability can still occur in the quiescent state ( less frequently ) , and produce type ii bursts .
the pulsed emission was apparent during the bursts , presumably due to the resumption of accretion to the magnetic poles because of the momentary shrinkage of the magnetosphere .
the pulsation stopped as the system recovered to the quiescent state . | we present further observational evidence of the effects of a centrifugal barrier in gro j1744 - 28 , based on continued monitoring of the source with rxte . |
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* d23 * , 1152 ( 1981 ) . | we review the direct cp and t violation in the three - body baryonic @xmath0 decays in the standard model .
in particular , we emphasize that the direct cp violating asymmetry in @xmath1 is around 22@xmath2 and the direct @xmath3 violating asymmetry in @xmath4 can be as large as @xmath5 , which are accessible to the current b factories at kek and slac as well as superb and lhcb . direct cp violation has been measured in both @xmath6 and @xmath7 systems @xcite , but it has not been observed and conclusive in @xmath8 and @xmath9 systems @xcite , respectively . on the other hand , t violation has been only seen in the @xmath6 process @xcite , related to the indirect cp violating parameter @xmath10 , whereas no t violating effect has been found in either @xmath8 or @xmath0 systems yet . in the standard model ( sm ) , it is clear that the unique phase of the cabbibo - kobayashi - maskawa ( ckm ) matrix @xcite is responsible for both observed cp and t violating effects . in this talk
, we would like to explore the possibility to detect the direct cp and t violation in the @xmath0 systems in the current b - factories as well as the future ones such as superb and lhcb .
in particular , we concentrate on the three - body charmless baryonic processes .
our goal of the talk is to test the ckm paradigm of cp violation and unfold new physics . in the framework of local quantum field theories ,
t - violation implies cp - violation ( and vice versa ) , because of the cpt invariance of such theories .
moreover , no violation of cpt symmetry has been found @xcite .
still , it will be worthwhile to remember that outside this framework of local quantum field theories , there is no reason for the two symmetries to be linked @xcite .
therefore , it would be interesting to directly investigate t violation in b decays , rather than inferring it as a consequence of cp - violation .
the characteristic observables of the direct cp and t violation are rate asymmetries and momentum correlations , respectively .
for example , in ( conjugate ) processes such as @xmath11 ( @xmath12 ) , the direct cp asymmetry arises if both the weak ( @xmath13 ) and strong ( @xmath14 ) phases are non - vanishing , given by a_cp&=&(b|*b*m)-(|b|m ) ( b|*b*m)+(|b|m ) , [ cpa ] whereas the direct t violation is related to the correlations known as triple product correlations ( tpc s ) , such as @xmath15 , given by _
t & = & 1 2(a_t-|a_t ) . where @xcite a_t = ( _ * b*(_*b*_m ) > 0 ) - ( _ * b*(_*b*_m ) < 0 ) ( _ * b*(_*b*_m ) > 0 ) + ( _ * b*(_*b*_m ) < 0 ) , [ atp ] and @xmath16 is the corresponding asymmetry of the conjugate process . it is interesting to note that to have a non - zero value of @xmath17 , both weak and strong phases are needed , whereas in the vanishing limit of the strong phase , @xmath18 is maximal . furthermore , there is no contribution @xcite to @xmath18 from final state interaction due to electromagnetic interaction
. from the effective hamiltonian at the quark level for @xmath0 decays @xcite , the amplitudes of @xmath19 and @xmath20 are approximately given by @xcite @xmath21\ , , \nonumber\\ { \cal a}_{k^*}&\simeq&\frac{g_f}{\sqrt 2}m_{k^*}f_{k^*}\varepsilon^{\mu}\alpha_{k^*}\langle p\bar p|\bar u\gamma_\mu(1-\gamma_5 ) b|b^-\rangle\;,\end{aligned}\ ] ] respectively , where @xmath22 is the fermi constant , @xmath23 is the meson decay constant , given by @xmath24 ( @xmath25 ) with @xmath26 ( @xmath27 ) being the four momentum ( polarization ) of @xmath28 ( @xmath29 ) , and @xmath30 and @xmath31 are defined by @xmath32\ ; , \nonumber\\ % \beta_k&\equiv & v_{ub}v_{us}^*a_1-v_{tb}v_{ts}^*\bigg[a_4- a_6\frac{2 m_k^2}{m_b m_s}\bigg]\;,\nonumber\\ \alpha_{k^*}&\equiv & v_{ub}v_{us}^*a_1-v_{tb}v_{ts}^*a_4\;,\end{aligned}\ ] ] where @xmath33 are the ckm matrix elements and @xmath34 ( @xmath35 ) are given by @xmath36 with @xmath37 being effective wilson coefficients ( wc s ) shown in ref .
@xcite and @xmath38 the color number for the color - octet terms .
we note that for the decay amplitudes in eq .
( [ eq1 ] ) we have neglected the small contributions @xcite from @xmath39 involving the @xmath40 time - like baryonic form factors @xcite , where @xmath41 can be ( axial-)vector or ( pseudo)scalar currents . however , in our numerical analysis we will keep all amplitudes including the ones neglected in eq .
( [ eq1 ] ) .
numerically , the ckm parameters are taken to be @xcite @xmath42 and @xmath43 with @xmath44 , @xmath45 , the values of @xmath46 are @xmath47 @xcite .
we remark that @xmath34 contain both weak and strong phases , induced by @xmath48 and quark - loop rescatterings .
explicitly , at the scale @xmath49 and @xmath38=3 , we obtain a set of @xmath50 , @xmath51 , and @xmath52 as follows : @xmath53\times 10^{-4 } \;,\nonumber\\ a_6&=&\big[(-595.5\mp 9.1\eta-3.9\rho)+i(-83.2\pm 3.9\eta-9.1\rho)\big]\times 10^{-4}\;,\end{aligned}\ ] ] for the @xmath54 ( @xmath55 ) transition . from eq .
( [ eq1 ] ) , we derive the simple results for the direct cp asymmetries of the @xmath56 modes as follows : @xmath57 where @xmath58 denote the values of the corresponding antiparticles .
it is easy to see that @xmath59 are independent of the phase spaces as well as the hadronic matrix elements . as a result ,
the hadron parts along with their uncertainties in @xmath59 are divided out in eq .
( [ acp2 ] ) .
we note that the cp asymmetries in eq .
( [ acp2 ] ) are related to the weak phase of @xmath60 @xcite .
our results on the direct cp violation are summarized in table [ pre ] . in the table
, we have included the current experimental data as well as the decay modes of @xmath61 .
we note that the possible fluctuations induced from non - factorizable effects , time - like baryonic form factors and ckm matrix elements for @xmath59 are about @xmath62 ( 0.04 ) , 0.003 ( 0.01 ) and 0.01 ( 0.01 ) , respectively .
the uncertainties from time - like baryonic form factors are constrained by the data of @xmath63 and @xmath64 @xcite and the errors on the ckm elements are from @xmath65 and @xmath48 given in ref .
@xcite .
it is interesting to point out that the large value of @xmath66=22% is in agreement with the babar data of @xmath67 .
however , taken at face value ; the sign of our prediction @xmath68 is different from those by babar @xcite and belle @xcite collaborations .
since the uncertainties of both experiments are still large it is too early to make a firm conclusion . for the direct t violation in the three - body charmless baryonic
b decays @xcite .
we concentrate on @xmath4 by looking for the tpc of the type @xmath69 .
it is interesting to note that @xcite : [ exbr ] br ( b^0 | p^- ) = ( 3.290.47 ) 10 ^ -6 br(b^- |p ) & < & 4.6 10 ^ -7 .
the enhancement of three - body decay over the two - body one is due to the reduced energy release in @xmath0 to @xmath70 transition by the fastly recoiling @xmath70 meson that favors the dibaryon production @xcite .
theoretical estimations baryonic b decays are made @xcite , in consistent with the experimental observations . in the factorization method ,
the decay amplitude of @xmath71 contains the @xmath72 transition and @xmath73 baryon - pair inducing from the vacuum .
the contributions to the decay at the quark level are mainly from @xmath74 , @xmath75 and @xmath76 operators . from these operators and the factorization approximation , the decay amplitude is given by @xcite @xmath77 where @xmath78 , @xmath79 and @xmath34 are defined in eq .
( [ a146 ] ) . from eq .
( [ m6 ] ) , the t - odd transverse polarization asymmetry @xmath80 is found to be @xmath81 where @xmath82 and @xmath83 are combinations of form factors , given by @xcite @xmath84\;,\ % \nonumber\\ a\;=\;f^{b \to \pi}_1(t)g_a(t)\;,\nonumber\\ s&=&\frac{m_b^2-m_\pi^2}{m_b - m_u}f^{b \to \pi}_0(t)f_s(t)\;,\ % \nonumber\\ p\;=\;\frac{m_b^2-m_\pi^2}{m_b - m_u}f^{b \to \pi}_0(t)g_p(t)\;.\end{aligned}\ ] ] it is noted that the @xmath85 ( @xmath86 ) term is from vector - scalar ( axialvector - pseudoscalar ) interference and there is no t - odd term from @xmath87 due to the same current structures . in eq .
( [ abfg ] ) , @xmath88 are the well known mesonic @xmath89 transition form factors @xcite , while @xmath90 , @xmath91 , @xmath92 , @xmath93 and @xmath94 are the @xmath95 time - like baryonic form factors , defined in ref .
@xcite . based on the qcd counting rules @xcite and
@xmath96 flavor symmetry , at @xmath97 one has that f_1(t)+ f_2(t)~g_a(t)~h_a(t)~f_s(t)~g_p(t)~ct^2 . in this limit @xmath98 and thus no t violation
is expected . however , at the finite @xmath99 there are some high power terms of the @xmath99 expansion .
a simple scenario of the power expansions for the baryonic form factors is as follows:@xcite [ ss ] f_1(t)+ f_2(t)=(ct^2+dt^3)^- , & & g_a(t)=(ct^2)^- , + f_s(t)=n_q(ct^2+dt^3)^- , & & g_p(t)=n_q(ct^2)^- , where @xmath100 , @xmath101 and @xmath102 and @xmath103 and @xmath104 are two new form factors .
we now evaluate the numerical values for the tpcs in this simple power expansion scenario in eq .
( [ ss ] ) .
our results of @xmath105 ( @xmath106 ) and @xmath107 are shown in table [ attable1 ] .
[ attable1 ] as an illustration , in the table we have also turned off the strong phase ( @xmath108 ) by taking the imaginary parts of the quark - loop rescattering effects to be zero . from the table , we see explicitly that @xmath18 is indeed nonzero and maximal in the absence of the strong phase .
we note that in our calculations we have neglected the final state interactions due to electromagnetic and strong interactions , which are believed to be small in three - body charmless baryonic decays @xcite .
we also note that @xmath109 in @xmath110 can be induced but it is too small to be measured .
it is interesting to point out that in order to observe @xmath105 ( @xmath16 ) in @xmath111 ( @xmath112 ) being at @xmath113% , we need to have about @xmath114 @xmath115 pairs at @xmath116 level .
this is within the reach of the present day @xmath0 factories at kek and slac and others that would come up .
it is clear that an experimental measurement of @xmath18 is a reliable test of the ckm mechanism of cp violation and , moreover , it could be the first evidence of the direct t violation in b decays .
finally , we remark that we have also explored the direct cp and t violation in @xmath117 @xcite and we have found that the direct cp violating effect is small but the t violating one is as large as that in @xmath118 . in summary , we have shown that the direct cp violating asymmetry in @xmath1 is around 22@xmath2 and the direct @xmath3 violating asymmetry in @xmath4 can be as large as @xmath5 , which are accessible to the current b factories at kek and slac as well as the future ones such as superb and lhcb . |
connecting the puzzling disturbances in both the gas and stellar disk of the milky way ( mw ) with the dark matter distribution of our galaxy and its dwarf companions may become possible in the gaia era ( perryman et al .
gaia will provide parallaxes and proper motions for a billion stars down to @xmath0 ( de bruijne et al .
2014 ) and radial velocities for stars with @xmath1 . by now
, a plethora of stellar tidal streams have been discovered , including the sagittarius ( sgr ) tidal stream ( ibata et al .
1997 ) , the monoceros stream ( newberg et al .
2002 ) , and many others ( belokurov et al .
a number of authors have attempted to infer the galactic potential by modeling stellar tidal streams ( e.g. johnston et al .
1999 ) , but the limitations of determining accurate phase space information for the stream and simplistic modeling ( for example static halos ) have led to large uncertainties in the reconstruction of the galactic potential .
more recently , observations of an asymmetry in the number density and bulk velocity of solar neighborhood stars have been interpreted as arising from a dark sub - halo or dwarf galaxy passing through the galactic disk , exciting vertical waves ( widrow et al . 2012 ; carlin et al . 2013 ; xu et al . 2015 ) .
this corroborates a similar previous suggestion that the disturbances in the outer hi disk of our galaxy may be due to a massive , perturbing satellite ( chakrabarti & blitz 2009 ; henceforth cb09 ) .
there is some evidence now for this predicted satellite , which may mark the first success of galactoseismology ( chakrabarti et al . 2016 ) .
galaxy outskirts hold particularly important clues to the past galactic accretion history and dynamical impacts .
extended hi disks reach to several times the optical radius ( walter et al . 2008 ) , presenting the largest possible cross - section for interaction with sub - halos at large distances ( where theoretical models _
expect _ them to be , e.g. springel et al .
the gas disk of our galaxy manifests large planar disturbances and is warped ( levine , blitz & heiles 2006 ) .
chakrabarti & blitz ( 2009 ; 2011 ) found that these puzzling planar disturbances in the gas disk of our galaxy could be reproduced by an interaction with a sub - halo with a mass one - hundredth that of the milky way , with a pericenter distance of @xmath2 7 kpc , which is currently at @xmath2 90 kpc .
this interaction also produces structures in the stellar disk that are similar to the monoceros stream at present day .
chakrabarti et al .
( 2015 ) found an excess of faint variables at @xmath3 , and chakrabarti et al .
( 2016 ) obtained spectroscopic observations of three cepheid candidates that are part of this excess .
the average radial velocities of these stars is @xmath2 163 km / s , which is large and distinct from the stellar disk of the galaxy ( which in the fourth quadrant is negative ) . using the period - luminosity relations for type
i cepheids , we obtained an average distance of 73 kpc for these stars ( chakrabarti et al .
2016 ) .
tidal interactions remain manifest in the stellar disk for many crossing times , but the gas is collisional and disturbances in the gas disk dissipate on the order of a dynamical time .
therefore , an analysis of disturbances in the gas disk can provide a constraint on the time of encounter ( chakrabarti et al . 2011 ) . ultimately , a joint analysis of the gas ( a cold , responsive , dissipative component that is extended such as the hi disk ) _ and _ the stars ( that retain memory of the encounter for many crossing times ) holds the most promise for unearthing clues about recent _ and _ past encounters .
1:100 mass ratio perturber , ( right ) an image of the stellar density distribution . from chakrabarti & blitz ( 2009 ) . ]
extended hi disks of local spirals have low sound speeds compared to their rotation velocity , and so are extremely sensitive to gravitational disturbances .
furthermore , in the outskirts , atomic hydrogen traces the bulk of the ism ( bigiel et al .
therefore , the outskirts of galaxies are less subject to the effects of feedback from supernovae and star formation that complicate the ism structure ( and the modeling thereof ) in the inner regions of galaxies ( christensen et al . 2013 ) . using the sensitivity of gaseous disks to disturbances , we constrained the mass and current radial distance of galactic satellites ( chakrabarti et al .
2011 ; cb11 ; cb09 ) and its azimuth to zeroth order by finding the best - fit to the low - order fourier modes ( i.e. , low m modes that trace large - scale structures , @xmath4 kpc- scale , in the disk ) of the projected gas surface density of an observed galaxy .
we tested our ability to characterize the galactic satellites of spirals with optically visible companions , namely , m51 and ngc 1512 , which span the range from having a very low mass companion ( @xmath2 1:100 mass ratio ) to a fairly massive companion ( @xmath2 1:3 mass ratio ) .
we accurately recover the masses and relative positions of the satellites in both these systems ( chakrabarti et al .
2011 ) . to facilitate a statistical study
, we developed a simplified numerical approach along with a semi - analytic method to study the excitation of disturbances in galactic disks by passing satellites , and derived a simple scaling relation between the mass of the satellite and the sum of the fourier modes ( chang & chakrabarti 2011 ) .
we later extended this method to also constrain the dark matter density profile of spiral galaxies ( chakrabarti 2013 ) .
of particular interest now with the advent of gaia , is if we can detect the kinematical signature of this interaction in the stars that it perturbed at pericenter . if the stars for which radial velocities were obtained by chakrabarti et al .
( 2016 ) are indeed part of the dwarf galaxy predicted by cb09 , then such a detection would enable a constraint on the orbit and angular momentum of this dwarf galaxy .
price - whelan et al . ( 2013 ) have noted that the gaia data can be complemented by measuring rr lyrae stars in the mid - infrared , which would allow for distances accurate to 2 % out to @xmath2 30 kpc , i.e. , this would give accurate distances for the outer hi disk .
the puzzles of the milky way disk
the large ripples in the gas disk , the many stellar streams , and the vertical waves in the galactic disk , need to be studied comprehensively . only for our galaxy
, can we connect the dots between the orbits , the dynamical evolution of the satellites , the disk structure , and its place in the broader context of galaxy formation . a joint analysis of the data from gaia and hi surveys of the milky way should enable this effort . | the gaia satellite will provide unprecedented phase - space information for our galaxy and enable a new era of galactic dynamics .
we may soon see successful realizations of galactoseismology , i.e. , inferring the characteristics of the galactic potential and sub - structure from a dynamical analysis of observed perturbations in the gas or stellar disk of the milky way . here , we argue that to maximally take advantage of the gaia data and other complementary surveys , it is necessary to build comprehensive models for both the stars and the gas .
we outline several key morphological puzzles of the galactic disk and proposed solutions that may soon be tested . |
in the standard model ( sm ) , the electroweak symmetry breaking results in a physical neutral cp - even higgs boson . there also exist various models extended by increasing higgs fields , such as the multi - higgs doublet model where there are extra two neutral and two charged physical higgs bosons for each additional doublet .
if cp is a good symmetry in the higgs sector , one of the extra neutral bosons is cp - even and the other is cp - odd .
if cp is not invariant , all of the higgs states which have same quantum numbers except for the cp property can be mixed in their mass eigenstates .
then , physical higgs bosons do not have definite cp parity .
one of the notable advantages of a photon linear collider ( plc ) is to provide information about the cp property of the higgs boson by use of linear polarizations of colliding photons . defining @xmath1 two - photon states as @xmath2 and @xmath3 where @xmath4 indicate their helicities with @xmath5 units
, the cp transformation leads to the other states : @xmath6 , @xmath7 .
then , the cp eigenstates are @xmath8 and @xmath9 ; the former is a @xmath1 component of parallel polarized photons and couples to a cp - even higgs boson ( @xmath10 ) , and the latter is of perpendicularly polarized photons and couples to a cp - odd one ( @xmath11 ) .
however , because colliding beams at plc are generated by the compton back - scattering between high energy electrons and laser photons , the energy spectrum of @xmath12 distributes broadly and the degrees of polarizations depend strongly on @xmath13 , where @xmath12 and @xmath14 are the center - of - mass energy of @xmath15 collisions and @xmath16 collisions at parent lc . in the case of the @xmath17 gev lc
, linear polarizations can be used effectively for relatively light higgs bosons whose masses are less than about a few hundred gev . for heavier higgs bosons ,
it is necessary that the electron energy is raised or we use other methods , conventionally .
we propose one method where we take advantage of interference between higgs - production and background amplitudes with circular polarized beams .
a broad peak of the @xmath12 spectrum in the range where the degrees of circular polarizations become large is helpful to the method , because we have an interest in the energy dependence of the interference effects .
as an example , we consider the process @xmath18 which receives contribution from the higgs - exchanged @xmath19-channel diagram and the top - quark - exchanged @xmath20-channel ones .
the helicity - dependent cross sections are expressed as @xmath21,\end{aligned}\ ] ] where @xmath22 and @xmath23 are the helicity amplitudes of higgs resonance ( @xmath24 = @xmath10 or @xmath11 ) and top continuum processes , @xmath25 denote the helicities of colliding photons in @xmath5 units , @xmath26 and @xmath27 the final @xmath28 and @xmath29 helicities in the center - of - mass frame in @xmath30 ( we also write @xmath31 ( @xmath32 ) as @xmath33 ( @xmath34 ) . ) .
there is another observable sensitive to cp parity .
when the decay of a top quark is taken into account , the cross sections for the processes @xmath38 can be written by @xmath39~ re \left [ { \cal d}_{l}^{\lambda } \overline{\cal d}_{l}^{\overline{\lambda } } { \cal d}_{r}^{\lambda * } \overline{\cal d}_{r}^{\overline{\lambda } * } \right ] \nonumber \\ & - & 2~im \left [ { \cal m}^{\lambda_1 \lambda_2 ll } { \cal m}^{\lambda_1 \lambda_2 rr * } \right]~ i m \left [ { \cal d}_{l}^{\lambda } \overline{\cal d}_{l}^{\overline{\lambda } } { \cal d}_{r}^{\lambda * } \overline{\cal d}_{r}^{\overline{\lambda } * } \right ] \biggr\}. \label{sigma - bw}\end{aligned}\ ] ] here , the decay amplitudes for the processes @xmath40 and @xmath41 are defined as @xmath42 and @xmath43 , the explicit forms of which are in the appendix of ref .
we notice the azimuthal angles of @xmath44 and @xmath45 in the @xmath28 and @xmath29 rest frame . describing them as @xmath24 and @xmath46 , they appear in the third and fourth terms in eq .
[ sigma - bw ] : @xmath47 \propto \cos(\phi- \overline{\phi } ) , \nonumber \\ i m \left [ { \cal d}_{l}^{\lambda } \overline{\cal d}_{l}^{\overline{\lambda } } { \cal d}_{r}^{\lambda * } \overline{\cal d}_{r}^{\overline{\lambda } * } \right ]
\propto \sin(\phi- \overline{\phi}).\end{aligned}\ ] ] therefore , we obtain @xmath48.\end{aligned}\ ] ] when colliding photons are polarized to be @xmath32 , @xmath49
\simeq i m \left [ { \cal m}^{++ ll}_{\phi } { \cal m}^{++ rr*}_{cont } \right]$ ] is satisfied considering @xmath50 .
since the higgs - production amplitudes @xmath51 and @xmath52 have opposite signs in the mssm - type models , @xmath53 tells us the cp parity of the higgs boson . a numerical calculation is shown in fig .
[ fig1](c ) .
though the quantity turns out to be rather small because of cancellation between the contributions from longitudinally and transversely polarized @xmath54 s , we can recover the sensitivity to the cp parity by taking account of @xmath54-decay distributions .
when the cp symmetry is not conserved in the higgs potential , the helicity amplitudes for the higgs - production are denoted by @xmath55 \left[\,\sigma\beta_t a_t -i b_t\right ] \delta_{\lambda_1 \lambda_2}\delta_{\sigma \overline\sigma}\ , .
\label{mephi}\end{aligned}\ ] ] where @xmath56 and @xmath57 are proportional to the cp - even components of vertices , @xmath58 and @xmath59 , @xmath60 and @xmath61 to the cp - odd components .
since \{@xmath62 } or / and \{@xmath63 } have non - zero values simultaneously , they induce complicated interference .
moreover , the amplitudes include six parameters for vertices ; @xmath62 are complex , whereas @xmath63 are real .
therefore , we need at least six observables to determine the cp property completely and are urged to use linear polarizations as well .
all observables obtained from various polarizations ( including the mixture of linear and circular ones ) are exhibited in ref .
we have discussed measurement of the cp property of the higgs boson at plc . it has been found that we can extract information about the cp property of the higgs boson from the observation of interference effects between higgs - production and background amplitudes .
if the higgs boson have definite cp parity , this method can be powerful in high @xmath64 region where linear polarizations of colliding photons become useless conventionally .
e. asakawa , j. kamoshita , a. sugamoto , and i. watanabe , _ eur .
j. _ * c14 * , 335 ( 2000 ) .
e. asakawa , phd thesis ( in preparation ) e. asakawa , s.y .
choi , k. hagiwara , and j.s .
lee , _ phys .
rev . _ * d62 * , 115005 ( 2000 ) . | we study measurement of the cp property of the higgs boson at a photon linear collider .
one method where we take advantage of interference between higgs - production and background amplitudes is proposed .
a broad peak of the photon energy spectrum is helpful in observing the energy dependence of the interference effects .
numerical results for the process @xmath0 are shown as an example . |
describing the laws of physics in terms of underlying symmetries has always been a powerful tool .
lie algebras and lie superalgebras are central in particle physics , and the space - time symmetries can be obtained by an inn - wigner contraction of certain lie ( super)algebras .
@xmath0lie algebras @xcite , a possible extension of lie ( super)algebras , have been considered some times ago as the natural structure underlying fractional supersymmetry ( fsusy ) @xcite ( one possible extension of supersymmetry ) . in this contribution
we show how one can construct many examples of finite dimensional @xmath0lie algebras from lie ( super)algebras and finite - dimensional fsusy extensions of the poincar algebra are obtained by inn - wigner contraction of certain @xmath0lie algebras .
the natural mathematical structure , generalizing the concept of lie superalgebras and relevant for the algebraic description of fractional supersymmetry was introduced in @xcite and called an @xmath0lie algebra .
we do not want to go into the detailed definition of this structure here and will only recall the basic points , useful for our purpose .
more details can be found in @xcite .
let @xmath5 be a positive integer and @xmath6 .
we consider now a complex vector space @xmath7 which has an automorphism @xmath8 satisfying @xmath9 .
we set @xmath10 , @xmath11 and @xmath12 ( @xmath13 is the eigenspace corresponding to the eigenvalue @xmath14 of @xmath8 ) .
hence , @xmath15 we say that @xmath7 is an @xmath0lie algebra if : 1 .
@xmath16 , the zero graded part of @xmath7 , is a lie algebra .
@xmath17 @xmath18 , the @xmath19 graded part of @xmath7 , is a representation of @xmath16 .
3 . there are symmetric multilinear @xmath20equivariant maps @xmath21 where @xmath22 denotes the @xmath0fold symmetric product of @xmath23 . in other words , we assume that some of the elements of the lie algebra @xmath16 can be expressed as @xmath0th order symmetric products of `` more fundamental generators '' .
4 . the generators of @xmath7 are assumed to satisfy jacobi identities ( @xmath24 , @xmath25 , @xmath11 ) : @xmath26,b_3\right ] + \left[\left[b_2,b_3\right],b_1\right ] + \left[\left[b_3,b_1\right],b_2\right ] = 0 , \nonumber \\
\left[\left[b_1,b_2\right],a_3\right ] + \left[\left[b_2,a_3\right],b_1\right ] + \left[\left[a_3,b_1\right],b_2\right ] = 0,\nonumber \\ \left[b,\left\{a_1,\dots , a_f\right\}\right ] = \left\{\left[b , a_1 \right],\dots , a_f\right\ } + \cdots + \left\{a_1,\dots,\left[b , a_f\right ] \right\ } , \nonumber \\
\sum\limits_{i=1}^{f+1 } \left [ a_i,\left\{a_1,\dots , a_{i-1 } , a_{i+1},\dots , a_{f+1}\right\ } \right ] = 0 .
\label{rausch : eq : jac}\end{aligned}\ ] ] the first three identities are consequences of the previously defined properties but the fourth is an extra constraint .
more details ( unitarity , representations , _ etc .
_ ) can be found in @xcite .
let us first note that no relation between different graded sectors is postulated .
secondly , the sub - space @xmath27 @xmath28 is itself an @xmath0lie algebra . from now on ,
@xmath0lie algebras of the types @xmath29 will be considered .
most of the examples of @xmath0lie algebras are infinite dimensional ( see _ e.g. _ @xcite ) .
however in @xcite an inductive theorem to construct finite - dimensional @xmath0lie algebras was proven : + * theorem 1 * _ let @xmath30 be a lie algebra and @xmath31 a representation of @xmath30 such that _
\(i ) @xmath32 is an @xmath0lie algebra of order @xmath33;. in this case the notion of graded @xmath34lie algebra has to be introduced @xcite .
@xmath35 , is a graded @xmath34lie algebra if ( i ) @xmath36 a lie algebra and @xmath31 is a representation of @xmath36 isomorphic to the adjoint representation , ( ii ) there is a @xmath37 equivariant map @xmath38 such that @xmath39 + \left[f_2 , \mu(f_1 ) \right ] = 0 , f_1,f_2 \in \ { g}_1 $ ] . ]
\(ii ) @xmath40 admits a @xmath41equivariant symmetric form @xmath42 of order @xmath43 .
then @xmath44 admits an @xmath0lie algebra structure of order @xmath45 , which we call the @xmath0lie algebra induced from @xmath46 and @xmath42 .
+ by hypothesis , there exist @xmath47equivariant maps @xmath48 and @xmath49 .
now , consider @xmath50 defined by @xmath51 where @xmath52 and @xmath53 is the group of permutations on @xmath54 elements . by construction , this is a @xmath47equivariant map from @xmath55 , thus the three first jacobi identities are satisfied .
the last jacobi identity , is more difficult to check and is a consequence of the corresponding identity for the @xmath0lie algebra @xmath46 and a factorisation property ( see @xcite for more details ) .
an interesting consequence of the theorem of the previous section is that it enables us to construct an @xmath0lie algebras associated to _
any _ lie ( super)algebras .
consider the graded @xmath34lie algebra @xmath56 where @xmath57 is a lie algebra , @xmath58 is the adjoint representation of @xmath57 and @xmath59 is the identity .
let @xmath60 be a basis of @xmath57 , and @xmath61 the corresponding basis of @xmath58 .
the graded @xmath34lie algebra structure on @xmath7 is then : @xmath62 = f_{ab}^{\ \ \ c } j_c , \qquad \left[j_a , a_b \right ] = f_{ab}^{\ \ \ c } a_c , \qquad \mu(a_a)= j_a,\end{aligned}\ ] ] where @xmath63 are the structure constants of @xmath57 , the second ingredient to construct an @xmath0lie algebra is to define a symmetric invariant form on @xmath64 .
but on @xmath64 , the adjoint representation of @xmath65 , the invariant symmetric forms are well known and correspond to the casimir operators @xcite .
then , considering a casimir operator of order @xmath66 of @xmath67 , we can induce the structure of an @xmath0lie algebra of order @xmath68 on @xmath69 .
one can give explicit formulae for the bracket of these @xmath0lie algebras as follows .
let @xmath70 be a casimir operator of order @xmath66 ( for @xmath71 , the killing form @xmath72 is a primitive casimir of order two ) .
then , the @xmath0bracket of the @xmath0lie algebra is @xmath73 for the killing form this gives @xmath74 if @xmath75 , the @xmath0lie algebra of order three induced from the killing form is the @xmath0lie algebra of @xcite .
the construction of @xmath0lie algebras associated to lie superalgebras is more involved .
we just give here a simple example ( for more details see @xcite ) : the @xmath0lie algebra of order @xmath76 @xmath77 induced from the ( i ) lie superalgebra @xmath78 and ( ii ) the quadratic form @xmath79 , where @xmath8 is the invariant symplectic form on @xmath80 and @xmath81 the invariant symplectic form on @xmath82 .
let @xmath83 be a basis of @xmath84 and @xmath85 be a basis of @xmath86 .
let @xmath87 be a basis of @xmath88 .
then the four brackets of @xmath7 take the following form @xmath89 it is interesting to notice that this @xmath0lie algebra admits a simple matrix representation @xcite : @xmath90 and @xmath91 .
it is well known that supersymmetric extensions of the poincar algebra can be obtained by inn - wigner contraction of certain lie superalgebras . in fact
, one can also obtain some fsusy extensions of the poincar algebra by inn - wigner contraction of certain @xmath0lie algebras as we now show with one example @xcite .
let @xmath92 be the real @xmath0lie algebra of order three induced from the real graded @xmath34lie algebra @xmath93 and the killing form on @xmath94 ( see eq .
[ eq:3-lie ] ) . using vector indices of @xmath95 coming from the inclusion @xmath96 ,
the bosonic part of @xmath97 is generated by @xmath98 , with @xmath99 and the graded part by @xmath100 .
letting @xmath101 after the inn - wigner contraction , @xmath102{\lambda } } q_{\mu \nu } , & j_{4 \mu } \to \frac{1}{\sqrt[3]{\lambda } } q_{\mu } , \end{array}\end{aligned}\ ] ] one sees that @xmath103 and @xmath104 generate the @xmath105 poincar algebra and that @xmath106 are the fractional supercharges in respectively the adjoint and vector representations of @xmath107 .
this @xmath0lie algebra of order three is therefore a non - trivial extension of the poincar algebra where translations are cubes of more fundamental generators .
the subspace generated by @xmath108 is also an @xmath0lie algebra of order three extending the poincar algebra in which the trilinear symmetric brackets have the simple form : @xmath109 where @xmath110 is the minkowski metric .
in this paper a sketch of the construction of @xmath0lie algebras associated to lie ( super)algebras were given .
more complete results , such as a criteria for simplicity , representation theory , matrix realizations _ etc .
_ , was given in @xcite .
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a 34 6413 - 6424 [ math.rt/0012058 ] . | @xmath0lie algebras are natural generalisations of lie algebras ( @xmath1 ) and lie superalgebras ( @xmath2 ) .
we give finite dimensional examples of @xmath0lie algebras obtained by an inductive process from lie algebras and lie superalgebras .
matrix realizations of the @xmath0lie algebras constructed in this way from @xmath3 are given .
we obtain a non - trivial extension of the poincar algebra by an inn - wigner contraction of a certain @xmath0lie algebras with @xmath4 . |
37 com is the primary star of a wide triple system ( tokovinin 2008 ) , but the synchronisation effect plays no role for its fast rotation and activity .
its significant photometric and caii h&k emission variabilities were presented by strassmeier et al .
( 1997 ; 1999 ) and de medeiros et al .
( 1999 ) and interpreted as signatures of magnetic activity .
observational data for 37 com were obtained with two twin fiber - fed echelle spectropolarimeters narval ( 2 m tbl at pic du midi observatory , france ) and espadons ( 3.6 m cfht ) .
we have collected 11 stokes v spectra for 37 com in the period january 2010 july 2010 .
the least squares deconvolution ( lsd ) multi - line technique was applied and the surface - averaged longitudinal magnetic field b@xmath1 was computed using the first - order moment method ( donati el al .
1997 ; wade et al .
the zeeman doppler imaging ( zdi ) tomographic technique was employed for mapping the large - scale magnetic field of the star ( donati et al .
with radial velocity ( rv ) , s - index , h@xmath0 and caii irt ( 854.2 nm ) .
* center : * normalized stokes v profiles observed profiles ( black ) ; synthetic fit ( red ) ; zero level ( dashes lines ) .
the error bars are on the left of each profile . *
right : * the magnetic map of 37 com .
the magnetic field strength is in gauss .
the vertical ticks on top of the radial map show the phases when there are observations.,title="fig:",width=151,height=226 ] with radial velocity ( rv ) , s - index , h@xmath0 and caii irt ( 854.2 nm ) .
* center : * normalized stokes v profiles observed profiles ( black ) ; synthetic fit ( red ) ; zero level ( dashes lines ) .
the error bars are on the left of each profile . *
right : * the magnetic map of 37 com .
the magnetic field strength is in gauss .
the vertical ticks on top of the radial map show the phases when there are observations.,title="fig:",width=113,height=226 ] with radial velocity ( rv ) , s - index , h@xmath0 and caii irt ( 854.2 nm ) .
* center : * normalized stokes v profiles observed profiles ( black ) ; synthetic fit ( red ) ; zero level ( dashes lines ) .
the error bars are on the left of each profile . *
right : * the magnetic map of 37 com .
the magnetic field strength is in gauss .
the vertical ticks on top of the radial map show the phases when there are observations.,title="fig:",width=226,height=226 ] there are significant variations of b@xmath1 in the interval from -2.5 g to 6.5 g with at least one sign reversal during the observational period ( fig .
[ fig : zdi ] left ) . also , radial velocity , s - index and line activity indicators h@xmath0 and caii irt ( 854.2 nm ) show significant variations , and clear correlations with each other as well as the longitudinal field . the zdi mapping ( fig .
[ fig : zdi ] center and right ) reveals that the large - scale magnetic field has a dominant poloidal component , which contains about 88% of the reconstructed magnetic energy .
the star has a differential rotation with the following parameters : @xmath2 rad / d ( the rotation rate at the equator ) and @xmath3 rad / d ( the difference in the rotation rate between the polar region and the equator ) ( petit et al . 2002 ) .
37 com shows simpler surface magnetic structure than the fast rotators v390 aur ( konstantinova - antova et al . 2012 ) and hd 232862 ( aurire et al . in prep . ) and shows more complex structure than the slow rotators ek eri ( aurire et al . 2011 ) and @xmath4 ceti ( tsvetkova et al . 2013 ) , which are suspected of being descendants of ap - stars .
the location of 37 com on the hertzsprung - russell diagram was determined on the basis of state - of - the - art stellar evolution models ( charbonnel & lagarde 2010 ) and the mass is found to be 5.25 @xmath5 , in a good agreement with the literature .
synthetic spectra in the region containing @xmath6cn and @xmath7cn molecular lines were calculated and compared to our spectra in order to infer the @xmath6c/@xmath7c ratio .
the best fit was achieved for @xmath6c/@xmath7c @xmath8 . from these results
, it appears that 37 com is in the core helium - burning phase . | we present the first magnetic map of the late - type giant 37 com .
the least squares deconvolution ( lsd ) method and zeeman doppler imaging ( zdi ) inversion technique were applied .
the chromospheric activity indicators h@xmath0 , s - index , caii irt and the radial velocity were also measured .
the evolutionary status of the star has been studied on the basis of state - of - the - art stellar evolutionary models and chemical abundance analysis .
37 com appears to be in the core helium - burning phase . |
spatial indexes has always been an important issue for multi dimensional data sets in relational databases ( dbs ) , in particular for those dealing with spherical coordinates , e.g. latitude / longitude for earth locations or ra / dec for celestial objects .
some db servers offer built - in capabilities to create indexes on these ( coordinate ) columns which consequently speed up the execution of queries involving them .
however 1 . the use of these facilities could be not easy , 2 .
they typically use a syntax quite different from the astronomical one , 3 .
their performance is inadequate for the astronomical use . within the mcs library project ( calderone & nicastro 2007 ; nicastro & calderone 2006 , 2007 ; ) we have implemented the dif package , a tool which performs and manages in a fully automatic way the sky pixelisation with both the htm ( kunszt et al .
2001 ) and healpix ( grski et al .
2005 ) schema . using a simple tool ,
any db table with sky coordinates columns can be easily indexed .
this is achieved by using the facilities offered by the mysql db server ( which is the only server mcs supports at the moment ) , i.e. triggers , views and plugins . having a table with sky coordinates ,
the user can make it fully indexed in order to perform quick queries on rectangular and circular regions ( cone ) or to create an healpix map file . an sql query to select objects in a cone will look like this : ` select * from mycatalogue where ` ` entriesincone(20 , 30 , 5 ) ` , where ( 20,30 ) are the coordinates of the center in degrees and 5 is the radius in arcmin .
the important thing to note is that the db manager needs to supply only a few parameters in the configuration phase , whereas the generic user does not need to know anything about the sky pixelisation either for ` select ` or ` insert ` or ` update ` queries .
it also demonstrates that there is no need to extend standard sql for astronomical queries ( see adql ) , at least if mysql is used as db server .
in terms of db table indexing , mapping a sphere with a pixel scheme means transforming a 2d into a 1d space , consequently a standard b tree index can be created on the column with the pixel ids . on a large astronomical table , depending on the `` depth '' of the pixelisation , this could lead to a gain of a 45 orders of magnitude in search efficiency .
the htm and healpix schema are widely used in astronomy and are now well mature to be considered as candidates for indexing tables containing astronomical data .
they are both open source and distributed as c++ libraries .
htm uses triangular pixels which can recursively be subdivided into four pixels .
the base pixels are 8 , 4 for each hemisphere .
these `` trixels '' are not equal - area but the indexing algorithm is very efficient for selecting point sources in catalogues .
healpix uses equal - area pseudo - square pixels , particularly suitable for the analysis of large - scale spatial structures .
the base pixels are 12 . using a 64 bit long integer to store the index ids leads to a limit for the pixels size of about 7.7 and 0.44 milli - arcsec on a side for htm and healpix , respectively . being able to quickly retrieve the list of objects in a given sky region is crucial in several projects .
for example hunting for transient sources like grbs requires fast catalogues lookup so to quickly cross match known sources with the detected objects .
the ir / optical robotic telescope rem ( nicastro & calderone 2006 ) uses htm indexed catalogues to get the list of objects in @xmath0 regions . in this case accessing one billion objects catalogues like the gsc2.3 takes some 10 msec . having a fully automatic htm and healpix indexing would be crucial for the management of the dbs of future large missions like gaia .
also the virtual observatory project would greatly benefit from adopting a common indexing scheme for all the various types of archive it can manage .
the relevant parameters for the two pixelisations are : max res .
( @xmath1 ) : = @xmath2 $ ] = = @xmath3 ( where @xmath4 ) * htm * * healpix
* + @xmath5 : @xmath6 @xmath3 ( where @xmath4 ) + i d range : @xmath7 $ ] @xmath8 $ ] + max @xmath9 : @xmath10 @xmath11 + max res .
( @xmath1 ) : @xmath12 @xmath13 ( @xmath14 ) + ' '' '' + @xmath15 ( depth ) : @xmath16 $ ] ; @xmath17 ( order @xmath18 resolution parameter ) : @xmath19 $ ] + as mentioned the maximum resolution is related to the usage of 64 bit integers and it is intrinsic to the htm and healpix c++ libraries .
mcs is a set of c++ high level classes aimed at implementing an application server , that is an application providing a service over the network .
mcs provides classes to interact with , manage and extend a mysql db server .
the included myro package allows a per row management of db grants whereas the dif package allows the automatic management of sky pixelisation with the htm and healpix schema .
see the for more information .
to enable dif , when installing mcs it is enough to give to the configure script the two options ` --enable - dif --with - mysql - source = path ` where ` path ` is the path to the mysql source directory .
the htm and healpix c++ libraries are included in the dif package .
a db named ` dif ` will be created containing an auxiliary table ` tbl ` and a _ virtual _ table ` dif ` which is dynamically managed by the dif db engine .
now let s assume one has a db ` mydb ` with a table ` mycat ` containing the two coordinates column ` racs ` and ` deccs ` representing the centi - arcsec converted j2000 equatorial coordinates ( this requires 4 bytes instead of the 8 necessary for a double value ) . to make the table manageable using both the htm and healpix pixelisation schema it is enough to give the command : where ` dif
` is the name of the script used to perform administrative tasks related to dif - handled tables , 6 is the htm depth and 8 is the healpix order whereas the 0 ( 1 ) selects the ring ( nested ) scheme .
the last two parameters are the sql expressions which convert to degrees the coordinate values contained in the table fields ` racs ` and ` deccs ` .
if the coordinates where already degrees , then it would have been enough to give their names , e.g. ` dif ... ra dec ` .
the mysql root password is needed . in a future release we ll add the possibility to perform simple cross matching between ( dif managed ) catalogues .
having an htm indexed catalogue , the query string to obtain the list of objects in a circular region centred on @xmath20 and @xmath21 with radius @xmath22 will be : + ` select * from mycat_htm where dif_htmcircle(60,30,40 ) ; ` + note the table name ` _ htm ` suffix which is needed to actually access the view handled by dif . for a rectangle with the same centre and sides @xmath23 along the @xmath24 axis and @xmath25 along the @xmath26 axis
: + ` select * from mycat_htm where dif_htmrect(60,30,50,20 ) ; ` + giving only three parameters would imply a square selection . having chosen to use both htm and healpix indexing ,
one could request all the healpix ids of the objects in a @xmath23 square by using an htm function : + ` select healpid from mycat_htm where dif_htmrect(60,30,50 ) ; ` + to simply get the ids of the pixels falling into a circular / rectangular region one can simply ` select i d from dif.dif where ... ` , i.e. no particular dif managed table is required . to obtain the order 10 ids in ring scheme one
can calculate them on the fly : + ` select dif_healplookup(0,10,racs/3.6e5,deccs/3.6e5 ) ` + ` from mycat_htm where dif_htmcircle(60,30,20 ) ; ` + giving 1 instead of 0 would give nested scheme ids . having ` ra ` and ` dec ` in degrees one would simply type ` ( 0,10,ra , dec ) ` . if one has just the healpix ids then entries on a circular region can be selected like in : + ` select * from mycat_healp where dif_healpcircle(60,30,40 ) ; ` + note the table name ` _ healp ` suffix .
rectangular selections for only - healpix indexed tables will be available in the future .
the current list of functions is : + ` dif_htmcircle ` , ` dif_htmrect ` , ` dif_htmrectv ` , ` dif_healpcircle ` , + ` dif_htmlookup ` , ` dif_healplookup ` , ` dif_sphedist ` .
+ ` dif_htmrectv ` accepts the four corners of a rectangle which can then have any orientation in the sky . `
dif_sphedist ` calculates the angular distance of two points on the sphere by using the haversines formula .
a first version of idl user contributed library and demo programs aimed at producing healpix maps from the output of sql queries is available at the .
calderone , g. , & nicastro , l. 2006 , in neutron stars and pulsars , mpe - report no .
291 , astro - ph/0701102 nicastro , l. , & calderone , g. 2006 , in neutron stars and pulsars , mpe - report no .
291 , astro - ph/0701099 nicastro , l. , & calderone , g. 2007 , grski k. m. , et al .
2005 , , 622 , 759 kunszt p. z. , szalay a. s. , & thakar a. r. 2001 , in mining the sky : proc . of the mpa / eso / mpe workshop , ed .
a. j. banday , s. zaroubi , m. bartelmann , 631 | in various astronomical projects it is crucial to have coordinates indexed tables . all sky optical and ir catalogues have up to 1 billion objects that will increase with forthcoming projects .
also partial sky surveys at various wavelengths can collect information ( not just source lists ) which can be saved in coordinate ordered tables .
selecting a sub - set of these entries or cross - matching them could be un - feasible if no indexing is performed .
sky tessellation with various mapping functions have been proposed .
it is a matter of fact that the astronomical community is accepting the htm and healpix schema as the default for object catalogues and for maps visualization and analysis , respectively . within the mcs library project ,
we have now made available as mysql - callable functions various htm and healpix facilities .
this is made possible thanks to the capability offered by mysql 5.1 to add external plug - ins .
the dif ( dynamic indexing facilities ) package distributed within the mcs library , creates and manages a combination of views , triggers , db - engine and plug - ins allowing the user to deal with database tables indexed using one or both these pixelisation schema in a completely transparent way . |
a @xmath0 is a finite set @xmath1 paired with a finite set @xmath2 of unordered pairs @xmath3 with @xmath4 .
a simple graph has no multiple connections and no self - loops : every @xmath5 appears only once and no @xmath6 is in @xmath2 .
elements in @xmath1 are called , elements in @xmath2 are called . given a simple graph @xmath0 , denote by @xmath7 the of a vertex @xmath8 .
it is a subgraph generated by the set of vertices directly connected to @xmath8 .
denote by @xmath9 the set of complete @xmath10 subgraphs of @xmath11 .
elements in @xmath9 are also called .
the set @xmath12 for example is the set of all triangles in @xmath11 .
of course , @xmath13 and @xmath14 .
if the cardinality of @xmath9 is denoted by @xmath15 , the of @xmath11 is defined as @xmath16 , a finite sum .
for example , if no tetrahedral subgraphs @xmath17 exist in @xmath11 , then @xmath18 , where @xmath19 is the , the number of vertices , @xmath20 is the , the number of edges and @xmath21 the number of @xmath22 . is defined inductively as @xmath23 with @xmath24 .
cyclic graphs , trees or the dodecahedron are examples of graphs of dimension @xmath25 , a triangle @xmath22 , an octahedron or icosahedron has dimension @xmath26 .
a tetrahedron has dimension @xmath27 .
a complete graph @xmath10 on @xmath28 vertices has dimension @xmath29 .
dimension is defined for any graph but can become a fraction . for a truncated cube @xmath11 for example ,
each unit sphere @xmath7 is a graph of @xmath27 vertices and one edge , a graph of dimension @xmath30 so that @xmath31 .
the euler characteristic of this graph @xmath11 is @xmath32 .
a is a function on @xmath9 which is antisymmetric in its @xmath33 arguments .
the set @xmath34 of all @xmath29-forms is a vector space of dimension @xmath15 .
the remaining sign ambiguity can be fixed by introducing an orientation on the graph : a @xmath10 subgraph is called a if it is not contained in a larger @xmath35 graph .
an attaches a @xmath29-form @xmath36 to each maximal simplex with value @xmath25 .
it induces forms on smaller dimensional faces .
if @xmath36 cancels on intersections of maximal graphs , it is a `` volume form '' and @xmath11 is called .
an icosahedron for example has triangles as maximal simplices .
it is orientable .
a wheel graph @xmath37 in which two opposite edges are identified models a mbius strip and is not orientable .
a @xmath38-form is a function on @xmath39 and also called a .
call @xmath40 the .
it is defined as a @xmath25-form if @xmath11 has an orientation . without an orientation , we can still look at the @xmath41 if @xmath42 is an edge attached to @xmath43 .
define the @xmath44 and the @xmath45 .
a vertex @xmath8 is a if @xmath46 .
if @xmath47 and @xmath11 is @xmath29-dimensional , a vertex @xmath8 is an if @xmath7 is a @xmath48-dimensional graph for which every point is an interior point within @xmath7 ; for @xmath49 we ask @xmath7 to be connected .
the base induction assumption is that an interior point of a one - dimensional graph has two neighbors .
a vertex @xmath8 of a @xmath29-dimensional graph @xmath11 is a if @xmath7 is a @xmath48-dimensional ( for @xmath49 connected ) graph in which every vertex is either a boundary or interior point and both are not empty .
the seed assumption is that for @xmath50 , the graph @xmath7 has one vertex .
a @xmath29-dimensional graph @xmath51 is a @xmath52 if every @xmath53 is an interior point or a boundary point .
glue two copies of @xmath51 along the boundary gives a graph @xmath11 without boundary .
a wheel graph @xmath54 is an example of a @xmath26-dimensional graph with boundary if @xmath55 .
the boundary is the cyclic one dimensional graph @xmath56 .
cut an octahedron in two gives @xmath57 .
for an oriented graph @xmath11 , the @xmath58 is defined as @xmath59 , where @xmath60 denotes a variable taken away .
for example @xmath61 is a function on triangles called the of a @xmath25-form @xmath62 .
a form is if @xmath63 .
it is if @xmath64 .
the vector space @xmath65 of closed forms modulo exact forms is a of dimension @xmath66 , the .
example : @xmath67 is the number of . the is @xmath68 . for a @xmath29-form define the @xmath69
. let @xmath70 be the number of @xmath10 subgraphs of @xmath71 .
especially , @xmath72 is the @xmath73 of @xmath8 , the order of @xmath7 .
the local quantity @xmath74 is called the of the graph at @xmath8 .
the sum is of course finite . for a @xmath26-dimensional graph without boundary ,
where @xmath7 has the same order and size , it is @xmath75 . for a 1-dimensional graph with or without boundary and trees in particular , @xmath76 .
for an arbitrary finite simple graph we have @xcite for an arbitrary finite simple graph and injective @xmath77 , we have @xcite assume @xmath62 is a @xmath48-form and @xmath11 is an oriented @xmath29-dimensional graph with boundary , then with boundary @xmath52 , the later remains a graph
. in general it is only a , an element in the group of integer valued functions on @xmath78 usually written as @xmath79 . ]
the * transfer equations * are . by definition of curvature ,
we have @xmath80 since the sums are finite , we can change the order of summation . using the transfer equations we get @xmath81 the number of @xmath29 simplices @xmath82 in the exit set @xmath83 and the number of @xmath29 simplices @xmath84 in the entrance set @xmath85 are complemented within @xmath7 by the number @xmath86 of @xmath29 simplices which contain both vertices from @xmath83 and @xmath85 . by definition , @xmath87 .
the index @xmath88 is the same for all injective functions @xmath77 .
the * intermediate equations * are .
let @xmath89 . because replacing @xmath62 and @xmath90 switches @xmath91 with @xmath92 and the sum is the same , we can prove @xmath93 instead . the transfer equations and intermediate equations give @xmath94 = 2v_0 + \sum_{k=0}^{\infty } ( -1)^k 2 v_{k+1 } = 2 \chi(g ) \ ; .\end{aligned}\ ] ] denote a @xmath29-simplex graph @xmath95 by @xmath96 . from @xmath97 and algebraic boundary @xmath98 = \sum_k ( -1)^k ( x_0 , ... ,
,x_n))$ ] , stokes theorem is obvious for a single simplex : @xmath99 gluing @xmath29-dimensional simplices cancels boundary .
a @xmath29-dimensional graph with boundary is a union of @xmath29-dimensional simplices identified along @xmath48- dimensional simplices .
a @xmath29-dimensional oriented graph with boundary can be built by gluing cliques as long as the orientation @xmath29-form can be extended .
we also used that the * boundary as a graph * agrees with the * algebraic boundary * if differently oriented boundary pieces cancel .
here are families of graphs , where the curvature is indicated at every vertex :
for the history of the classical stokes theorem , see @xcite . the history of topology @xcite .
the collection @xcite contains in particular an article on the history of graph theory .
a story about euler characteristic and polyhedra is told in @xcite . for an introduction to gauss - bonnet with historical pointers to early discrete approaches
see @xcite . for poincar - hopf , the first volume of @xcite or @xcite .
for morse theory and reeb s theorem @xcite .
poincar proved the index theorem in chapter viii of @xcite .
hopf extended it to arbitrary dimensions in @xcite .
gauss - bonnet in higher dimensions was proven first independently by allendoerfer @xcite and fenchel @xcite for surfaces in euclidean space and extended jointly by allendoerfer and weil @xcite to closed riemannian manifolds .
chern gave the first intrinsic proof in @xcite .
y. tong m. desbrun , e. kanso .
discrete differential forms for computational modeling . in j.
sullivan g. ziegler a. bobenko , p. schroeder , editor , _ discrete differential geometry _
, oberwohlfach seminars , 2008 . | by proving graph theoretical versions of green - stokes , gauss - bonnet and poincar - hopf , core ideas of undergraduate mathematics can be illustrated in a simple graph theoretical setting . in this pedagogical exposition
we present the main proofs on a single page and add illustrations . while discrete stokes is at least 100 years old , the other two results for graphs were found only recently . |
the dimensionality of the 115 materials , cerhin@xmath1 , ceirin@xmath1 , and cecoin@xmath1 , appears to be related to their superconducting transition temperature .
the material with the highest t@xmath2 , cecoin@xmath0 , has the most 2d - like fermi surface ( fs ) of the three .
@xcite cerhin@xmath0 has a high t@xmath2 ( @xmath32.1 k ) , but only under a pressure of @xmath316 kbar . at ambient pressures ,
cerhin@xmath0 is an anti - ferromagnet .
the fs of cerhin@xmath0 was the subject of one of our recent publications.@xcite in order to confirm the link between the superconducting state and fs dimensionality , the fs as a function of pressure in cerhin@xmath0 should be measured .
if the fs becomes more 2d - like as the critical pressure is approached , then this will be evidence for making a connection . in these materials
it seems that superconductivity does not appear until the overlap between the _ f _ electron wavefunctions is sufficient to allow band - like behavior .
measurements of the fs as a function of pressure should show this increasing overlap as a change in topography . here
we present measurements up to 7.9 kbar , about half the critical pressure for cerhin@xmath1 .
we have designed and built small pressure cells , capable of running in a dilution refrigerator and in a rotator .
measuring torque inside a pressure cell is impossible , so we have made small compensated pickup coils which fit into the cell .
each coil has four to five thousand turns .
the filling factor approaches unity because we are able to situate the coil along with the sample inside the cell .
a small coil is wound on the exterior of the cell to provide an ac modulation of the applied field .
we have measured the fs of cerhin@xmath0 under several pressures . at each pressure
we measure fs frequencies and their amplitude dependence as a function of temperature . from this
we can extract information about how the effective mass of the quasiparticles is changing as the pressure is increased .
the figures show the fourier spectra of cerhin@xmath0 under @xmath37.9 kbar .
the crystal was oriented so that the a - b axis plane is perpendicular to the applied field .
at @xmath37.9 kbar and at ambient pressures ( measured in the pressure cell prior to pressurization ) reveals little that is suggestive of change . ]
we show the 7.9 kbar data compared with two sets of data taken at ambient pressure . in fig .
[ highfft ] the fs at 7.9 kbar is compared with the ambient data taken with a torque cantilever ( the same data reported in @xcite ) . because the modulation field for the ac measurements ( in the pressure cell ) was so small ,
the lowest frequencies can be ignored .
notice that the 1411 t ( f@xmath4 , the designation given in ref .
@xcite ) and 1845 t peaks are reproduced exactly in the ambient and the pressure data sets .
the 1845 t peak was not included in ref .
@xcite because of its small amplitude in ambient pressure torque measurements .
the 3600 t ( f@xmath5 ) and 6120 t ( f@xmath6 ) peaks are present in both data sets ; however , the f@xmath5 appears to have split and the f@xmath6 appears to have shifted down in frequency .
such changes could be explained as slight differences of sample alignment with respect to the applied field between the torque measurement and the pressure cell measurement .
three other frequencies , 2076 t , 2710 t , and 4613 t , emerge in the pressure data which are close to to some reported in ref .
@xcite to be observed only at the lowest temperatures ( 25 mk ) .
all but the first of these frequencies are seen also in ambient pressure data taken with the sample in the pressure cell prior to pressurization as shown in fig .
[ lowfft ] .
thus , assuming the differences in frequency between the torque measurements and pressure cell measurements are due to differences in alignment , we can make frequency assignments that follow ref .
@xcite ( also shown in fig .
[ lowfft ] ) .
the relative increase in amplitude with increasing pressure of these three peaks could be a result of the increase of the coupling factor between the sample and the coil as the two are compressed together .
the lack of any clear differences in the fs up to 7.9 kbar suggests that if the fs changes , then such change is not a linear function of pressure . nor is there a compelling reason to think that it should be a linear function .
possibly , at some pressure closer the the critical pressure , the transition to _ f _ electron itinerate behavior will take place leading to more noticable changes in the fs .
the fs of cerhin@xmath1 appears to remain topographically stable under the application of pressure up to 7.9 kbar .
additional measurements which approach the critical pressure ( @xmath316 kbar ) are of prime importance .
this work was performed at the national high magnetic field laboratory , which is supported by nsf cooperative agreement no .
dmr-9527035 and by the state of florida .
work at los alamos was performed under the auspices of the u. s. dept . of energy .
donavan hall , e.c .
palm , t.p .
murphy , s.w .
tozer , eliza miller - ricci , lydia peabody , charis quay huei li , u. alver , r.g .
goodrich , j.l .
sarrao , p.g .
pagliuso , j. m. wills , and z.fisk .
b _ * 64 * , 064506 ( 2001 ) , cond - mat/0011395 | measurements of the de haas - van alphen effect have been carried out on the heavy fermion anti - ferromagnet cerhin@xmath0 at temperatures between 25 mk and 500 mk under pressure .
we present some preliminary results of our measurements to track the evolution of the fermi surface as the pressure induced superconducting transition is approached .
, , , , , de haas - van alphen ; heavy fermions ; superconductivity ; high pressure |
for many years the forest has been considered a different class of objects with respect to galaxies .
the available sensitivity was too low to detect any sign of non primordial composition in the intergalactic gas clouds at high redshift .
thanks to the advent of high resolution and signal to noise spectroscopy , the old idea on the majority of quasar absorption lines has been revisited and opened in the last few years a still pending debate on the connection between the forest and the galaxy formation of the early universe .
the detection of ions different from civ in optically thin clouds is made complicated by harder observational conditions , whereas the still too poor knowledge of the ionisation mechanisms which determine the ion abundances in those clouds has often discouraged attempts of metal content estimations as a function of redshift and of hi column density .
however abundance investigation of the clouds has fundamental implications in the understanding of the enrichment processes in the igm by pop iii stars in the @xmath3 universe .
the sample of optically thin absorption lines with @xmath4 has been obtained by high resolution spectroscopy , mainly hiras / keck ( songaila 1997b ) but also by emmi / ntt for the @xmath5 systems ( savaglio et al .
for all the systems civ and/or siiv and cii detections or upper limits are given in redshift coverage @xmath6 .
the lower bound in @xmath7 is due to the very rare metal detection in lower column density systems . in this range even if the line can be saturated ( depending on the doppler width ) monte carlo simulations showed that fitting procedures of synthetic individual lines with similar resolution and s / n ratio of the observed spectra give hi column density errors which are less than a few tens of @xmath8 ( for @xmath9 , @xmath10 , fwhm = 12 and s / n = 20 this is typically 0.1 @xmath8 ) .
the blending effect has a much more dramatic impact on column density uncertainties and for this reason , we consider in the case of complex structures as an individual cloud the total column densities of hi and of metal lines . estimating the heavy element content in the clouds is mostly complicated by the poor knowledge of the ionising sources . as a first simplification
, we assume that this is dominated by photoionisation of the uv background and neglect any other mechanism .
collisional ionisation is important when the gas temperature exceeds @xmath11 k. at that temperature , the doppler parameter for hi is 41 , well above the mean value typically found in clouds .
the analysis of metal lines in clouds ( rauch et al . , 1997 ) shows that the mean `` doppler '' temperature in these clouds is @xmath12 k , making any evidence of collisional ionisation hard to justify .
once the photoionisation equilibrium is assumed , we first consider the subsample of clouds which show both civ and siiv absorption . to calculate the metallicity we use cloudy and
assume six different shapes for the uv background normalized to the value at the lyman limit ( @xmath13 erg s@xmath14 @xmath15 hz@xmath14 sr@xmath14 ) changing the parameter @xmath16 in the range @xmath17 .
we varied the [ c / h ] and gas density in such a way to reproduce the observed civ .
we also assume the relative silicon to carbon abundance to be between 0 and three times solar and consider the cloud size along the line of sight to be in the range 1 kpc @xmath18 kpc . given these assumptions ,
we obtain for this subsample a set of 18 [ c / h ] measurements shown in fig .
carbon abundance in clouds with detected carbon and silicon has a large spread with mean values of [ c / h ] @xmath19 and no evidence of redshift evolution .
we notice that this sample might consist of metal
rich clouds since it has been selected because of the siiv detection and might not be representative of the whole population of clouds . in a recent work ,
songaila ( 1997a ) has estimated the total universal metallicity at @xmath20 ( assuming that at that time the baryonic matter of the universe mostly resides in the forest ) to be in the range 1/2000 and 1/630 relative to solar . in a different approach
, we consider the whole sample and regard the global observed properties instead of the individual systems and compare with models .
results of column density ratios on the @xmath21 and @xmath7 planes are shown in figs .
[ f1 ] and [ f2 ] . in fig . 2 we investigate the redshift evolution of observed column densities in the case of @xmath22 and @xmath23 as reported . the discussed trend of siiv / civ ( cowie et al .
, this conference proceedings ) can be reproduced by a redshift evolution of @xmath22 from 200 at @xmath24 to 3000 at @xmath25 .
the same model can take into account other observed ion ratios . in fig .
3 we compare observations with cloudy models assuming that all the clouds of the sample are at the same mean redshift of @xmath26 with @xmath27 and the gas density proportional to the square root of @xmath7 , as given in the case of spherical clouds in photoionisation equilibrium with the uvb . in both figures the solid lines are obtained for metallicity [ c / h ] @xmath19 and [ si / c ] = [ o / c ] = 0.5 , [ n / c ] = 0 .
models of photoionisation equilibrium can include the majority of metal detections ( also considering the metallicity spread ) but cii / hi which , as function of @xmath7 , looks to be steeper than calculated .
additional observations of cii would probably cast further light on the discussion on the ionisation state and metal content in the clouds . in both figures , the numerous upper limits falling below the dashed curve [ c / h ] @xmath28 is an indication that in many clouds the metallicity is lower than the values found in the selected sample .
the investigation of low and intermediate redshift ( @xmath2 ) observations of ovi and nv in @xmath29 clouds might succeed in answering the question of how efficient the mixing processes in the igm at high redshift has been .
relative abundances can provide new hints on the study of metal production by pop iii stars . in particular nv since it has been predicted to be underproduced in massive stars with low initial metallicity ( arnett 1995 ) .
more observations of the siiv / civ ratio for @xmath30 and @xmath31 are a challenging probe of the redshift evolution of the uvb , though this can be one of the many possible reasons for the observed siiv / civ trend ( another would be redshift evolution of the gas density being lower at lower redshift ) .
more interesting conclusions await outcomes from new high quality data of keck observations .
arnett d. , 1995 , ara&a , 33 , 115 rauch m. , sargent w.l.w .
, womble d.s . ,
barlow t.a . , 1997 , apj , 467 , l5 savaglio s. , cristiani s. , dodorico s. , fontana a. , giallongo e. , molaro p. , 1997 ,
a&a , 318 , 347 songaila a. , 1997a , apjl , _ in press _ ,
ph/9709046 songaila a. , 1997b , _ in preparation _ | we present a detailed analysis of the ionisation state and heavy element abundances in the intergalactic medium ( igm ) .
the civ doublet is shown by 30 % of the 182 selected optically thin clouds in 10 qso lines of sight .
direct metallicy calculations have been performed on individual systems with detected civ and siiv ( 10% of the sample ) varying the uv photoionising source , cloud density and size and silicon relative abundance .
the best solutions for carbon content in this subsample ( redshift coverage @xmath0 ) span between 1/6 and 1/300 of the solar value with no evidence of redshift evolution in both the metallicity and the ionising source .
global properties of the whole sample indicate that the metallicity in clouds with civ and siiv is not typical of the igm .
the redshift evolution of the uvb is one of the possible sources of the observed siiv / civ trend presented by cowie and collaborators during this meeting .
future detection of heavy elements in lower hi column density ( @xmath1 ) clouds relies on the presence of ovi and nv at @xmath2 . |
dpvs were discovered in the small magellanic cloud after a search for be stars in the ogle - ii database ( mennickent et al .
they were clearly distinguished from other variables by showing 2 linked photometric cycles ( @xmath1 and @xmath2 ) . a spectroscopic monitoring of some of them allowed to associate the short periodicity to the orbital period of a binary ( mennickent et al .
2005 ) whereas the long term variations were found to be reddish and non strictly constant ( mennickent , assman , & sabogal 2006 , michalska et al.2009 ) . the current census of dpvs amounts to 114 in the magellanic clouds and 11 in our galaxy ( see magnitud - color and period - period diagrams in mennickent & koaczkowski 2009a ) .
after the discovery of additional variability in v393sco ( pilecki & szczygiel 2007 ) , we recognized it as the first dpv in our galaxy .
later we found that in the past an additional long cycle was also reported for the galactic dpv aumon ( lorenzi 1985 ) .
both stars were also found during our independent search for galactic dpvs in the asas database .
few dpvs have been studied in detail , but we can get insights on dpvs as a class based on well studied and representative cases . cumulative evidence indicates that dpvs are interacting binaries with a component ( the donor ) filling their roche lobe and transferring mass to the gainer ( the primary ) .
broad and variable hei lines probably probe an accretion disc that sometimes hides the primary .
hi ( sometimes hei ) line emission is the rule ( although usually not quite prominent ) .
it is probable that the deeper dpv eclipse corresponds mostly to the occultation of the circumprimary disc .
we observed a loop in the color - magnitude diagram of lmc - dpv1 during the long cycle that interpreted in terms of mass loss ( mennickent et al .
2008 , hereafter m08 ) .
the same star shows discrete pa@xmath3 and pa@xmath4 absorption components following a saw - teeth pattern with the orbital period indicating outflows through the outer lagrangian points ( m08 ) .
the same phenomenon could explain the depressed blue wings observed in the hei 10833 infrared spectra of v393sco near secondary eclipse ( fig.1 ) .
we observe ( minor ) variability in the shape of the light curve for v393sco during main minima that could indicate changes in the properties of the circumprimary disc .
in addition , the h@xmath5 emission line strength increases during supercycle maximum ( mennickent & koaczkowski 2009b ) .
most dpvs with 2mass data seems to show infrared excess . in the studied cases mass ratios ( donor / gainer ) are always less than one .
all these singular characteristics , plus the presence of two distinct periodicities , suggest that dpvs can be observed as a new class of interacting binaries , at least from the observational point of view .
we propose that dpvs are case - a / b mass transfer binaries after mass ratio reversal in algol - like configurations .
they are more massive than ordinary algols ( mennickent & koaczkowski 2009a ) , so it is possible that the mass transfer rate is larger , and the primary is rotating at critical velocity . under these circumstances ,
accretion is stopped and the disc starts cumulating mass that is periodically ejected from the system .
our observations indicate that mass loss occurs permanently in dpvs , mainly through the outer lagrangian points .
however , the long term periodicity implies that there is another clock governing mass loss in the long term .
we believe that during the supercycle the disc cumulates extra matter that is is expelled from the binary during supermaximum .
the remarkable behavior of hei in v393sco ( fig.2 ) suggests that the rotational velocity of the circumprimary disc is larger during supermaximum and modulated with supercycle phase .
the mechanism for this supercycle is unknown .
we analyzed the possibility that the disc outer radius grows until the 3:1 resonance radius and disc starts to precess , as happens in low mass ratio suuma stars ( mennickent & koaczkowski 2009a ) .
in this view precession enhances mass loss into the interstellar medium .
however , the fact that @xmath0 maintains the same orbital behavior during supercycle ( fig.2 ) suggests that there is no disc precession .
other more speculative hypothesis is that the primary experiences instabilities around critical velocity , gaining extra momentum during accretion until attains a velocity just above the critical one , then relaxes below critical velocity giving the extra momentum to the disc that partly escapes from the binary .
additional studies are needed to confirm this view .
we have initiated a program to study dpvs with high resolution optical / infrared spectrographs and robotic telescopes with the aim of shedding light on this phenomenon .
in table 1 we summarize our view for dpvs in the context of algols and w serpentid stars .
it is possible that the critical velocity of the gainer can be maintained only until the mass of the donor ( @xmath6 ) drops to certain value . during this period of high mass transfer rate
the star behaves as a w serpentid ( with a thick circumprimary disc and chaotic mass loss ) or as a dpv ( with slightly lower @xmath7 allowing the dpv instability to operate ) .
when @xmath7 drops even more , tidal forces spin down the gainer , the orbital separation ( @xmath8 ) increases , and the system becomes a typical algol star . in algols mass transfer rate if present is comparatively small , partly due to the less massive donor and also to the larger @xmath8 . @xmath3
lyr probably still is not a dpv , as suggested by their very small long period amplitude and position in the @xmath9 diagram ( fig.1 ) .
ccccc systems & key facts & @xmath6 , @xmath7 & mass loss & age , @xmath10 + w ser & polar jets , variable eclipse , large @xmath11 & large & large & young , yes + dpv & 2-periods , small ecl .
variability , @xmath12 & medium & cyclic & middle , yes + algol & small / no additional variability , @xmath12 & small & small & old , no + _ s.m .
: what about blends ?
they are always of concern in other galaxies . + _
mennickent _ : dpvs are also observed in the galaxy .
we have discarted the possibility of blends in the case of dpvs . | we introduce the class of intermediate mass binaries named double periodic variables ( dpvs ) , characterized by orbital photometric variability ( ellipsoidal or eclipsing ) in time scales of few days and a long photometric cycle lasting roughly 33 times the orbital period . after a search conducted in the ogle and asas catalogues
, we identified 114 of these systems in the magellanic clouds and 11 in the galaxy .
we present results of our photometric and spectroscopic campaigns on dpvs conducted during the last years , outlining their main observational characteristics .
we present convincing evidence supporting the view that dpvs are semidetached interacting binaries with optically thick discs around the gainer , that experience regular cycles of mass loss into the interstellar medium .
the mechanism regulating this long - term process still is unknown but probably is related to relaxation cycles of the circumprimary disc .
a key observational fact is the modulation of the @xmath0 of hei 5875 with the long cycle in v393sco .
the dpv evolution stage is investigated along with their relationship to algols and w serpentid stars .
we conclude that dpvs can be used to test models of non - conservative binary evolution including the formation of circumbinary discs . |
main sequence stars with mass in the range 0.9 - 9 m@xmath2 evolve through a double shell burning phase , refered to as the asymptotic giant branch ( agb ) phase of evolution .
this phase is characterized by carbon dredge up of the core to the surface after each thermal pulse - helium shell flash - ( iben & renzini 1983 ) .
the temperatures of these objects are very badly known .
although they are highly variable , their determination from static models such as assumed in the basel library can be justified as a first approximation . in order to explore the capabilities of the basel library ( lejeune , cuisinier & buser 1997 , 1998 and references therein , see also lastennet , lejeune & cuisinier , these proceedings ) to predict correct temperatures for such cool agb stars , we compare our results from synthetic infrared photometry of the stellar photosphere with the detailed study of lorenz - martins & lefvre ( 1994 ) of the agb carbon star r fornacis .
their work is based on a modelling of the spectral energy distribution of the dust envelope , where they put tight constraints on the temperature of the heating source .
table 1 gives the jhklm photometry of r for ( hip 11582 ) that we used ( le bertre , 1992 ) .
the photometric errors in the individual jhklm magnitudes are not provided so we assume an error of 0.2 on each magnitude , according to the maximum uncertainty estimated from fig . 1 of le bertre ( 1988 ) . ccccccc j & h & k & l & m & t@xmath0@xmath3 & t@xmath0@xmath4 + & & & & & ( k ) & ( k ) + 5.76 & 3.97 & 2.32 & 0.21 & @xmath50.28 & 2650 & 2440 - 2520 + @xmath3 lorenz - martins & lefvre ( 1994 ) ; + @xmath4 basel jhkm synthetic photometry ( this work , see text for details ) .
although the dust may have a significant contribution in the ir _ bands _ of this star , especially l and m , it should only have a secondary influence on the photospheric _
colours_. we intend of course to correct for the predicted differences by a dust model ( lorenz - martins & lefvre , 1993 ) due to the envelope .
however in a first step we merely compare the observed colours of r fornacis with the photospheric predictions of the basel library ( basel-2.2 version , with spectral corrections ) by minimizing their @xmath6 differences .
+ this @xmath6-minimization method is similar to the one applied in lastennet et al .
( 2001 ) : we derived the t@xmath0 and log g values matching simultaneously the observed jhklm photometry listed in tab . 1 , assuming a solar metallicity ( [ fe / h]@xmath70 ) .
we have tested various colour combinations of the j ( 1.25 @xmath8 ) , h ( 1.65 @xmath8 ) , k ( 2.2 @xmath8 ) , l ( 3.4 @xmath8 ) , and m ( 5.0 @xmath8 ) magnitudes : ( j@xmath5h ) , ( h@xmath5k ) , ( k@xmath5l ) , ( j@xmath5k ) and ( k@xmath5 m ) .
they all give t@xmath0 estimates in agreement with the work of lorenz - martins & lefvre ( 1994 ) .
+ since better constraints should be obtained by matching more than 1 colour , we chose the ( j@xmath5h ) and ( k@xmath5 m ) colours which give the best @xmath6-scores .
the solutions we get to match simultaneously the observed ( j@xmath5h ) and ( k@xmath5 m ) are presented in fig .
our best basel - infrared solution is t@xmath0@xmath72440k , but all the solutions inside the 1-@xmath9 contour are good fits to the observed photometric data .
the effective temperature of the central star of r for found by lorenz - martins & lefvre is t@xmath0@xmath72650 k ( shown as a vertical line on fig .
1 ) . this is larger by @xmath1100k than the 1-@xmath9 basel contour but still inside the 2-@xmath9 contour .
additionally the basel models show that this star has a surface gravity log g @xmath1@xmath50.5@xmath100.4 , which is what one expects for carbon stars .
we reported a preliminary study to determine the t@xmath0 and surface gravity of the central star of r fornacis by exploring the best @xmath6-fits to the infrared photometric data .
these results are in a surprising good agreement - given the approximation we made ( no envelope absorption / emission correction ) - with the detailed study of lorenz - martins & lefvre ( 1994 ) .
therefore , while detailed spectra studies are obviously highly preferred ( see e.g. loidl , lanon & jrgensen , 2001 ) , our method may provide a good starting point .
if our r fornacis result is confirmed with other agb stars , this would mean that the basel jhklm synthetic photometry is suited to derive ( teff - log g ) estimates for cool agb stars .
iben i. , renzini a. , 1983 , ara&a , 21 , 271 lastennet e. , lignires f. , buser r. , lejeune th .
, lftinger th .
, cuisinier f. , vant veer - menneret c. , 2001 , , 365 , 535 le bertre t. , 1988 , , 190 , 79 le bertre t. , 1992 , , 94 , 377 lejeune th . , cuisinier f. , buser r. , 1997 , , 125 , 229 lejeune th . , cuisinier f. , buser r. , 1998 , , 130 , 65 loidl r. , lanon a. , jrgensen u.g . , 2001 , , 371 , 1065 lorenz - martins s. , lefvre j. , 1993 , , 280 , 567 lorenz - martins s. , lefvre j. , 1994 , , 291 , 831 | we discuss the possibilities of the basel models in its lowest temperature boundary ( t@xmath0@xmath12500 k for cool giants ) to provide the t@xmath0 of agb stars .
we present the first step of our work , by comparing our predictions for the agb star r fornacis with the results of lorenz - martins & lefvre ( 1994 ) based on the dust spectral energy distribution . |
measurements of the integrated light from a galaxy at 2000 provides a fairly direct measure of the instantaneous rate of star formation , since the massive stars that provide most of this radiation are short - lived compared with the age of the galaxy .
knowledge of the star formation rate also gives a measure of the rate of heavy element production in a galaxy , or in the universe when a large sample of galaxies are measured ( @xcite ) .
the integrated light from these galaxies contributes to the extragalactic background light at ultraviolet wavelengths , whose main sources are hot stars and active galactic nuclei .
measurements of galaxy number counts in the ultraviolet have been made by @xcite using the foca balloon - borne uv telescope , @xcite and @xcite using hst archival fields .
these data have been interpreted with models that predict number counts based on galaxy spectral energy distributions ( sed s ) and luminosity functions , such as those of @xcite and @xcite .
the total far - ultraviolet extragalactic background has been measured to be as high as 500 ph @xmath2 s@xmath3 @xmath3 and as low as 30 ph @xmath2
s@xmath3 @xmath3 ( see review by @xcite ) .
predictions for the number of galaxies that might be detected in deep ultraviolet optical monitor ( om ) images are given by @xcite .
in this paper , we detect galaxies in a deep uv image taken with the optical monitor ( om ) and use these galaxy number counts to place constraints on galaxy luminosity evolution via a a galaxy evolution model similar to that of @xcite .
we also find a lower limit to the galaxy contribution to the extragalactic uv background .
the om 13 hr deep field ( at j2000.0 13 34 37.00 , + 37 54 44.0 ) was observed for approximately 200 ks with xmm - newton around june 22 , 2001 .
details of the om exposures used in this study are shown in table [ tab : tab1 ] .
lcl + filter & central wavelength & exposure time + & ( ) & ( ksec ) + + b & 4200 & 10 + u & 3900 & 10 + uvw1 & 3000 & 20 + uvm2 & 2500 & 31.5 + uvw2 & 2000 & 30 + + several exposures of typically 7 ks were brought to a common astrometric reference frame and coadded .
we searched each image for sources using sextractor and made a catalog of the sources we found .
we concentrate here on sources in the uvw2 image ( fig .
[ tsasseen - f7_fig1 ] ) and use measurements in the other filters to differentiate between stars , galaxies and qso s .
we also use a deep r band image ( to r@xmath427 ) of this field taken with the 8 m subaru telescope on mauna kea ( fig .
[ tsasseen - f7_fig2 ] ) to check for source shape and possible confusion .
we perform two checks to discriminate stars from galaxies . first , we compare the sed of each uvw2 source ( determined from om photometry ) against stellar templates .
second , we compute an inferred distance , as if the source were a main sequence star , from u - b color and b magnitude , as shown in fig .
[ tsasseen - f7_fig3 ] .
we find these checks form reliable stellar discriminators for more than 90% of the sources
brighter than ab=22 . where @xmath5 is given in ergs @xmath2 s@xmath3 hz@xmath3 ( @xcite ) .
] we also find a number of qso s in the field that show uv excess and appear point - like in the om and subaru images .
we categorize these separately in our galaxy number counts .
further work remains to completely discriminate any remaining stellar content and the qso populations .
we plot the detected galaxy counts as a function of magnitude in fig .
[ tsasseen - f7_fig4 ] .
our counts are in approximate agreement with that of @xcite ( also shown in fig .
[ tsasseen - f7_fig4 ] ) in the range of overlap , and we extend these counts to ab=22 .
we have constructed a model is similar to that of @xcite and use it to predict galaxy counts at 2000 as a function of apparent magnitude .
the model uses a schechter absolute luminosity distribution function for 6 different galaxy types at redshifts between zero and 1.2 , along with k - corrections and a single parameter luminosity evolution factor for each galaxy type .
we have normalized the schechter function using observed counts at bj=17 , and set our evolution parameters to agree with the modeled galactic evolution of @xcite , following @xcite .
our model implicitly includes the effects of dust absorption and scattering because it is based on observed uv sed s . like armand & milliard ,
our model predicts fewer galaxies in each magnitude band than our measured number counts , as shown in figure [ tsasseen - f7_fig4 ] .
we also compare the observed counts with the model of @xcite , whose model explicitly includes expected contributions to the observed galaxy counts from starburst galaxies and dust .
our model agrees well with the granato et al .
model that includes dust , but our observed counts are higher than both models that include dust .
the summed the flux from non - stellar sources detected in the uvw2 image totals 3236 ph @xmath2 s@xmath3 sr@xmath3 @xmath3 , with the higher limit including the contribution from qso s and active galaxies .
the integrated far - ultraviolet light from discrete galaxies has been measured recently by @xcite to be 144195 ph @xmath2 s@xmath3 sr@xmath3 @xmath3 , based on galaxies detected in the range ab = 24 to 29.5 and a model to infer the flux from brighter galaxies .
these authors claim there appears to be a break in the slope of the galaxy number counts that occurs around ab = 24 , with substantial flattening of function at fainter magnitudes .
our measurements show an intriguing downturn in galaxy counts at the faint end , which may indicate the start of the change in the slope of the number counts .
there still remains some uncertainty in the number counts in the gap between our measurements and those of @xcite , which indicates the total integrated flux of galaxies is still uncertain .
the discrepancy between the models shown in fig .
[ tsasseen - f7_fig4 ] and both our data and that of @xcite may indicate that we are missing some components in our understanding of how galaxies evolve .
some possible reasons for the descrepancy between their model and measurements are given by @xcite , including faster evolution of the star formation rate or the possiblity that there is a population of blue galaxies that is substantially more numerous at z = 0.7 than they are today .
there are a number of effects we have not yet evaluated in detail that may affect our measurement and conclusions .
these include the effects of galaxy inclination , morphology and apertures on our photometry , the effects of comparing measurements made in slightly different bandpasses , and the detailed effects of dust absorption and possible evolution in galaxies ( @xcite ) .
our simple model assumes a smooth evolution in star formation , but there is evidence that star formation may be espisodic or occur in bursts , possibly because of merger activity , _
e.g. _ @xcite .
galaxies change over time in many ways and our model predicts only one facet of these changes , namely an evolving star formation rate . the full picture of galaxy evolution is certainly more complicated .
it remains to explore further the connections between changes in the star formation rate and changes in galaxy appearance and morphology , metallicity , gas content , spectral energy output , and merger activity that have been discussed at length by other researchers .
\1 ) we have obtained galaxy counts at 2000 to a magnitude of ab = 22 in deep images from the optical monitor on xmm - newton .
the long om exposure allows us to measure galaxy counts 1.5 magnitudes fainter than @xcite , and we find similar counts in range of overlap .
2 ) two evolutionary models underpredict the observed galaxy counts , and may indicate that several process may be at work , including episodic star formation , changes in the optical depth within galaxies to 2000 radiation , or a new population of galaxies that is less visible in the present epoch .
3 ) the total integrated flux from the galaxies we detect to ab=22 is 3236 ph @xmath2 s@xmath6 @xmath3 sr@xmath3 .
this flux is a lower limit to the integrated extragalactic background light at 2000 , and represents about 2025% of the integrated , far - ultraviolet flux from galaxies inferred from the deep hst measurements of @xcite .
hill , r. , gardener , j. , heap , s. malamuth , e. & collins , n. , 1997 in the ultraviolet universe at low and high redshift : probing the progress of galaxy evolution , ed . w. h. waller et al .
( new york : american institute of physics ) , p. 21
sasseen , t. p. , crdova , f. , ho , c. & priedhorsky , w. , 1997 , in the ultraviolet universe at low and high redshift : probing the progress of galaxy evolution , ed . w. h. waller et al .
( new york : american institute of physics ) , p. 21
this research was supported by nasa grant nag5 - 7714 .
we would also like to thank the optical monitor team , and esa for their successful program to produce the first rate space observatory , xmm - newton , | we use galaxies detected in a deep ultraviolet xmm - newton optical monitor image and a model that predicts uv galaxy counts based on local counts and evolution parameters to constrain galaxy evolution to z=1.2 .
the 17 square 2000 ( uvw2 filter ) image was taken as part of the xmm - om team s guaranteed time program .
we detect sources in this image to a flux limit of 2.7 @xmath0 10@xmath1 ergs @xmath2 s@xmath3 @xmath3 ( ab magnitude = 22 ) .
since some of the sources may be stars , we perform a number of checks , including shape , color and implied distance to remove stars from the detected counts .
we find galaxy number counts as a function of magnitude roughly in agreement @xcite , but again find these counts are in excess of evolution models .
the excess counts at faint magnitudes may provide evidence for either a new population of galaxies emerging around z=0.7 or more dramatic evolution than some earlier predictions .
the integrated light from the detected galaxies totals 3236 ph @xmath2 s@xmath3 @xmath3 sr@xmath3 , placing a firm lower limit on the integrated uv light from galaxies . |
the atmosphere is the most important part of the detector in ground - based gamma - ray astronomy , but it is also the part that has the greatest systematic uncertainty and over which we have the least control .
it falls upon us to instead monitor and characterise the atmospheric conditions at the time of observations so that we can either feed this information into monte carlo simulations or reject data when conditions go out of acceptable parameters . after being generated in the upper atmosphere
cherenkov light will either reach the ground or be attenuated through the process of rayleigh scattering on the molecular component of the atmosphere , or mie scattering on the aerosol component ( variously dust .
silicates , pollens , etc ) .
the molecular component tends to change relativiely slowly , through seasonal variations ; whereas the aerosol component can change more rapidly , depending on eg wind conditions .
it becomes vitally important to characterise this aerosol component of the atmosphere through regular monitoring .
a lidar is generally used to measure the atmospheric transmission ( eg @xcite ) from backscattered laser light . at the h.e.s.s .
site a lidar centred at 355 and 532 nm has been running in conjunction with observations since mid-2011 . whilst lidars are excellent instruments for determining the presence of aerosols they are not without complications .
firstly a lidar , due to geometric viewing considerations , only becomes effective above a minimum altitude .
secondly , in order to obtain a transmission profile relevant to the cherenkov spectrum the laser wavelengths are close to the peak in the emission , this means the lidar is operated only inbetween observing runs to avoid any light contamination to the telescope images . in this paper
we look at utilising another piece of the h.e.s.s . atmospheric monitoring equipment to fill in some of this missing information .
the atmosphere is split into regions according to its temperature behaviour .
the troposphere is the lowest , most dense , part of the atmosphere where most of the weather happens and is characterised by a linear decline in temperature with increasing altitude and vertical mixing .
the molecular density profile falls off exponentially , with a scale height of a few km ; the vertical air motion in this region mixes in the larger aerosols which have a smaller scale height of order a km .
the molecular component is an inefficient black - body radiator in the 8 - 14@xmath2 m region of the spectrum , water vapour and aerosols are slightly more efficient and clouds are very efficient .
this makes an infra - red radiometer an effective cloud monitor , with clouds showing up as a large brightness temperature compared to a relatively cold " sky @xcite .
employ heitronics kt19.82 radiometers with 2@xmath3 field of view to monitor for the presence of clouds , with each telescope having a paraxially mounted unit and a further one continuosly scanning the whole sky .
the infra - red luminosity of the sky ( @xmath4 ) is a collective sum of the emission of a number of different constituent parts @xmath5 where @xmath6 is the emissivity of the lens ( @xmath7 ) and the water vapour @xmath8 , the aerosols @xmath9 , and the molecular ( @xmath10 ) profiles of the atmosphere , etc and t is the relevant integrated temperature profile in the line of sight . according to @xcite the aerosol component
can contribute up to 30wm@xmath0 to the bolometric luminosity , which can mean the difference between a brightness temperature of -56@xmath3c or -70@xmath3c in the presence or absence of aerosols respectively .
this leads to the prospect of changing aerosol conditions leading to a noticeable change in the sky brightness temperature ( @xmath11 ) measurements .
the august to september period at the h.e.s.s .
site often has noticeable aerosol contamination due to biomass burning in neighbouring countries and the resultant smoke being blown downwind . in figure [ fig:20110820 ] we see an `` ideal '' night which has no measurable aerosol contribution ( the large particles having sedimented out of the atmosphere ) ; within the space of a week figure [ fig:20110829 ] shows `` hazy '' conditions , with a prominent aerosol boundary layer that extends up to about @xmath12 km ; a couple of days later figure [ fig:20110901 ] shows the aerosols sedimenting out once more , with the boundary layer close to the lidar effective altitude threshold at @xmath13 km ( characteristic of `` normal '' observing conditions ) . in figure
[ fig : rates ] we show the telescope trigger rates as a function of zenith angle for all observing runs for that osberving period that have 4 telescopes participating , stable rates ( ie no clouds or data acquisition issues ) and noted as clear by the observers in the shift logs .
the data points are sub - divided according to the aerosol boundary layer conditions and the @xmath11 at zenith for that run , the correlation between warm sky temperature , aerosol presence and lowered telescope trigger rate is clearly apparent .
but for the night of 29/08/2011 . there is a prominent aerosol component up to a boundary layer of @xmath14 km and the infra - red lumonisity is substantially increased.,title="fig : " ] but for the night of 29/08/2011 .
there is a prominent aerosol component up to a boundary layer of @xmath14 km and the infra - red lumonisity is substantially increased.,title="fig : " ] but for the night of 01/09/2011 .
there is a noticeable aerosol component up to a boundary layer of @xmath15 km and the infra - red lumonisity is moderately increased.,title="fig : " ] but for the night of 01/09/2011 .
there is a noticeable aerosol component up to a boundary layer of @xmath15 km and the infra - red lumonisity is moderately increased.,title="fig : " ] km , squares when the boundary layer reaches @xmath12 km and crosses for when there are no measurements available .
the red points are when @xmath16 at zenith is @xmath17c , blue points when it is lower . ]
the atmospheric clarity conditions according to lidar and infra - red radiometer measurements have been presented here .
the presence of aerosols in the atmosphere show up clearly in the lidar returns and also as a clear increase in @xmath16 .
the data selected here come from a single two week period to ensure no seasonal temperature effects can bias the dataset .
the @xmath16 will still change somewhat due to the day - to - day ambient temperature variation , however this would be expected to produce no more than a @xmath18% difference not the observed @xmath19200% . during the most severe periods of aerosol contamination
the boundary layer can be seen to extend to relatively high altitudes .
as the production height for air shower photons is above these aerosol layers they should act like filters only , but since the light of muon ring images ( commonly used to determine the atmosphere s contribution to the systematic uncertainty ) develop within these layers they will have a distinctly different and more complicated response to different boundary layer altitudes .
this will be something to examine in future work . in summary ,
the lidar is extremely useful in determining the presence of aerosol layers and measuring the transmission profiles , but has limited resolution at altitudes @xmath201 km and limitations as to when it can be operated ; the infra - red radiometer is sensitive to the presence or absence of aerosols , operates all of the time and will be most sensitive to low altitude aerosols .
together they have the potential to quantify atmospheric opacity entirely independently of the telescope systematics . | the attenuation of atmospheric cherenkov photons is dominated by two processes : rayleigh scattering from the molecular component and mie scattering from the aerosol component .
aerosols are expected to contribute up to 30 wm@xmath0 to the emission profile of the atmosphere , equivalent to a difference of @xmath1c to the clear sky brightness temperature under normal conditions . here
we investigate the aerosol contribution of the measured sky brightness temperature at the h.e.s.s .
site ; compare it to effective changes in the telescope trigger rates ; and discuss how it can be used to provide an assessment of sky clarity that is unambiguously free of telescope systematics .
address = department of physics , university of durham , durham , dh1 3le .
u.k .
address = lupm , un .
montpellier ii cc-072 , place eugenie bataillon , 34095 montpellier , france . |
in this appendix , we explain how the line width was extracted from the numerical data .
we begin by determining the spectral function , defined by @xmath115 this consists of a set of delta functions .
we then define the integrated spectral function @xmath116 .
this consists of a set of step functions ( see fig .
[ steps](a ) ) . for each step
, we identify the energy values corresponding to @xmath117 of the step , @xmath118 of the step , and @xmath119 of the step . the energy spacing between the @xmath117 and @xmath119 points
is taken to be the linewidth of this spectral line .
we track how this line width scales with @xmath0 .
we note that there is in general a wide distribution of line widths for any @xmath0 ( fig .
[ steps](b ) ) . as a result ,
the mean and the median linewidth scale very differently ( see fig.5 of the main text ) .
an understanding of the difference between the scaling of the mean and typical line width is an important challenge for future work .
( a ) the procedure for determining the linewidth .
the blue curve is an integrated spectral function .
the green squares divide each step into half , the red diamonds mark @xmath117 and the light blue circles mark @xmath120 of each step .
( b ) probability distribution of the linewidth @xmath109 for different values of coupling to the bath @xmath0 for a system with @xmath69 and @xmath121 averaged over 10 disorder configurations .
lines are a guide to the eye . ] | we use exact diagonalization to study the breakdown of many - body localization in a strongly disordered and interacting system coupled to a thermalizing environment .
we show that the many - body level statistics cross over from poisson to goe , and the localized eigenstates thermalize , with the crossover coupling decreasing with the size of the bath in a manner consistent with the hypothesis that an infinitesimally small coupling to a thermodynamic bath should destroy localization of the eigenstates .
however , signatures of incomplete localization survive in spectral functions of local operators even when the coupling to the environment is sufficient to thermalize the eigenstates .
these include a discrete spectrum and a gap at zero frequency .
both features are washed out by line broadening as one increases the coupling to the bath .
we also determine how the line broadening scales with coupling to the bath .
isolated quantum systems with quenched disorder can enter a ` localized ' regime where they fail to ever reach thermodynamic equilibrium @xcite . while we have an essentially complete understanding of localization in non - interacting systems @xcite ,
the theory of many - body localization ( mbl ) is still under construction @xcite .
numerical investigations using exact diagonalization @xcite _ do _ indicate that all eigenstates of a strongly interacting disordered system can be localized .
most of the theoretical research so far has been in the limit of a perfectly isolated system .
however , experimental tests of mbl ( @xcite ) will always include some finite coupling to the environment .
what then can we expect to see in experiments designed to probe many body localization ?
a recent theory of mbl systems weakly coupled to heat baths proposed that while eigenstates are delocalized by an infinitesimally weak coupling to a heat bath , signatures of localization persist in spectral functions of local operators for weak coupling to a bath @xcite .
this theory has yet to face stringent numerical tests .
moreover , it did not discuss the spectral functions of the physical degrees of freedom , the quantities of direct relevance for experiments , focusing instead on the spectral functions of certain localized integrals of motion that are believed to exist @xcite , but which are related to the physical degrees of freedom by an unknown unitary transformation .
this work directly addresses these issues .
we use exact numerical diagonalization to establish the behavior of many body localized systems weakly coupled to heat baths .
we show that coupling @xmath0 to a bath results in a crossover from poisson to gaussian orthogonal ensemble ( goe ) eigenvalue statistics , which becomes exponentially steeper with increasing bath size . a similar rapid crossover to thermalization is seen in the eigenstates .
however , the prospect for seeing mbl in experiments is still realistic because signatures of incomplete localization remain in the spectral functions of local ( in real space ) operators .
indeed , we find that the spectral functions of the microscopic degrees of freedom look completely different in the localized and thermal phases ( see fig .
1 ) . the thermal phase has a continuous spectrum whereas the local spectral function in the localized phase is discrete , with a hierarchy of gaps , and a gap at zero frequency that survives even after spatial averaging .
increasing @xmath0 causes lines to broaden and fill in these gaps .
however , as long as the typical line broadening is less than the largest gaps , gap - like features remain .
our work also reveals how the line broadening scales with @xmath0 . _ the model _ : we choose the antiferromagnetic heisenberg spin-@xmath1 chain with random fields along @xmath2 : @xmath3 we set the interaction @xmath4 .
the on - site fields @xmath5 are independent random variables , uniformly distributed between @xmath6 and @xmath7 ; @xmath7 measures the disorder strength in the system .
this model with periodic boundary conditions has been shown to have a many - body localization transition at @xmath8 in the infinite temperature limit @xcite .
the hamiltonian in eq .
[ eq : h_pbit ] is written in terms of the physical degrees of freedom @xmath9 ( ` @xmath10-bits , ' in the language of @xcite , where @xmath10=physical ) .
in general , its eigenstates are quite complicated and non - trivial .
as shown @xcite , one can perform a unitary transformation to rewrite @xmath11 in terms of localized constants of motion @xmath12 .
the @xmath13 are dressed versions of the @xmath9 operators , which are localized in real space , with exponential tails , and are referred to in @xcite as ` @xmath14-bits ' ( @xmath14=localized )
. a unitary transformation to this ` @xmath14-bit ' basis can always be performed , if the system is in the regime where all the many body eigenstates are localized . in this @xmath14-bit basis
, the hamiltonian becomes @xmath15 the values of the coefficients @xmath16 and @xmath17 will depend upon the parent hamiltonian ( 1 ) , although these coefficients all fall off exponentially with distance .
the eigenstates of ( 2 ) are just products of @xmath18 .
motivated by the representation ( 2 ) of the hamiltonian ( 1 ) , it is instructive to consider the simpler hamiltonian @xmath19 where the @xmath20 and @xmath21 as independent random variables taken from a log - normal distribution with @xmath22 and @xmath23 , and similarly for @xmath24 .
we take @xmath25 and work with open - boundary conditions .
this hamiltonian also has the feature that eigenstates are product states of @xmath26 , and is simpler to work with numerically .
for the bath , we use a non - integrable hamiltonian that has been recently studied @xcite .
it consists of @xmath27 interacting spins with the hamiltonian : @xmath28 while using open boundary conditions , we add a boundary term @xmath29 to @xmath30 .
we use @xmath31 , @xmath32 and @xmath33 , values for which @xmath30 has been numerically shown by @xcite to have fast entanglement spreading .
( we use periodic boundary conditions only for @xmath10-bits with @xmath34 . ) the interaction between the system and bath should be local for both @xmath10- and @xmath14-bits .
we first study @xmath14-bit eigenstates , choosing the coupling : @xmath35 later we examine @xmath10-bit spectra , using the coupling @xmath36 the total hamiltonian is thus @xmath37 , where @xmath11 and @xmath38 are given by eq .
( 3 ) and ( 5 ) in the first part of this work , and by eq .
( 1 ) and ( 6 ) in the latter part of this work .
we will indicate the transition clearly in the text .
we use open boundary conditions except where periodic boundaries are explicitly mentioned .
we start by analyzing the breakdown of localization when the @xmath14-bit hamiltonian ( 3 ) is coupled to a bath according to ( 5 ) , by examining the many - body eigenvalue statistics as @xmath0 is increased from @xmath39 .
we perform exact diagonalization on a system with @xmath40 spins coupled to @xmath41 spins in the bath .
the many body level - spacing is @xmath42 , where @xmath43 is the energy of the @xmath44th eigenstate .
following @xcite , we define the ratio of adjacent gaps as @xmath45 .
we average this over eigenstates and several different realizations of the disorder to get a probability distribution @xmath46 at a particular value of @xmath0 . in fig .
[ fig : level_space ] , we show how @xmath46 evolves from poisson to goe like as @xmath0 is increased . in a localized system
we expect that @xmath47 , and for a thermalizing system , we expect that @xmath48 .
-bit hamiltonian as @xmath0 is increased .
results are for a system with @xmath40 spins and bath with @xmath41 spins averaged over @xmath49 eigenstates obtained from several disorder configurations .
the dark blue solid line is the poisson distribution expected for localized systems , and the light blue dashed line is the goe distribution expected for thermalizing systems . ]
the transition from poisson to goe statistics happens gradually for this finite size system . a simple analytical estimate of the characteristic value of @xmath0 at the crossover point proceeds as follows ( see also @xcite ) : if @xmath50 is the bandwidth of the bath and @xmath51 is the many body level spacing in the bath , then the system couples to @xmath52 states , with a typical matrix element to each state of order @xmath53 .
the coupling to the bath will be effective in thermalizing the system when this matrix element becomes of order the level spacing in the bath , i.e. when @xmath54 .
this indicates that the crossover coupling @xmath55 . since @xmath56
, the critical value of @xmath0 is expected to scale as @xmath57 . to quantitatively compare this crossover estimate to the data ,
we define @xmath58 . after averaging over disorder distributions
, @xmath59 should be @xmath60 in the goe regime and @xmath61 in the localized regime @xcite .
it is convenient to define the normalized quantity @xmath62=(@xmath63 , such that @xmath64 if the level statistics are goe and @xmath65 if they are poisson .
fig .
3(a ) shows how @xmath66 varies with @xmath0 for systems of size @xmath67 .
fig .
[ fig : r_trans](b ) shows that scaling of the form @xmath68 is successful in making the data for different @xmath27 in fig .
[ fig : r_trans](a ) collapse onto one curve .
data collapse occurs also for @xmath69 and @xmath70 , indicating clearly that it is @xmath27 which controls the finite size scaling .
we get the best collapse when the constant in the exponential is @xmath71 which is in good agreement with the analytical estimate @xmath72 .
this implies that the crossover to thermalization is at a coupling @xmath73 that is exponentially small in system size , so that level statistics become goe at infinitesimal @xmath0 in the thermodynamic limit .
( defined in the text ) in the @xmath14-bit hamiltonian as @xmath0 is increased for system sizes @xmath74 and @xmath75 .
data is averaged over @xmath49 eigenstates obtained from several disorder configurations .
( b ) collapse of data in ( a ) is in good agreement with analytic arguments for the finite size scaling presented in the main text , and depends only on @xmath27 . ]
another test of thermalization is checking whether the eigenstates obey the eigenstate thermalization hypothesis ( eth ) @xcite . the eth states that the expectation value of a local operator should be the same in every eigenstate within a small energy window . for a localized system
this will not be the case . in fig .
[ fig : eth ] , we show how eigenstate thermalization sets in as @xmath0 is increased .
we choose an energy window around the center of the band and calculate the standard deviation of the expectation value of @xmath76 for all eigenstates within the window .
explicitly , we define @xmath77,\ ] ] where the overline denotes averaging over an energy window of width @xmath78 in the middle of the band and @xmath79 is an eigenstate of the coupled system and bath .
we choose @xmath80 . after averaging over disorder distributions ,
we expect to find @xmath81 for a thermalized system .
fig .
[ fig : eth](a ) shows how @xmath82 approaches 0 as @xmath0 is increased for different system sizes . fig .
[ fig : eth](b ) shows that @xmath82 scales with @xmath0 similar to @xmath66 .
the exponent here is @xmath83 , also close to the estimated analytical value .
-bit hamiltonian as @xmath0 is increased for system sizes @xmath69 , @xmath84 , @xmath85 , @xmath86 , @xmath87 and @xmath75 .
@xmath82 as defined in the text is measured at the site of the central spin .
data is averaged over @xmath49 eigenstates obtained from several disorder configurations .
( b ) collapse of data in ( a ) agrees with analytical estimates of finite size scaling for @xmath88 . for a finite size system with @xmath27 spins in the bath ,
the eigenstates become effectively thermal for @xmath89 , implying that eigenstates in the thermodynamic limit become thermal for infinitesimal @xmath0 . ]
we now turn to an analysis of the spectral functions of local operators .
henceforth we are working with the physical degrees of freedom , eq .
( 1 ) and ( 6 ) .
we examine the spectral function from an exact eigenstate @xmath90 where @xmath91 is the @xmath92 eigenstate of the combined system and bath .
we note that since we are working with a finite size system with a discrete spectrum , the spectral function will always consist of a set of delta functions . at @xmath93 ,
the delta functions should have minimum spacing @xmath94 , equal to the many body level spacing in the system . at non - zero @xmath0 , each ` parent ' delta function will split into exponentially many descendants , with a typical spacing @xmath95 . a fine binning in energy with bin size greater than @xmath95
will then yield a smooth spectral function , with the ` parent ' delta functions of the system having been ` broadened ' by coupling to the bath . to investigate this broadening ,
it is convenient to take @xmath96 .
we therefore take @xmath97 and @xmath98 , and investigate how the ` line broadening ' evolves with @xmath0 for @xmath99 .
details of the procedure are outlined in the supplementary material , and the results are illustrated in fig .
[ fig : linewidth ] for @xmath100 .
the mean and median linewidth at a particular value of @xmath0 are significantly different .
this is a result of the long tails in the distribution of the linewidth ( see supplement ) .
fig .
[ fig : linewidth ] shows that at the larger values of @xmath0 we study , a log - log plot of the median vs @xmath0 appears to fit well to a straight ( dashed ) line . for
the system sizes that we are able to access , the straight line fit suggests @xmath101 , where @xmath102 increases as the size of the bath increases , reaching @xmath103 for @xmath104 .
we note that while a simple application of the golden rule predicts @xmath105 , a more careful analysis @xcite suggests that the true scaling should be @xmath106 .
the solid lines in fig .
[ fig : linewidth ] are a fit to this theoretical prediction , and are consistent with the data , except at smallest @xmath0 .
the discrepancy at smallest @xmath0 and the difference between median and mean are worthwhile topics for future work . for a system of @xmath10-bits with @xmath69 and
@xmath107 averaged over more than 38000 eigenstates obtained from several disorder configurations at @xmath100 .
@xmath108 for the sizes shown here .
the mean and the median of the probability distribution of the linewidth @xmath109 are extracted from the data as discussed in the appendix .
the dotted lines are linear fits to the data .
the solid lines are fits to the theoretical prediction .
[ fig : linewidth ] ] finally , we analyze the behavior of the spectral function averaged over all sites and eigenstates of the system , for @xmath110 .
we note that the hamiltonian ( 1 ) has a delocalization - localization phase transition at @xmath8 .
fig .
[ fig : pbits](a ) shows @xmath111 on the delocalized side of the transition for a small value of @xmath0 .
@xmath111 is smooth everywhere .
( the graininess is a result of the small system size . )
fig .
[ fig : pbits](b ) is on the localized side of the transition , with the system almost decoupled from the bath . here
, @xmath111 consists of clusters of narrow spectral lines , with a hierarchy of energy gaps , just as was shown to be the case for @xmath14-bit spectral functions in @xcite .
@xmath111 vanishes at @xmath112 .
thus , local spectral functions can distinguish between extended and localized phases . in fig .
[ fig : pbits](c - e ) we examine how the @xmath10-bit spectral functions evolve as @xmath0 increases .
we see that the line broadening increases and different lines start to overlap with each other , washing out the weaker spectral features , but larger gaps remain .
the zero - frequency gap also fills in with increasing @xmath0 .
the spectral functions retain signatures of localization even for @xmath113 when the eigenstates of the combined system and bath are effectively thermal , and get washed out when @xmath0 becomes comparable to the characteristic energy scales in the system ( i.e. @xmath114 ) . in conclusion
, we have investigated the signatures of localization in a disordered system weakly coupled to a heat bath using exact diagonalization .
the wave functions are found to exhibit a crossover to thermalization as a function of coupling to the bath .
the crossover coupling is proportional to the many body level spacing in the bath , and vanishes exponentially fast in the limit of a large bath size .
in contrast , the spectral functions of local operators are found to show more robust signatures of proximity to a localized phase .
while the spectral functions are smooth and continuous in the delocalized phase ( after coarse graining on the scale of the many body level spacing ) , the spectral functions in the localized phase consist of narrow spectral lines , and contain a hierarchy of gaps , as well as a gap at zero frequency that persists even after spatial averaging .
increasing the coupling to the bath increases the line broadening ( in a manner that we calculate ) and washes out these features .
however , signatures of localization survive in the spectral functions even at couplings to the bath where the exact eigenstates are effectively thermal ( fig .
1 ) . _
acknowledgments : _ rn would like to thank sarang gopalakrishnan and david huse for a collaboration on related ideas .
this work was supported by doe grant de - sc0002140 .
rnb . acknowledges the hospitality of the institute for advanced study , princeton while this work was being done .
rn was supported by a pcts fellowship .
sj was supported by the porter ogden jacobus fellowship of princeton university .
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a few years after paczyski s proposal ( paczyski 1986 ) , the collaboration engaged in long term microlensing observations towards the magellanic clouds in order to probe the galactic halo . 1 and experiments set strong limits on the maximum contribution of low mass objects to the halo of the milky way ( alcock et al .
1998 ) . towards the
, the optical depth has been estimated by as @xmath0 , from 8 events ( alcock et al .
1997a ) ; the time scales associated with these events indicate high mass lenses ( @xmath1 ) that are not observed visually .
based on 2 candidates , 1 gave an upper limit on the halo mass fraction in s ( ansari et al .
1996 ) that is below that required to explain the rotation curve of our galaxy .. ] it has been suggested that the lenses might be in the bar / disk of the itself ( sahu 1994,wu 1994 ) ; but simple dynamical arguments seem to rule out this possibility ( gould 1995 ) . nevertheless , more complicated models allow for a larger optical depth ( @xmath2 ) .
microlensing search provides a test of the halo - lens hypothesis ; in this model both the optical depth and the typical durations should be similar towards the and the .
to date , two events have been observed ; they are significantly longer than the average for events
. however , no definite conclusion can be drawn from this without more events .
one candidate , -97 - 1/-97 - 1 was found in this analysis ( alcock 1997b , palanque - delabrouille 1998 ) .
the result of a microlensing fit leads to an einstein radius crossing time @xmath3 days .
the @xmath4 is 261 for 279 d.o.f .
, taking into account the @xmath5 intrinsic variability of the amplified star ( @xmath6 days , see palanque - delabrouille et al . 1998 , udalski et al .
this single event allows us to constrain the halo composition , in particular we exclude that more than 50 % of the standard dark halo is made of @xmath7 objects .
the collaboration sent a first level alert for this event on may @xmath8 , 1998 , followed by an announcement that a caustic crossing had occurred on june @xmath9 .
a second caustic crossing was predicted around june @xmath10 .
after a planned technical maintenance , we could only observe in great detail the end of the second caustic crossing . using this data alone , we could extract a limit on the caustic crossing time , which together with public data from enabled us to determine ( at a 90% likelihood ) that the deflector is in the ( afonso et al .
this result has been confirmed and improved by other groups , leading to a common publication ( afonso et al .
1999 , and references therein ) .
since august 1996 , we have been monitoring 66 one - square - degree fields towards the .
of these , data prior to may 1998 from 25 square - degrees spread over 43 fields are being analyzed .
this represents 450 gbytes of raw data , and about 100 days of to produce the light curves .
.results of microlensing fits to the candidate 2 - -1 and 2 - -2 .
@xmath11 is the einstein radius crossing time , @xmath12 is the impact parameter , and @xmath13 are the blending coefficients in both colors . [ cols="<,<,^,^,^,^,^",options="header " , ] about 90 images of each field were taken , with exposure times from 3 min in the center to 12 min in the outermost regions ; the sampling is one point every 5 days on average .
we report a preliminary analysis of the light curves of 17.5 million stars using a new set of selection criteria to isolate microlensing candidates . starting from the images we built a star catalog using the photometry package , and then removed the 90% most stable stars . among stars with the most significant variations
, we used the quality of the microlensing fit to select the candidates . in order to maximize the number of surveyed stars and to study the background of microlensing searches
, we did not remove any star based solely on its position in the color - magnitude diagram . with this strategy
, we characterized the blue bumper stars that mimic a microlensing signal . in this way we removed the stars , located in the upper left of the color - magnitude diagram , that pass all cuts , but have the following features : @xmath14 , and @xmath15 , where @xmath16 are the red(blue ) observed amplifications . among the 17.5 million light curves
, two events passed all the cuts ( see table [ cand1 ] ) .
event 2 - -1 is a main sequence star blended in red ( 76% of the visible flux was magnified ) .
event 2 - -2 is located just under the red giant clump , and necessitates a deeper photometry study to confirm its validity ; it is consistent nevertheless with being achromatic . to set conservative limits on the halo mass fraction @xmath17 comprised of compact objects of mass @xmath18
, we can assume that the observed events are in the dark halo .
we only consider the standard spherical halo model described in palanque - delabrouille et al .
the most probable mass associated with both candidates is determined by finding the mass for which the ( near gaussian ) distribution of @xmath19 peaks at the geometric mean @xmath20 the resulting mass is found to be @xmath21 .
we can also define a 68% confidence interval as follows : the upper ( lower ) bound is determined as the mass for which 16% of detected events would have durations greater ( less ) than @xmath22 .
this mass interval is found to be : @xmath23 \ , { \rm m}_\odot$ ] .
let @xmath24 be the total expected number of events for the standard halo model ( considering our detection efficiency ) . to be conservative
, we simply consider our two candidates without taking their mass into account . in this way ,
the 95% cl poisson limit for a given mass is obtained by computing the expected number of events @xmath25 compatible with the observations : @xmath26 , where @xmath27 is the poisson probability of observing @xmath28 events where @xmath29 are expected .
the fraction @xmath17 for each mass @xmath18 is given by @xmath30 .
this allows us to put a preliminary constraint excluding ( at 95 % cl ) that 60 % of the dark halo is composed of objects in the range @xmath31 \ ; \rm{m}_\odot$ ] ( see fig . [ exclusion ] ) .
there is growing evidence , from three different data sets ( 1- , 2- , and 2- ) that the standard spherical halo model fully comprised of @xmath32 \ ; m_{\odot}$ ] s is inadequate .
the only way to evade this limit is to suppose that the masses of the s are greater than @xmath33 , or to consider non spherical halos .
another way to understand the observed events is to assume that they are due to self - lensing , in which case it is important to study their spatial distribution on the face of the . in that respect ,
it is worth noting that our limit is derived from more than 17 million stars spread over 43 square degrees , in comparison with the experiment that monitored 9 millions stars covering 11 square degrees of the bar ( alcock et al .
finally , more exotic microlensing events ( parallax effect , binary lens ... ) would allow us to locate precisely some lenses , and so to test the self - lensing hypothesis .
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udalski , a. et al .
1994 , apj , 435 , 66 . | 2 is a second generation microlensing experiment operating since mid-1996 at the european southern observatory ( eso ) at la silla ( chile ) .
we present the two year analysis from our microlensing search towards the small magellanic cloud ( ) , and report on the intensive observation of the caustic crossing event -98 - 1 and the limit derived on the location of the lens .
we also give preliminary results from our search towards the large magellanic cloud ( ) ; 25 square degrees are being analyzed and two candidates have been found .
this allows us to set another limit on the halo mass fraction comprised of compact objects . |
it is by now well - established that neutrinos are massive and mixed , and that these properties lead to the oscillations observed in measurements of neutrinos produced in the sun @xcite@xcite , in the atmosphere @xcite , by accelerators @xcite , and by reactors @xcite .
the mixing model predicts not only neutrino oscillations in vacuum , but also the effects of matter on the oscillation probabilities ( the ` msw ' effect ) @xcite . to date , the effects of matter have only been studied in the solar sector , where the neutrinos passage through the core of both the sun and the earth can produce detectable effects .
the model predicts three observable consequences for solar neutrinos : a suppression of the @xmath6 survival probability below the average vacuum value of @xmath16 for high - energy ( @xmath4b ) neutrinos , a transition region between matter - dominated and vacuum - dominated oscillations , and a regeneration of @xmath6s as the neutrinos pass through the core of the earth ( the day / night effect ) .
in addition to improved precision in the extraction of the total flux of @xmath4b neutrinos from the sun , an advantage of the low energy threshold analysis ( leta ) presented here is the enhanced ability to explore the msw - predicted transition region and , in addition , more stringent testing of theories of non - standard interactions that affect the shape and position of the predicted rise in survival probability @xcite@xcite .
we present in this article a joint analysis of the data from the first two data acquisition phases of the sudbury neutrino observatory ( sno ) , down to an effective electron kinetic energy of @xmath0 mev , the lowest analysis energy threshold yet achieved for the extraction of neutrino signals with the water cherenkov technique .
the previous ( higher threshold ) analyses of the two data sets have been documented extensively elsewhere @xcite , and so we focus here on the improvements made to calibrations and analysis techniques to reduce the threshold and increase the precision of the results .
we begin in section [ sec : detector ] with an overview of the sno detector and physics processes , and provide an overview of the data analysis in section [ sec : anal_overview ] . in section [ sec : dataset ]
we briefly describe the sno phase i and phase ii data sets used here .
section [ sec : montecarlo ] describes changes to the monte carlo detector model that provides the distributions used to fit our data , and section [ sec : hitcal ] describes the improvements made to the hit - level calibrations of pmt times and charges that allow us to eliminate some important backgrounds .
sections [ sec : recon]- [ sec : beta14 ] describe our methods for determining observables like position and energy , and estimating their systematic uncertainties .
section [ sec : cuts ] describes the cuts we apply to our data set , while section [ sec : treff ] discusses the trigger efficiency and section [ sec : ncap ] presents the neutron capture efficiency and its systematic uncertainties .
we provide a detailed discussion of all background constraints and distributions in section [ sec : backgrounds ] .
section [ sec : sigex ] describes our ` signal extraction ' fits to the data sets to determine the neutrino fluxes , and section [ sec : results ] gives our results for the fluxes and mixing parameters .
sno was an imaging cherenkov detector using heavy water ( @xmath10h@xmath17o , hereafter d@xmath17o ) as both the interaction and detection medium @xcite .
sno was located in vale inco s creighton mine , at @xmath18 n latitude , @xmath19 w longitude .
the detector was 1783 m below sea level with an overburden of 5890 meters water equivalent , deep enough that the rate of cosmic - ray muons passing through the entire active volume was just 3 per hour .
one thousand metric tons ( tonnes ) of d@xmath17o was contained in a 12 m diameter transparent acrylic vessel ( av ) .
cherenkov light produced by neutrino interactions and radioactive backgrounds was detected by an array of 9456 hamamatsu model r1408 20 cm photomultiplier tubes ( pmts ) , supported by a stainless steel geodesic sphere ( the pmt support structure or psup ) .
each pmt was surrounded by a light concentrator ( a ` reflector ' ) , which increased the effective photocathode coverage to nearly @xmath20% .
the channel discriminator thresholds were set to 1/4 of a photoelectron of charge . over seven kilotonnes ( 7@xmath21 kg ) of h@xmath17o shielded the d@xmath17o from external radioactive backgrounds : 1.7 kt between the av and the psup , and 5.7 kt between the psup and the surrounding rock .
extensive purification systems were used to purify both the d@xmath17o and the h@xmath17o .
the h@xmath17o outside the psup was viewed by 91 outward - facing 20 cm pmts that were used to identify cosmic - ray muons .
an additional 23 pmts were arranged in a rectangular array and suspended in the outer h@xmath17o region to view the neck of the av .
they were used primarily to reject events not associated with cherenkov light production , such as static discharges in the neck .
the detector was equipped with a versatile calibration - source deployment system that could place radioactive and optical sources over a large range of the @xmath22-@xmath23 and @xmath24-@xmath23 planes ( where @xmath23 is the central axis of the detector ) within the d@xmath17o volume .
deployed sources included a diffuse multi - wavelength laser that was used to measure pmt timing and optical parameters ( the ` laserball ' ) @xcite , a @xmath25n source that provided a triggered sample of 6.13 mev @xmath26s @xcite , and a @xmath4li source that delivered tagged @xmath27s with an endpoint near 14 mev @xcite . in addition , 19.8 mev @xmath26s were provided by a @xmath28 ( ` pt ' ) source @xcite and neutrons by a @xmath29cf source .
some of the sources were also deployed on vertical lines in the h@xmath17o between the av and psup .
` spikes ' of radioactivity ( @xmath30na and @xmath31rn ) were added at times to the light water and d@xmath17o volumes to obtain additional calibration data .
table [ tbl : cal_sources ] lists the primary calibration sources used in this analysis . | results are reported from a joint analysis of phase i and phase ii data from the sudbury neutrino observatory .
the effective electron kinetic energy threshold used is @xmath0 mev , the lowest analysis threshold yet achieved with water cherenkov detector data . in units of @xmath1 @xmath2 s@xmath3
, the total flux of active - flavor neutrinos from @xmath4b decay in the sun measured using the neutral current ( nc ) reaction of neutrinos on deuterons , with no constraint on the @xmath4b neutrino energy spectrum , is found to be @xmath5 these uncertainties are more than a factor of two smaller than previously published results . also presented are the spectra of recoil electrons from the charged current reaction of neutrinos on deuterons and the elastic scattering of electrons .
a fit to the sno data in which the free parameters directly describe the total @xmath4b neutrino flux and the energy - dependent @xmath6 survival probability provides a measure of the total @xmath4b neutrino flux @xmath7 . combining these new results with results of all other solar experiments and the kamland reactor experiment yields best - fit values of the mixing parameters of @xmath8 degrees and @xmath9 ev@xmath10 .
the global value of @xmath11 is extracted to a precision of @xmath12% . in a three - flavor analysis
the best fit value of @xmath13 is @xmath14 .
this implies an upper bound of @xmath15 ( 95% c.l . ) . |
despite a few important successes ( e.g. , bean et al . 2007 , and references therein ) , astrometric measurements with mas precision have so far proved of limited utility when employed as either a follow - up tool or to independently search for planetary mass companions orbiting nearby stars ( see for example sozzetti 2005 , and references therein ) . in several past exploratory works
( casertano et al . 1996 ; lattanzi et al .
1997 , 2000 ; sozzetti et al 2001 , 2003 ) , we have shown in some detail what space - borne astrometric observatories with @xmath0as - level precision , such as gaia ( perryman et al .
2001 ) , can achieve in terms of search , detection and measurement of extrasolar planets of mass ranging from jupiter - like to earth - like . in those studies we adopted a qualitatively correct description of the measurements that each mission will carry out , and we estimated detection probabilities and orbital parameters using realistic , non - linear least squares fits to those measurements .
those exploratory studies , however , need updating and improvements . in the specific case of planet detection and measurement with gaia
, we have thus far largely neglected the difficult problem of selecting adequate starting values for the non - linear fits , using perturbed starting values instead .
the study of multiple - planet systems , and in particular the determination of whether the planets are coplanar within suitable tolerances is incomplete .
the characteristics of gaia have changed , in some ways substantially , since our last work on the subject ( sozzetti et al 2003 ) .
last but not least , in order to render the analysis truly independent from the simulations , these studies should be carried out in double - blind mode .
we present here a substantial program of double - blind tests for planet detection with gaia ( preliminary findings were recently presented by lattanzi et al .
( 2005 ) ) , with the three - fold goal of obtaining : a ) an improved , more realistic assessment of the detectability and measurability of single and multiple planets under a variety of conditions , parametrized by the sensitivity of gaia ; b ) an assessment of the impact of gaia in critical areas of planet research , in dependence on its expected capabilities ; and c ) the establishment of several centers with a high level of readiness for the analysis of gaia observations relevant to the study of exoplanets .
we carry out detailed simulations of gaia observations of synthetic planetary systems and develop and utilize in double - blind mode independent software codes for the analysis of the data , including statistical tools for planet detection and different algorithms for single and multiple keplerian orbit fitting that use no a priori knowledge of the true orbital parameters of the systems .
overall , the results of our earlier works ( e.g. , lattanzi et al . 2000 ; sozzetti et al . 2001 , 2003 ) are essentially confirmed , with the fundamental improvement due to the successful development of independent orbital fitting algorithms applicable to real - life data that do not utilize any a priori knowledge of the orbital parameters of the planets . in particular , the results of the t1 test ( planet detection ) indicate that planets down to astrometric signatures @xmath1 @xmath0as , corresponding to @xmath2 times the assumed single - measurement error , can be detected reliably and consistently , with a very small number of false positives ( depending on the specific choice of the threshold for detection ) .
the results of the t2 test ( single - planet orbital solutions ) indicate that : 1 ) orbital periods can be retrieved with very good accuracy ( better than 10% ) and small bias in the range @xmath3 yrs , and in this period range the other orbital parameters and the planet mass are similarly well estimated .
the quality of the solutions degrades quickly for periods longer than the mission duration , and in particularly the fitted value of @xmath4 is systematically underestimated ; 2 ) uncertainties in orbit parameters are well understood ; 3 ) nominal uncertainties obtained from the fitting procedure are a good estimate of the actual errors in the orbit reconstruction . modest discrepancies between estimated and actual errors arise only for planets with extremely good signal ( errors are overestimated ) and for planets with very long period ( errors are underestimated ) ; such discrepancies are of interest mainly for a detailed numerical analysis , but they do not touch significantly the assessment of gaia s ability to find planets and our preparedness for the analysis of perturbation data .
the results of the t3 test ( multiple - planet orbital solutions ) indicate that 1 ) over 70% of the simulated orbits under the conditions of the t3 test ( for every two - planet system , periods shorter than 9 years and differing by at least a factor of two , @xmath5 , @xmath6 ) are correctly identified ; 2 ) favorable orbital configurations ( both planet with periods @xmath7 yr and astrometric signal - to - noise ratio @xmath8 , redundancy of over a factor of 2 in the number of observations ) have periods measured to better than 10% accuracy @xmath9 of the time , and comparable results hold for other orbital elements ; 3 ) for these favorable cases , only a modest degradation of up to @xmath10 in the fraction of well - measured orbits is observed with respect to single - planet solutions with comparable properties ; 4 ) the overall results are mostly insensitive to the relative inclination of pairs of planetary orbits ; 5 ) over 80% of the favorable configurations have @xmath11 measured to better than 10 degrees accuracy , with only mild dependencies on its actual value , or on the inclination angle with respect to the line of sight of the planets ; 6 ) error estimates are generally accurate , particularly for fitted parameters , while modest discrepancies ( errors are systematically underestimated ) arise between formal and actual errors on @xmath11 .
g dwarf primary at 200 pc , while the blue curves are for a 0.5-@xmath12 m dwarf at 25 pc .
the radial velocity curve ( pink line ) is for detection at the @xmath13 level , assuming @xmath14 m s@xmath15 , @xmath16 , and 10-yr survey duration . for transit photometry ( green curve ) , @xmath17 milli - mag , @xmath18 , @xmath19 @xmath12 , @xmath20 @xmath21 , uniform and dense ( @xmath22 datapoints ) sampling .
black dots indicate the inventory of exoplanets as of october 2007 .
transiting systems are shown as light - blue filled pentagons .
jupiter and saturn are also shown as red pentagons.,scaledwidth=75.0% ]
[ nplan ] in figure [ detmeas ] we show gaia s discovery space in terms of detectable and measurable planets of given mass and orbital separation around stars of given mass at a given distance from earth ( see caption for details ) . from the figure
, one would then conclude that gaia could discover and measure massive giant planets ( @xmath23 @xmath24 ) with @xmath25 au orbiting solar - type stars as far as the nearest star - forming regions , as well as explore the domain of saturn - mass planets with similar orbital semi - major axes around late - type stars within 30 - 40 pc .
these results can be turned into a number of planets detected and measured by gaia , using galaxy models and the current knowledge of exoplanet frequencies . by inspection of tables [ nplan ] and [ nmult ]
, we then find that gaia could measure accurately thousands of giant planets , and accurately determine coplanarity ( or not ) for a few hundred multiple systems with favorable configurations .
in conclusion , gaia s main strength continues to be the ability to measure actual masses and orbital parameters for possibly thousands of planetary systems .
the gaia data have the potential to a ) significantly refine our understanding of the statistical properties of extrasolar planets : the predicted database of several thousand extrasolar planets with well - measured properties will allow for example to test the fine structure of giant planet parameters distributions and frequencies , and to investigate their possible changes as a function of stellar mass with unprecedented resolution ; b ) help crucially test theoretical models of gas giant planet formation and migration : for example , specific predictions on formation time - scales and the role of varying metal content in the protoplanetary disk will be probed with unprecedented statistics thanks to the thousands of metal - poor stars and hundreds of young stars screened for giant planets out to a few aus ; c ) improve our comprehension of the role of dynamical interactions in the early as well as long - term evolution of planetary systems : for example , the measurement of orbital parameters for hundreds of multiple - planet systems , including meaningful coplanarity tests will allow to discriminate between various proposed mechanisms for eccentricity excitation ; d ) aid in the understanding of direct detections of giant extrasolar planets : for example , actual mass estimates and full orbital geometry determination for suitable systems will inform direct imaging surveys about where and when to point , in order to estimate optimal visibility , and will help in the modeling and interpretation of giant planets phase functions and light curves ; e ) provide important supplementary data for the optimization of the target selection for darwin / tpf : for example , all f - g - k - m stars within the useful volume ( @xmath26 pc ) will be screened for jupiter- and saturn - sized planets out to several aus , and these data will help probing the long - term dynamical stability of their habitable zones , where terrestrial planets may have formed , and maybe found . | in this paper , we first summarize the results of a large - scale double - blind tests campaign carried out for the realistic estimation of the gaia potential in detecting and measuring planetary systems .
then , we put the identified capabilities in context by highlighting the unique contribution that the gaia exoplanet discoveries will be able to bring to the science of extrasolar planets during the next decade . |
in this supplementary material , we compare the value of the penetration depth obtained from experiments @xcite with the prediction from homes law ; for the latter , we use a combination of the experimental data obtained from optical - conductivity and dc transport . for each value of the doping ( @xmath8 )
, we estimate the ( approximate ) dc resistivity ( @xmath80 ) by extrapolating the curves to @xmath9 , from the transport data in fig.1(b ) of ref.@xcite .
we estimate the value of @xmath81 , where @xmath23 is the superconducting gap , from the data for optical conductivity in the superconducting state , as shown in fig .
3(b ) of ref . @xcite . since @xmath7 remains relatively unchanged as a function of @xmath8 in the vicinity of optimal doping , we assume @xmath82 to be independent of @xmath8 such that @xmath83@xmath84s@xmath85 .
then , in the dirty limit , _ s = _ . in order to obtain the penetration depth
, we need to restore various dimensionful constants such that , _
l^2(0)= , where @xmath86 m / s ) is the speed of light and @xmath87 f / m ; 1 f=1 @xmath88s ) is the permitivity of free space .
the values obtained are shown in the table below and have been presented in fig . 2 of the main text , along with a comparison to the experimental data @xcite . | we present a theory for the large suppression of the superfluid - density , @xmath0 , in bafe@xmath1(as@xmath2p@xmath3)@xmath1 in the vicinity of a putative spin - density wave quantum critical point at a p - doping , @xmath4 .
we argue that the transition becomes weakly first - order in the vicinity of @xmath5 , and disorder induces puddles of superconducting and antiferromagnetic regions at short length - scales ; thus the system becomes an electronic micro - emulsion .
we propose that frustrated josephson couplings between the superconducting grains suppress @xmath0 .
in addition , the presence of ` normal ' quasiparticles at the interface of the frustrated josephson junctions will give rise to a highly non - trivial feature in the low - frequency response in a narrow vicinity around @xmath6 .
we propose a number of experiments to test our theory . _
introduction.- _ an important focus of the study of high temperature superconductivity ( sc ) has been on the role of antiferromagnetism ( afm ) and its relation to sc @xcite .
there is clear evidence across many different families of compounds that sc appears in close proximity to an afm phase @xcite ; these families include the iron - pnictides , the electron - doped cuprates and the heavy - fermion superconductors .
moreover , the optimal transition temperature ( @xmath7 ) of the sc is often situated where the normal state afm quantum critical point ( qcp ) would have been located , in the absence of superconductivity .
the experimental detection of the qcp is often challenging in the normal state , and more so in the superconducting state .
recently , a number of measurements were reported in a member of the pnictide family , bafe@xmath1(as@xmath2p@xmath3)@xmath1 , as a function of the isovalent p - doping , @xmath8 .
the experiments show a phase transition involving onset of spin - density wave ( sdw ) order in the normal state above @xmath7 , which extrapolates to a @xmath9 sdw qcp ( see @xcite and references therein ) .
these experiments include : ( _ i _ ) a sharp enhancement in the effective mass , @xmath10 , upon approaching a critical doping from the overdoped side , as obtained from de haas - van alphen oscillations @xcite and from the jump in the specific - heat at @xmath7 @xcite , and , ( _ ii _ ) a vanishing curie - weiss temperature ( @xmath11 ) , extracted from the @xmath12 measurements using nmr .
as we will review below , a number of puzzling results have appeared from experiments investigating whether the sdw qcp actually survives `` under the sc dome . '' here we propose a resolution of these puzzles by postulating a weakly first - order transition for the onset of sdw order in the presence of sc order ( see fig .
[ ph]a ) .
our results are independent of the specific microsopic mechanism responsible for rendering the transition weakly first - order @xcite .
it is well known that ` random bond ' disorder has a strong effect on symmetry - breaking first - order transitions @xcite , and ultimately replaces them with a disorder - induced second order transition in two dimensional systems .
our main claim is that the inhomogeneities associated with these highly relevant effects of disorder can resolve the experimental puzzles .
the possiblity of a qcp within the sc state was investigated by measurements @xcite of the zero temperature london penetration depth , @xmath13 ( @xmath14 superfluid - density ) , as a function of @xmath8 .
a sharp peak in @xmath15 was observed at @xmath16 and interpreted as evidence for a qcp @xcite .
however , this interpretation is at odds with general theoretical considerations @xcite concerning a qcp associated with the onset of sdw order in the presence of a superconductor with gapped quasiparticle excitations @xcite .
these considerations suggest that such systems will display a _ monotonic _ variation in @xmath15 across the qcp , rather than a sharp peak ( see dashed - blue / solid - red curves in fig .
[ ph]b ) @xcite . as a first step toward resolving this discrepancy ,
it is useful to place measurements of @xmath0 in the context of what is known about the normal state conductivity of the bafe@xmath1(as@xmath2p@xmath3)@xmath1 system , as these quantities are intimately related through a sum rule .
the low temperature superfluid density of a spatially homogeneous superconductor can be estimated from the missing area " relation , _ s_0 ^ 2/ ( z)dz , [ homese ] where @xmath17 is the elastic scattering rate and @xmath18 . in the dirty limit where @xmath19 , the above relation yields homes law @xcite , @xmath20 , whereas in the clean limit @xmath21 where @xmath22 is the conductivity spectral weight in the normal state
. eqn .
[ homese ] is particularly useful when the normal state resistivity data can reasonably be extrapolated to @xmath9 . by combining dc transport data as a function of @xmath8 @xcite and a measurement of 2@xmath23 from optical conductivity @xcite , eq .
[ homese ] provides a lower bound on @xmath15 ( with the assumption that @xmath23 is independent of @xmath8 ) .
fig.[homes ] shows @xmath15 as a function of @xmath8 obtained under this assumption ( details of the procedure are presented as supplementary information ) .
the decrease of superfluid density on the underdoped side reflects the growth in residual resistivity that begins as @xmath8 drops below about 0.33 .
the values of @xmath15 estimated from eq .
[ homese ] form a baseline for comparison with the experimental results presented in ref .
@xcite . on the same graph in fig .
[ homes ] , we show the experimentally measured @xmath15 @xcite . the data generally reflect the trend expected from the variation in the residual resistivity , with the exception of the sample with @xmath24 , in which the condensate spectral weight is suppressed by about 40% from the homes law estimate . given the constraints imposed by the sum rule ,
there are two possible sources of this discrepancy : ( _ i _ ) the quasiparticle mass could be renormalized at this value of @xmath8 , corresponding to an intrinsic decrease in @xmath22 , or , ( _ ii _ ) a considerable fraction of the ( unrenormalized ) @xmath22 could fail to contribute to the low temperature superfluid density .
the latter possibility is suggested within the scenario that we develop here .
we analyze the above experiments by assuming a weakly first - order transition @xcite , and argue that the presence of quenched disorder leads to formation of a _ micro - emulsion _ at small scales @xcite .
the system consists of sc puddles , where some of the puddles additionally have sdw order ( see fig .
[ ph]a inset ) .
the sdw(+sc ) regions , which have a locally well - developed antiferromagnetic moment but no long - range orientational order , act as barriers between the different sc grains . upon moving deeper into the ordered side of the transition , the sdw(+sc )
regions start to percolate and crossover to a state with long - range sdw order ; this is the regime with a microscopically coexistent sc+sdw . as a function of decreasing @xmath8 ,
the micro - emulsion is therefore a transitional state ( shown as grey region in fig . [ ph]a ) between a pure sc and a coexistent sc+sdw .
recent experiments in the vicinity of optimal doping using neutron - scattering and nmr have found results broadly consistent with our proposed phase diagram @xcite .
we note that the granular nature of superconductivity should have no effect on the bulk @xmath7 in the presence of percolating sc channels . _
model.- _ when the system is well described in the vicinity of @xmath5 by a micro - emulsion as explained above , the phase fluctuations associated with the sc grains ( shown as purple regions in fig .
[ ph]a inset ) , can be modeled by the following effective theory , h_= - _ a , bj_ab(_a-_b ) , where @xmath25 represent the josephson junction ( jj ) couplings between grains ` @xmath26 ' and ` @xmath27 ' .
we have ignored the capacitive contributions .
the josephson current across the junction will be given by @xmath28 , and @xmath25 may therefore be interpreted as the lattice version of the local superfluid density , @xmath29 , i.e. @xmath30 , with @xmath31 representing the superfluid - current and velocity respectively . having a frustrated jj ( also known as a @xmath32junction ) with a negative value of @xmath25 leads to a local suppression in @xmath0 .
similar ideas have been discussed in the past in a variety of contexts ( see refs .
@xcite for a specific example ) , though the mechanism considered here will be different .
we shall now propose an explicit scenario under which a suppression in @xmath0 arises in the vicinity of putative magnetic qcps , utilizing the sc gap structure in the material under question .
the basic idea is as follows : suppose that the tunneling of electrons between the two grains is mediated by the sdw moment in the intervening region @xcite , and is accompanied by a transfer of finite momentum that scatters them from a hole - like to an electron - like pocket . because the sc gaps on the two pockets have a relative phase - difference of @xmath33 , the jj coupling will be frustrated @xcite .
let us first focus on a single grain .
in order to capture the multi - band nature of the scs , we introduce two superconducting order parameters , @xmath34 with @xmath35 to model the @xmath36 state on the two pockets .
microscopically , these belong to regions in the grain having different momenta , @xmath37 , parallel to the junction .
the gaps are related to the microscopic degrees of freedom @xcite via the following relation , _
i(z)=___i v__,____- _ , where @xmath38 creates an electron at position @xmath39 with momentum @xmath37 parallel to the junction and spin @xmath40 .
@xmath41 is the pairing interaction in the cooper channel and @xmath39 is the coordinate perpendicular to the junction with area @xmath42 .
the regions @xmath43 are defined as , @xmath44 and @xmath45 , where @xmath46 is an arbitrary momentum scale chosen such that @xmath47 ( see fig . [ jj ] for an illustration ) .
we ll assume that such a prescription is valid for each grain , with possibly different values of @xmath46 .
let us then write down a model for the two coupled sc grains with an intervening proximity coupled sdw that has a well developed moment , @xmath48 .
our notation is as follows : we use @xmath49 to denote the grain index and @xmath35 to denote the band index within each grain . from now on , we relabel @xmath37 as @xmath50 .
we introduce the nambu spinor , @xmath51 , where now @xmath52 creates an electron with momentum @xmath50 parallel to the junction and at a position @xmath39 ( label suppressed ) , which belongs to a region of band @xmath53 " within grain @xmath54 " .
the effective hamiltonian is given by , [ heff ] h_&=&h_+h_t , + h_&=&_,i , _
i,,^_i,,^ , + h_t&=&g_k ( ^a_+,,[_^0]_-,,^b + & & + ^a_-,,[_^0]_+,,^b ) + , where @xmath55 is the tunneling matrix element , @xmath56 @xmath57 act in nambu space and @xmath58 @xmath57 act in spin space . in the above
, @xmath59 corresponds to the bare pairing hamiltonian written for the @xmath60 bands within each of the two grains .
@xmath61 represents the sdw moment mediated hopping of electrons from one grain to the other ( represented by the @xmath62 superscripts ) and simultaneously scattering from one band to the other ( represented by the @xmath60 subscripts ) .
therefore , @xmath48 imparts a finite momentum ( along the interface ) to the electrons when it scatters them from the electron ( hole ) pocket on one grain to the hole ( electron ) pocket on the other grain ( shown as the black arrows in fig .
[ jj ] ) . _
results.- _ using the ambegaokar - baratoff relation @xcite , we can write the josephson coupling ( at @xmath9 ) between the two grains as , j_ab= where @xmath63 and @xmath64 represent the band indices on the different grains . since @xmath65 , the coupling @xmath66 .
note that the specific nature of the frustrated tunneling arises from the same spin - fluctuation mediated mechanism that is predominantly responsible for the @xmath67 pairing symmetry @xcite .
however , there will also be a direct tunneling term ( not included in eqn .
[ heff ] ) in the hamiltonian , which does not scatter the electrons from one pocket to the other , as they hop across the junction .
the contribution to the jj coupling from this term will be unfrustrated ( i.e. @xmath68 ) .
the ratio of the tunneling amplitudes in the two different channels is non - universal and depends on various microscopic details .
in particular , the emulsion is associated with a distribution of josephson - couplings , @xmath69 , with a mean coupling strength , @xmath70 .
if a substantial fraction of the jj couplings become negative due to the mechanism proposed above , @xmath71 will be small , and the superfluid density will be suppressed ( see green curve in fig.[ph]b ) .
we now propose a resolution as to the fate of the uncondensed spectral weight ( highlighted in fig .
[ homes ] ) , which can potentially be tested by measurements of the low frequency optical conductivity .
frustrated @xmath32junctions host gapless states at the interface between the two grains @xcite , giving rise to a finite density of states around zero energy ( see fig [ sigw ] inset ) . as a result of the gapless ` normal'-fluid component at the interface , a fraction @xmath72 of the spectral weight will be displaced from the superfluid - density to non - zero frequencies ( shaded region in fig . [ sigw ] ) .
given that the weight of the condensate is proportional to @xmath73 , the 40% suppression in @xmath0 for bafe@xmath1(as@xmath2p@xmath3)@xmath1 in the vicinity of the putative qcp corresponds to @xmath74 .
our proposed optical conductivity , @xmath75 , in the vicinity of penetration depth anomaly is shown in in fig [ sigw ] .
the spectrum shows clearly that the connection between normal state conductivity and superfluid density implied by eq .
[ homes ] will break down .
in particular , @xmath76 ( which is a property of the normal state ) , could vary monotonically with isovalent - doping across @xmath6 , while the abundance of low - energy excitations in the immediate vicinity of @xmath6 would give rise to a non - monotonic variation in the superfluid density .
this allows for an unusual way of rearranging spectral weight in the _ superconducting _ state below the gap , without violating optical sum - rules
. the above scenario will give rise to a number of interesting low temperature thermodynamic and transport properties , as we now discuss .
first of all , there should be a striking enhancement in the low - temperature thermal conductivity and specific - heat , as a function of @xmath8 in the narrow vicinity of @xmath6 , due to the ` normal'-component .
it is important to recall that this material has loop - like nodes on the electron - pockets @xcite .
however , the geometry of the electron - pockets and the magnitude of the gap do not change substantially in the vicinity of @xmath6 , and therefore it is unlikely that the contribution to the above quantities from the nodal - quasiparticles will have a drastic modificiation .
it should therefore be relatively straightforward to disentangle the contribution arising from the nodal versus the ` normal ' quasiparticles .
studying the nmr - spectra as a function of decreasing temperature ( across @xmath7 ) and down to sufficiently low temperatures in the vicinity of @xmath6 should also reveal the spatial inhomogeneity associated with the sdw regions .
a large residual density of states in the superconducting state has been detected at a particular p - doping via the power - law temperature dependence of @xmath77 @xcite . within our scenario
, there should be a striking enhancement in this quantity as a function of doping around @xmath6 .
finally , we note that a promising direction for future studies would be to measure the magnetic - field distribution due to the propagating currents in the emulsion using nv - based magnetometers @xcite . _
discussion.- _ the theoretical study in this paper was motivated by a number of remarkable experiments carried out in bafe@xmath1(as@xmath2p@xmath3)@xmath1 , as a function of @xmath8 in the normal and superconducting phases .
our primary objective was to provide an explanation for the striking enhancement of the london penetration depth in the vicinity of a putative sdw qcp in the sc state .
we developed a scenario based on the idea that true sdw criticality is masked by a weak first - order phase transition in the superconducting state at @xmath9 . in this picture ,
quenched disorder naturally gives rise to an _ emulsion _ at small length scales with puddles of sc and sdw(+sc ) .
it is then , in principle , possible for sdw moments at the interface of the sc grains to generate frustrated josephson couplings , which deplete the local superfluid - density .
our proposed scenario naturally calls for a number of experimental tests that should be carried out in the near future , which should directly look for both the spatial inhomogeneities associated with the emulsion @xcite , and probe the gapless excitations using thermodynamic probes , as explained above .
in addition to experiments on bafe@xmath1(as@xmath2p@xmath3)@xmath1 , it should be important to further investigate the contrasting behavior of the electron - doped system , ba(fe@xmath2co@xmath3)@xmath1as@xmath1 , where @xmath78 behaves monotonically as a function of @xmath8 across the putative qcp @xcite .
electron - doping leads to significantly higher amounts of disorder compared to the isovalently - doped case , and would therefore lead to puddles with typically much smaller size @xcite .
our proposed mechanism for the strong suppression of the superfluid - density in the isovalently - doped material relies on the existence of an emulsion with puddles of appreciable size , in the presence of an optimal amount of disorder .
a comparison of the nmr spectra in the narrow vicinity of the putative qcp in the electron and isovalently doped materials would shed light on these microscopic differences between the two families . finally , though we have hypothesized that the sdw onset transition _ inside _ the sc is , in the absence of disorder , a weak first order transition , we emphasize that the normal state properties are consistent with the presence of a hidden " qcp around optimal doping @xcite .
it is plausible that in the normal state , different experimental techniques are probing the critical fluctuations associated with not one , but distinct qcps as a function of @xmath8 . for instance
, @xmath10 extracted from high - field quantum oscillations is dominated by the vicinity of ` hot - spots ' , where quasiparticles are strongly damped due to coupling to the sdw fluctuations @xcite . on the other hand , strong critical fluctuations associated with the nematic order - parameter @xcite , that couple to the entire fermi - surface ,
would dominate @xmath10 extracted at zero - field from the jump in the specific heat at @xmath7 . _
acknowledgements.- _ we thank a. carrington , a. chubukov , n. curro , j.c .
davis , r. fernandes , k. ishida , m .- h .
julien , s. kivelson , y. matsuda , a. millis and a. vishwanath for useful discussions .
we thank k. hashimoto and y. matsuda for providing us with the data shown in fig.[homes ] .
dc is supported by the harvard - gsas merit fellowship and acknowledges the boulder summer school for condensed matter physics - modern aspects of superconductivity " , where some preliminary ideas for this work were formulated .
dc and ss were supported by nsf under grant dmr-1360789 , the templeton foundation , and muri grant w911nf-14 - 1 - 0003 from aro .
ts was supported by department of energy desc-8739- er46872 , and partially by a simons investigator award from the simons foundation .
jo acknowledges the office of basic energy sciences , materials sciences and engineering division , of the u.s .
department of energy under contract no .
de - ac02 - 05ch11231 for support .
part of this work was completed when jo was visiting mit as a moore visitor supported by grant gbmf4303 .
research at perimeter institute is supported by the government of canada through industry canada and by the province of ontario through the ministry of research and innovation .
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12 url # 1#1urlprefix[2][]#2 | we study the coupling of magneto - acoustic waves to alvn waves using 2.5d numerical simulations . in our experiment
, a fast magnetoacoustic wave of a given frequency and wavenumber is generated below the surface .
the magnetic field in the domain is assumed homogeneous and inclined .
the efficiency of the conversion to alfvn waves near the layer of equal acoustic and alfven speeds is measured calculating their energy flux .
the particular amplitude and phase relations between the oscillations of magnetic field and velocity help us to demonstrate that the waves produced after the transformation and reaching upper atmosphere are indeed alfvn waves .
we find that the conversion from fast magneto - acoustic waves to alfvn waves is particularly important for the inclination @xmath0 and azimuth @xmath1 angles of the magnetic field between 55 and 65 degrees , with the maximum shifted to larger inclinations for lower frequency waves .
the maximum alfvn flux transmitted to the upper atmosphere is about 23 times lower than the corresponding acoustic flux .
conversion from fast - mode high-@xmath2 magneto - acoustic waves ( analog of @xmath3 modes ) to slow - mode waves in solar active regions is relatively well studied both from analytical theories and numerical simulations ( e.g. , @xcite ) , see @xcite for a review . in a two - dimensional situation ,
the transformation from fast to slow magnetoacoustic modes is demonstrated to be particularly strong for a narrow range of the magnetic field inclinations around 2030 degrees to the vertical .
however , no generalized picture exists so far for conversion from magneto - acoustic to alfvn waves in a three - dimensional situation .
studies of this conversion were initiated by cally & goossens @xcite , who found that the conversion is most efficient for preferred magnetic field inclinations between 30 and 40 degrees , and azimuth angles between 60 and 80 degrees , and that alfvnic fluxes transmitted to the upper atmosphere can exceed acoustic fluxes in some cases .
newington & cally @xcite studied the conversion properties of low - frequency gravity waves , showing that large magnetic field inclinations can help transmitting an important amount of the alfvnic energy flux to the upper atmosphere .
time - height variations of the three projected velocity components corresponding to @xmath4 ( alfven wave , left ) , @xmath5 ( fast wave , middle ) and @xmath6 ( slow wave , right ) for @xmath7 mhz in a simulation with @xmath8 inclined by @xmath9 and @xmath10 .
the solid line marks the position @xmath11 , and the dashed line marks the cut - off layer @xmath12 .
the colour scaling is the same in all panels .
the amplitudes are scaled with @xmath13 ( first two panels ) @xmath14 ( last panel).,width=566 ] motivated by these recent studies , here we attack the problem by means of 2.5d numerical simulations .
the purpose of our study is to calculate the efficiency of the conversion from fast - mode high-@xmath2 magneto - acoustic waves to alfvn and slow waves in the upper atmosphere for various frequencies and wavenumbers as a function of the field orientation .
we limit our study to a plane parallel atmosphere permeated by a constant inclined magnetic field , to perform a meaningful comparison with the work of cally & goossens @xcite
. numerical simulation will allow generalization to more realistic models in our future work .
we numerically solve the non - linear equations of ideal mhd assuming all vectors in three spatial directions and all derivatives in two directions ( i.e. 2.5d approximation , see @xcite ) , though perturbations are kept small to approximate the linear regime .
an acoustic wave of a given frequency and wave number is generated at @xmath15 mm below the solar surface in a standard model atmosphere permeated by a uniform inclined magnetic field .
the top boundary of the simulation box is 1 mm above the surface , and 0.8 mm above the layer where the acoustic speed , @xmath16 , and the alfvn speed , @xmath17 , are equal .
we consider frequencies @xmath18 and 5 mhz and wave numbers @xmath19 mm@xmath20 and @xmath21 .
the simulation grid covers field inclinations @xmath0 from 0@xmath22 to 80@xmath22 and field azimuths @xmath1 from 0@xmath22 to 160@xmath22 .
the field strength is kept at @xmath23 g. to separate the alfvn mode from the fast and slow magneto - acoustic modes in the magnetically dominated atmosphere we use velocity projections onto three characteristic directions : @xmath24 ; \nonumber\\ { \hat\mathbf{e}}_{\rm perp } & = & [ - \cos\phi \sin^2\theta \sin\phi , \ , 1-\sin^2\theta \sin^2\phi , \ , - \cos\theta \sin\theta \sin\phi ] ; \\
\nonumber { \hat\mathbf{e}}_{\rm trans } & = & [ -\cos\theta , \ , 0 , \ , \cos\phi \sin\theta].\end{aligned}\ ] ] to measure the efficiency of conversion to alfvn waves near and above the @xmath11 equipartition layer , we calculate acoustic and magnetic energy fluxes , averaged over time : @xmath25 figure [ fig : modes ] shows an example of the projected velocities in our calculations as a function of space and time . in this representation
the larger inclination of the ridges mean lower propagation speeds and vice versa . note , that by projecting the velocities , we are able to separate the modes only in the magnetically dominated atmosphere , i.e. above the solid line in fig . [
fig : modes ] .
the figure shows how the incident fast mode wave propagates to the equipartition layer and then splits into several components .
the alfvn wave is produced by mode conversion above 0.2 mm ( left panel ) and propagates upwards with the ( rapid ) alfvn speed , confirmed by almost vertical inclination of the ridges .
conversely , the essentially magnetic fast - mode low-@xmath2 wave produced in the upper atmosphere ( middle panel ) is reflected , and its velocity variations in the upper layers vanish with height . the ( acoustic ) slow - mode low-@xmath2 wave escapes to the upper atmosphere tunnelling over the cut - off layer due to the field inclination of @xmath9 .
the amplitudes of the velocity variations of the alfvn wave are comparable to those of the slow wave .
left panel : log@xmath26 of the ratio @xmath27 to @xmath28 for projected velocities and magnetic field variations , averaged over all @xmath1 , as a function of @xmath0 .
black line : fast mode ( @xmath5 projection ) ; red line : alfvn mode ( @xmath29 ) ; blue line : slow mode ( @xmath6 ) .
right panel : phase shift between the projected variations of @xmath30 and @xmath27 , as a function of @xmath0 for selected @xmath1 .
red lines : alfvn mode ; black lines : fast mode.,title="fig : " ] left panel : log@xmath26 of the ratio @xmath27 to @xmath28 for projected velocities and magnetic field variations , averaged over all @xmath1 , as a function of @xmath0 .
black line : fast mode ( @xmath5 projection ) ; red line : alfvn mode ( @xmath29 ) ; blue line : slow mode ( @xmath6 ) .
right panel : phase shift between the projected variations of @xmath30 and @xmath27 , as a function of @xmath0 for selected @xmath1 .
red lines : alfvn mode ; black lines : fast mode.,title="fig : " ] to confirm the alfvn nature of the transformed waves , as revealed by the projection calculations , we checked the amplitude and phase relations for all three modes reaching the upper atmosphere . for the alfvn mode the magnetic field @xmath27 and velocity variations
@xmath30 should be in equipartition ( i.e. @xmath31 ) , and both magnitudes should oscillate in phase ( see priest @xcite ) .
figure [ fig : phases ] presents the calculations of the amplitude ratio @xmath32 and temporal phase shift between @xmath27 and @xmath30 , where both velocity and magnetic field variations are projected in the corresponding characteristic direction for each mode ( eq . [ eq : directions ] ) .
this calculation confirms that , indeed , for all magnetic field orientations @xmath0 and @xmath1 , the amplitude ratio for the alfvn mode ( @xmath29 projection ) is around one ( left panel ) .
this is clearly not the case for the slow and fast modes . for the fast mode ,
the amplitude ratio is two orders of magnitude larger , and for the slow mode , it is two orders of magnitude lower than one . for the alfvn mode the phase shifts group around zero for all @xmath1 , unlike the case of the fast mode ( right panel ) .
we did not calculate the phase shifts for the slow mode as the variations of the magnetic field are negligible .
thus , we conclude that the properties of the simulated alfvn mode separated by the projection correspond to those expected for a classical alfvn mode . examples of the height dependence of the magnetic ( solid line ) and acoustic ( dashed line ) vertical fluxes , defined by eq .
[ eq : fluxes ] , for @xmath7 mhz and several @xmath0 and @xmath1 .
solid vertical line marks the position @xmath11 , dashed vertical line marks the cut - off layer @xmath12 .
, title="fig : " ] examples of the height dependence of the magnetic ( solid line ) and acoustic ( dashed line ) vertical fluxes , defined by eq . [ eq : fluxes ] , for @xmath7 mhz and several @xmath0 and @xmath1 .
solid vertical line marks the position @xmath11 , dashed vertical line marks the cut - off layer @xmath12 .
, title="fig : " ] examples of the height dependence of the magnetic ( solid line ) and acoustic ( dashed line ) vertical fluxes , defined by eq . [ eq : fluxes ] , for @xmath7 mhz and several @xmath0 and @xmath1 .
solid vertical line marks the position @xmath11 , dashed vertical line marks the cut - off layer @xmath12 .
, title="fig : " ] an example of the height variations of the acoustic and magnetic fluxes is given in figure [ fig : fluxes2 ] .
the total vertical flux ( dotted line ) is conserved in the simulations except for the limitations caused by the finite grid resolution not resolving slow small - wavelength waves in the deep layers ( see fig . [
fig : modes ] ) .
both acoustic and magnetic fluxes show strongest variations near the conversion layer and become constant above it between 0.5 and 1 mm height .
the fluxes reaching the upper atmosphere depend crucially on the orientation of the field . in this example
, the acoustic flux decreases with @xmath0 whilst the magnetic flux increases with @xmath0 and becomes larger than the acoustic fluxes for @xmath33 . as the fast wave
is already reflected in the upper atmosphere ( see fig . [
fig : modes ] ) , the magnetic flux at these heights is due to the propagating alfvn wave .
vertical fluxes measured at the top of the atmosphere at 1 mm for waves with @xmath7 mhz ( left panels ) and 3 mhz ( right panels ) .
upper panels give magnetic fluxes and lower panels give acoustic fluxes .
, title="fig:",width=226 ] vertical fluxes measured at the top of the atmosphere at 1 mm for waves with @xmath7 mhz ( left panels ) and 3 mhz ( right panels ) .
upper panels give magnetic fluxes and lower panels give acoustic fluxes .
, title="fig:",width=226 ] finally , figure [ fig : fluxes ] gives the time averages of the vertical magnetic and acoustic fluxes at the top of the atmosphere as a function of the field orientation .
as proven above , the magnetic flux at 1 mm corresponds to the alfvn mode . at @xmath7 mhz
, the maximum of the magnetic flux corresponds to @xmath34 and @xmath35 .
this maximum is shifted to larger inclinations @xmath36 for waves with @xmath18 mhz .
the presence of the sharp maximum of the alfvnic flux transmission agrees well with the conclusions made previously by cally & goossens @xcite , though the exact position of the maximum is shifted to somewhat larger inclinations .
the maximum of the transmitted acoustic flux corresponds to inclinations @xmath37 for @xmath7 mhz waves , and to @xmath38 for @xmath18 mhz waves , again , in agreement with previous calculations @xcite .
the absolute value of the fluxes is about 30 times lower for 3 mhz compared to 5 mhz . at some angles the afvn magnetic flux transmitted to the upper atmosphere is larger than the acoustic flux .
however , at angles corresponding to the maximum of the transmission , the alfvn flux is 2 - 3 times lower than the corresponding acoustic flux .
it is important to realize that quantitatively simulating mode transformation numerically is a challenge , as any numerical inaccuracies are amplified in such second - order quantities as wave energy fluxes .
the tests presented in this paper prove the robustness of our numerical procedure and offer an effective way to separate the alfvn from magneto - acoustic modes in numerical simulations .
this will allow us in future to study the coupling between magneto - acoustic and alfvn waves in more realistic situations resembling complex solar magnetic structures . |
we would like to thank f.s .
navarra for fruitiful conversations .
this work has been partly supported by fapesp and cnpq - brazil . for a review and references to original works ,
see e.g. , s. narison , _ qcd as a theory of hadrons , cambridge monogr . part .
* 17 * , 1 ( 2002 ) [ hep - h/0205006 ] ; _ qcd spectral sum rules , world sci .
notes phys . _
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84 * , 263 ( 1982 ) . | we use the qcd sum rules to evaluate the mass of a possible scalar mesonic state that couples to a molecular @xmath0 current .
we find a mass @xmath1 gev , which is in a excellent agreement with the recently observed @xmath2 charmonium state .
we consider the contributions of condensates up to dimension eight , we work at leading order in @xmath3 and we keep terms which are linear in the strange quark mass @xmath4 . we also consider a molecular @xmath5 current and we obtain @xmath6 , around 200 mev above the mass of the @xmath7 charmonium state .
we conclude that it is possible to describe the @xmath2 structure as a @xmath8 molecular state .
there is growing evidence that at least some of the new charmonium states recently discovery in the b - factories are non conventional @xmath9 states . some possible interpretations for these states
are mesonic molecules , tetraquarks , or / and hybrid mesons .
some of these new mesons have their masses very close to the meson - meson threshold like the @xmath10 @xcite and the @xmath11 @xcite .
therefore , a molecular interpretation for these states seems natural .
the most recent aquisiton for this list of peculiar states is the narrow structure observed by the cdf collaboration in the decay @xmath12 .
the mass and width of this structure is @xmath13 , @xmath14 @xcite .
since the @xmath2 decays into two @xmath15 vector mesons , it has positive @xmath16 and @xmath17 parities .
there are already some theoretical interpretations for this structure .
its interpretation as a conventional @xmath9 state is complicated because , as pointed out by the cdf collaboration @xcite , it lies well above the threshold for open charm decays and , therefore , a @xmath9 state with this mass would decay predominantly into an open charm pair with a large total width . in ref .
@xcite , the authors interpreted the @xmath2 as the molecular partner of the charmonium - like state @xmath7 , which was observed by belle and babar collaborations near the @xmath18 threshold @xcite .
they concluded that the @xmath2 is probably a @xmath19 molecular state with @xmath20 or @xmath21 . in ref .
@xcite they have interpreted the @xmath2 as an exotic hybrid charmonium with @xmath22 . in this work ,
we use the qcd sum rules ( qcdsr ) @xcite , to study the two - point function based on a @xmath8 current with @xmath20 , to see if the new observed resonance structure , @xmath2 , can be interpreted as such molecular state . in previous calculations ,
the hidden charm mesons @xmath23 and @xmath24 have been studied using the qcdsr approach as tetraquark or molecular states @xcite . in some cases a very good agreement with the experimental mass was obtained . the starting point for constructing a qcd sum rule to evaluate the mass of a hadronic state , @xmath25 ,
is the correlator function ( q)=id^4x e^iq.x0 |t[j_h(x)j_h^(0)]|0 , where the current @xmath26 creates the states with the quantum numbers of the hadron @xmath25 .
a possible current describing a @xmath27 molecular state with @xmath28 is j=(|s_a_c_a)(|c_b^s_b ) , [ field ] where @xmath29 and @xmath30 are color indices .
the qcd sum rule is obtained by evaluating the correlation function in eq .
( [ 2po ] ) in two ways : in the ope side , we calculate the correlation function at the quark level in terms of quark and gluon fields .
we work at leading order in @xmath3 in the operators , we consider the contributions from condensates up to dimension eight and we keep terms which are linear in the strange quark mass @xmath4 . in the phenomenological side , the correlation function is calculated by inserting intermediate states for the @xmath27 molecular scalar state . parametrizing the coupling of the scalar state , @xmath31 , to the current , @xmath32 , in eq .
( [ field ] ) in terms of the parameter @xmath33 : [ eq : decay ] 0 | j|h=. [ lam ] the phenomenological side of eq .
( [ 2po ] ) can be written as ^phen(q^2)=^2m_h^2-q^2+_0^ds ^cont(s)s - q^2 , where the second term in the rhs of eq.([phe ] ) denotes higher scalar resonance contributions .
it is important to notice that there is no one to one correspondence between the current and the state , since the current in eq .
( [ field ] ) can be rewritten in terms of sum a over tetraquark type currents , by the use of the fierz transformation .
however , the parameter @xmath33 , appearing in eq . ( [ lam ] ) , gives a measure of the strength of the coupling between the current and the state .
the correlation function in the ope side can be written as a dispersion relation : ^ope(q^2)=_4m_c^2^ds
^ope(s)s - q^2 , where @xmath34 is given by the imaginary part of the correlation function : @xmath35 $ ] . as usual in the qcd sum rules method
, it is assumed that the continuum contribution to the spectral density , @xmath36 in eq .
( [ phe ] ) , vanishes bellow a certain continuum threshold @xmath37 . above this threshold , it is given by the result obtained with the ope .
therefore , one uses the ansatz @xcite ^cont(s)=^ope(s)(s - s_0 ) , to improve the matching between the two sides of the sum rule , we perfom a borel transform . after transferring the continuum contribution to the ope side , the sum rules for the scalar meson , considered as a scalar @xmath38 molecule , up to dimension - eight condensates , using factorization hypothesis , can be written as : ^2e^-^2/m^2=_4m_c^2^s_0ds e^-s / m^2 ^ope(s ) , [ sr1 ] where ^ope(s)=^pert(s)+^(s ) + ^g^2(s)+^mix(s)+^^2(s)+^mix(s ) , with [ eq : pert ] & & ^pert(s)=32 ^ 9 ^6_^ d^3 _ ^1-d^2(1 - - ) ^3(-4m_cm_s ) , + & & ^(s)=32 ^ 5 ^ 4_^ d\{m_s(m_c^2-(1-)s)^21 - - m_c_^1-d .
+ & & . }
, + & & ^g^2(s)=m_c^22 ^ 8 ^ 6_^ d^3_^1-d(1 - - ) , + & & ^mix(s)=-m_0 ^ 22 ^ 6 ^ 4\ { 3m_c_^d [ m_c^2-(1-)s ] -m_s(8m_c^2-s ) } , + & & ^^2(s)=m_c^28 ^ 2\ { ( 2m_c - m_s)-m_sm_c^2_0 ^ 1d ( s - m_c^2(1- ) ) } , [ dim6 ] where the integration limits are given by @xmath39 , @xmath40 , @xmath41 , and we have used @xmath42 .
we have neglected the contribution of the dimension - six condensate @xmath43 , since it is assumed to be suppressed by the loop factor @xmath44 .
we also include a part of the dimension-8 condensate contributions , related with the mixed condensate - quark condensate contribution : ^mix(s)&=&-m_cm_0 ^ 2 ^ 216 ^ 2_0 ^ 1 d ( s - m_c^2(1- ) ) .
[ dim8 ] it is important to point out that a complete evaluation of the dimension-8 condensate , and higher dimension condensates contributions , require more involved analysis @xcite , which is beyond the scope of this calculation . to extract the mass @xmath45 we take the derivative of eq .
( [ sr ] ) with respect to @xmath46 , and divide the result by eq .
( [ sr ] ) . for a consistent comparison with the results obtained for the other molecular states using the qcdsr approach , we have considered here the same values used for the quark masses and condensates as in refs .
@xcite : @xmath47 , @xmath48 , @xmath49 , @xmath50 , @xmath51 with @xmath52 , @xmath53 .
the borel window is determined by analysing the ope convergence and the pole contribution . to determine the minimum value of the borel mass we impose that the contribution of the dimension-8 condensate should be smaller than 20% of the total contribution . in fig .
[ figconv ] we show the contribution of all the terms in the ope side of the sum rule . from this figure
we see that for @xmath54 gev@xmath55 the contribution of the dimension-8 condensate is less than 20% of the total contribution .
therefore , we fix the lower value of @xmath56 in the sum rule window as @xmath57 gev@xmath55 . the maximum value of the borel mass is determined by imposing that the pole contribution must be bigger than the continuum contribution . in table
i we show the values of @xmath58 . in our numerical analysis , we will consider the range of @xmath56 values from 2.3 @xmath59 until the one allowed by the pole dominance criterion given in table i. + [ cols="^,^",options="header " , ] taking into account the incertainties given above we finally arrive at = ( 4.140.09 ) , [ ymass ] in an excellent agreement with the mass of the narrow structure @xmath2 observed by cdf .
one can also deduce , from eq .
( [ sr1 ] ) , the parameter @xmath33 defined in eq .
( [ lam ] ) .
we get : = ( 4.220.83 ) 10 ^ -2 ^5 , [ la1 ] from the above study it is very easy to get results for the @xmath60 molecular state with @xmath20 . for this
we only have to take @xmath61 and @xmath62 in eqs .
( [ dim6 ] ) , ( [ dim8 ] ) .
this study was already done in ref .
@xcite considering @xmath63 .
although in the case of the @xmath64 scalar molecule we get a worse borel convergence than for the @xmath38 scalar molecule , as can be seen by fig .
[ opedd ] , there is still a good ope convergence for @xmath65 . if we allow also for the @xmath60 molecule values of the continuum threshold in the range @xmath66 we get @xmath67 .
therefore , from a qcd sum rule study , the difference between the masses of the states that couple with scalar @xmath8 and @xmath60 currents , is consistent with zero . the mass obtained with the @xmath60 scalar current is about 100 mev above the @xmath68 threshold .
this could be an indication that there is a repulsive interaction between the two @xmath69 mesons .
strong interactions effects might lead to repulsive interactions that could result in a virtual state above the threshold .
therefore , this structure may or may not indicate a resonance .
however , considering the errors , it is not compatible with the observed @xmath70 charmonium - like state . in fig .
[ dif ] we show the relative ratio @xmath71 as a function of the borel mass for @xmath72 .
from this figure we can see that the ratio is very stable as a function of @xmath56 and the difference between the masses is smaller than 0.5% .
although the ratio is shown for @xmath72 , the result is indiscernible from the one shown in fig .
[ dif ] for other values of the continuum threshold in the range @xmath73 .
this result for the mass difference is completely unexpected since , in general , each strange quark adds approximately 100 mev to the mass of the particle .
therefore , one would naively expect that the mass of the @xmath38 state should be around 200 mev heavier than the mass of the @xmath64 state .
this was , for instance , the result obtained in ref .
@xcite for the vector molecular states @xmath74 and @xmath75 , where the masses obtained were : @xmath76 and @xmath77 . for the value of the parameter @xmath33
we get : _ d^*d^ * = ( 4.200.96)10 ^ -2 ^5 . [ la2 ] therefore , comparing the results in eqs .
( [ la1 ] ) and ( [ la2 ] ) we conclude that the currents couple with similar strength to the corresponding states , and that both , @xmath8 and @xmath60 scalar molecular states have masses compatible with the recently observed @xmath2 narrow structure .
however , since the @xmath2 was observed in the decay @xmath78 , the @xmath8 assignment is more compatible with its quark content . in conclusion , we have presented a qcdsr analysis of the two - point function for possible @xmath8 and @xmath60 molecular states with @xmath20 .
our findings indicate that the @xmath2 narrow structure observed by the cdf collaboration in the decay @xmath12 can be very well described by using a scalar @xmath8 current . although the authors of ref .
@xcite interpreted the @xmath2 as a @xmath27 molecular scalar state and the @xmath7 as a @xmath5 molecular scalar state , we have obtained similar masses for the states that couple with the scalars @xmath27 and @xmath5 currents .
therefore , from a qcd sum rule point of view , the charmonium - like state @xmath7 , observed by belle and babar collaborations , has a mass around 200 mev smaller than the state that couples with a @xmath5 scalar current and , therefore , can not be well described by such a current .
while this work has been finalized , a similar calculation was presented in ref .
@xcite .
however , the author of ref .
@xcite arrived to a different conclusion . |
this work is supported by the national sciences foundations of china under grant no . 10775148 , and by the cas knowledge innovation project
kjcx3-syw - n2 .
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b*63 * , 237 ( 1975 ) . | target mass corrections to the twist-4 terms @xmath0 as well as to the leading - twist @xmath1 are discussed .
pacs : 13.60.hb , 12.38.aw , 12.38cy ; 12.40.dh keywords : target mass corrections ; nachtmann moment ; higher - twist .
+ we know that different approaches [ 1 - 7 ] have been employed to study higher - twist effect to the nucleon structure functions . there were also several phenomenological analyses of the nucleon structure functions to study quark - hadron duality and to extract the higher - twist contributions ( like the ones of the twist-3 and twist-4 terms ) from experimental measurements [ 8 - 11 ] .
those analyses are going to be more and more accurate since the more and more precise measurements of the nucleon spin structure functions @xmath2 and @xmath3 are becoming available [ 11 - 12 ] .
the high precision data have been employed to study the validity of the quark - hadron duality for the nucleon structure function @xmath4 [ 13 ] and even for spin asymmetry @xmath5 by hermes [ 14 ] recently .
several experiments to test the higher - twist effect on the nucleon spin structure functions are being carried out in the jefferson laboratory [ 9,15 ] .
it has been pointed out , in the literature , that the target mass corrections ( tmcs ) should be considered in the studies of the nucleon structure functions [ 16 ] in a moderate @xmath6 region , and of the bloom - gilman quark - hadron duality [ 17 - 18 ] .
therefore , only after the important target mass corrections are removed from the experimental data , one can reasonably extract the higher - twist effect [ 18 ] .
there were several papers about the target mass corrections to @xmath7 and @xmath8 in the past [ 19 ] .
recently , the target mass corrections to the nucleon structure functions for the polarized deep - inelastic scattering have been systematically studied [ 20 - 21 ] . in our previous work
[ 22 ] , tmcs to the twist-3 matrix element in the nucleon structure functions are addressed . in this report
, tmcs to the twist-4 terms @xmath0 as well as to the leading - twist @xmath1 will be discussed .
consider the cornwall - norton ( cn ) moments @xmath9 , we know that the first cn moment of @xmath2 can be generally expanded in inverse powers of @xmath6 in operator production expansion ( ope ) [ 1 - 2 ] as @xmath10 with the coefficients @xmath11 relating to the nucleon matrix elements of operators of twist @xmath12 . in eq .
( 1 ) , the leading - twist ( twist-2 ) component @xmath13 is determined by the matrix elements of the axial vector operator @xmath14 , summed over various quark flavors .
the coefficient of @xmath15 term , @xmath16 , contains the contributions from the twist-2 @xmath1 , twist-3 @xmath17 , and twist-4 @xmath18 , respectively . usually , @xmath17 is extracted from the third moments of the measured @xmath19 and @xmath20 by using @xmath21 .
however , it is pointed out that this method for @xmath17 ignores the target mass corrections to the third moments of @xmath22 , and the target mass corrections play a sizeable role to @xmath17 [ 22 ] in a moderate @xmath6 region . to further estimate tmcs to the twist-4 of the nucleon spin structure functions
, one may assume that the contributions from higher - twist term with @xmath23 can be ignored [ 23 ] or assume this term to be a constant ( neglecting any possible @xmath6-dependence ) [ 8 ] .
based on the first assumption , we have @xmath24 when no tmcs are considered , @xmath1 and @xmath17 can be simply expressed by the cn moments of the nucleon spin structure functions , and we get @xmath25 when tmcs are considered , we have to employ the nachtmann moments @xmath26g_1(x , q^2)-y^2x^2\frac{4n}{n+2}g_2(x , q^2)\bigg \ } , \nonumber \\
m^{(n)}_2(q^2)&=&\int^1_0dx\frac{\xi^{n+1}}{x^2 } \bigg \{\frac{x}{\xi}g_1(x , q^2 ) + \big [ \frac{n}{n-1}\frac{x^2}{\xi^2}- \frac{n}{n+1}y^2x^2\big ] g_2(x , q^2)\bigg \},\end{aligned}\ ] ] where the nachtmann variable @xmath27 ( with @xmath28 ) , @xmath29 , and @xmath30 is the bjorken variable .
the two nachtmann moments are simultaneously constructed by the two spin structure functions @xmath22 .
if @xmath8 are replaced by the ones with tmcs ( see refs . [
20 - 22 ] ) , one can easily expand the two nachtmann moments with respect to @xmath31 .
the results are @xmath32 , and @xmath33 .
the two expressions explicitly tell that , different from the cn moments , one can get the contributions of a pure twist-2 with spin - n and a pure twist-3 with spin-(n-1 ) operators from the nachtmann moments .
the advantage of the nachtmann moments means that they contain only dynamical higher - twist , which are the ones related to the correlations among the partons . as a result , they are constructed to protect the moments of the nucleon spin structure functions from the target mass corrections .
consequently , to extract the higher - twist effect , say twist-3 or twist-4 contribution , one is required to consider the nachtmann moments instead of the cn moments .
we use the nachtmann moments to express @xmath34 and @xmath35 and obtain @xmath36\end{aligned}\ ] ] thus , tmcs to the twist-4 contribution , due to the two different moments , is @xmath37 . here
, we employ the parametrization forms of the spin structure functions of the proton , neutron and deuteron [ 11 - 12 ] to estimate @xmath38 .
note that the well - known wandzura and wilczek ( ww ) relation [ 24 ] @xmath39 is valid if only the leading - twist is considered , and tmcs to the twist-2 contribution do not break the ww relation .
however , if the higher - twist operators , like twist-3 and twist-4 , are considered , the ww relation @xmath40 no longer preserves .
thus , one may write @xmath41 [ 8,9 ] , where @xmath42 represents the violation of the ww relation . the non - vanishing value of @xmath42 just results from the higher - twist effect .
one can calculate @xmath38 with the parametrizations of @xmath22 .
the results are plotted in fig .
1 .
we see that the typical values of the differences are in order of @xmath43 .
there are several theoretical estimated values for the twist-4 term @xmath18 in the literature ( see table 1 ) , like the ones of the bag model [ 4 ] , of the qcd sum rule [ 5,6 ] , of the empirical analyses of the experimental measurements [ 8 , 23 ] , and of the instanton model [ 25 ] . comparing the estimated differences in fig . 1 to those estimated values displayed in table 1 ,
we conclude that tmcs to the twist-4 term @xmath18 are negligible ( less than 2% ) .
we also find that @xmath38 of the proton and deuteron are always larger than that of the neutron .
in addition , we check tmcs to the leading twist term ( with spin-3 ) @xmath1 . if no tmcs are considered , @xmath44 . when tmcs are taken into account , we get , from the nachtmann moments , @xmath45g_1(x , q^2 ) -\frac{12}{5}y^2x^2g_2(x , q^2)\bigg \}.\end{aligned}\ ] ] fig
. 2 displays the @xmath6-dependence of the ratio @xmath46 for the proton , neutron and deuteron targets .
the sizable effect of tmcs is clearly seen , since the ratios all diverge from unity obviously .
when @xmath47 , the effect of tmcs is still about 10% for the proton and deuteron targets .
in addition , the effect on the proton and deuteron targets is much larger than that on the neutron . here
the @xmath6-dependences of the three ratios are similar to those of the twist-3 terms [ 22 ] .
the sizeable effect tells that tmcs should be taken into account .
therefore , to estimate the matrix element of @xmath1 , the nachtmann moments are required to be employed .
the solid , dashed and dotted - dashed curves are the results of the proton , neutron and deuteron , respectively .
, width=377,height=264 ] .
the solid , dashed and dotted - dashed curves are the results of the proton , neutron and deuteron , respectively .
, width=377,height=264 ] table 1 , the estimated values for @xmath18 in different approaches in the literature . + [ cols="^,^,^,^,^,^",options="header " , ] in summary , we have explicitly shown the target mass corrections to the twist-4 @xmath18 term and to the leading - twist one ( spin-3 ) @xmath1 .
it is reiterated that in order to precisely and consistently extract the contributions of the leading - twist @xmath1 , of the twist-3 @xmath17 and of the twist-4 @xmath18 with a definite spin and with a moderate @xmath6 value , one is required to employ the nachtmann moments @xmath48 instead of the cn moments .
our results show that tmcs play an evidently role to @xmath1 when @xmath6 is small .
the above conclusion does not change if different parameterizations of the structure functions are employed .
we also show that tmcs to the twist-4 term is much smaller than those to the twist-3 term and to the leading - twist term
. finally , the expressions of the differences @xmath38 and @xmath49 between the cn and nachtmann moments are @xmath50 \nonumber \\ & & + \big [ 87g_2^{(5 ) } -258y^2g_2^{(7)}+798y^4g_2^{(9)}\big ] \bigg \}+{\cal o}(y^8),\nonumber \\
\delta a_2&=&\tilde a_2-\tilde a_2 ^ 0=2m^{(3)}_1 - 2g_1^{(3 ) } = y^2\bigg \ { \big [ -\frac{168}{25}g_1^{(5 ) } + \frac{108}{5}y^2g_1^{(7)}-\frac{352}{5}y^4g_1^{(9)}\big ] \nonumber \\ & & + \big [ -\frac{24}{5}g_2^{(5 ) } + \frac{96}{5}y^2g_2^{(7)}-\frac{336}{5}y^4g_2^{(9)}\big ] \bigg \ } + { \cal o}(y^8).\end{aligned}\ ] ]
one sees that the two expressions mainly depend on the higher - moment of the nucleon spin structure functions , and therefore , on the spin structure function in the large - x region . in the most of the empirical analyses of the ellis - jaffe sum rule ( the first moment of @xmath2 ) ,
the contribution from the spin structure function in the large - x region is assumed to be trivial , since it behaves like @xmath51 .
when the higher - moment of the spin structure function is considered , the effect of the spin structure functions in the large - x region becomes important .
consequently , the measurement of the nucleon spin structure functions in the large - x region with a high precision is required . |
employing the surface brightness fluctuation signal of unresolved stars in distant galaxies is an effective and inexpensive new way to measure accurate distances to early - type ( dwarf ) galaxies . unlike other extragalactic distance indicators ( e.g. trgb , rr lyrae stars )
, this method does _ not _ require resolved stars therefore allowing distance measurements for early - type galaxies far beyond the practical limits of any of the classical distance indicators ( @xmath05mpc ) . with fourier analysis techniques , the sbf method quantifies the mean stellar flux per ccd pixel and rms variation due to poisson noise across a designated area in a dwarf galaxy .
initially the sbf method was almost exclusively applied on nearby giant ellipticals and mw globular clusters ( e.g. tonry et al .
1989 , 1994 ) but was found to work equally well with dwarf elliptical ( de ) galaxies ( e.g. jerjen et al . 1998 , 2000 , 2001 , 2004 , and rekola et al . 2005 ) . as de
galaxies are by far the most numerous galaxy type at the current cosmological epoch , the sbf method in combination with wide - field ccd imaging offers the opportunity for the first time to spatially locate des in vast numbers and thereby to map in 3d the densest environments of the local universe ( for first results see contributions by ct et al . ,
jerjen , jordan et al . , and rekola et al .
in this volume ) .
first sbf distances are published for des as distant as 15mpc ( using 2 m ground - based telescopes ) and 25mpc ( using 8 m vlt+fors and hst & acs ) .
the _ minimal requirements _ for the sbf analysis of an early - type galaxy are : * galaxy morphology : the light distribution of the stellar system must be radially symmetric and have minimal structure .
an overall elliptical shape of the galaxy is crucial as this is modelled and subtracted as part of the sbf analysis .
* photometry : calibrated ccd images are required in two photometric bands , e.g. ( @xmath1 ) or ( @xmath2 , @xmath3 ) , as the fluctuation magnitude shows a colour dependency . *
image quality : fwhm @xmath4/20 $ ] , where @xmath5 is the half - light radius of the galaxy .
* integration time : @xmath6s / n@xmath7 , where @xmath8 is the mean surface brightness of the galaxy , @xmath9 the surface brightness of the sky background , @xmath10 the estimates distance modulus of the galaxy , @xmath11 the fluctuation luminosity of the underlying stellar population , and @xmath12 the magnitude of a star providing 1 count / sec on the ccd detector at the telescope . to give a general idea of these constraints , fig .
[ fig1 ] illustrates the depth required for an image of a de at the distance of the fornax cluster observed with vlt+fors1 .
the sbf amplitude above the shot noise level ( signal - to - noise ) in the power spectrum is shown as a function of integration time and mean effective surface brightness of the galaxy .
a sbf distance can be determined when the s / n is approximately 0.5 , ( see fig . 8 in rekola
et al . 2005 ) , but that depends largely on the image quality i.e. seeing .
for example , to achieve a s / n@xmath02 in the galaxy power spectrum , the minimum exposure time required for a de with a mean surface brightness of 25 magarcsec@xmath13 is 1600s .
it is interesting to note that this exposure time is by a factor of 20 shorter than the 32,000s of hst time spent by harris et al .
( 1998 ) to measure the trgb distance of a dwarf elliptical at a similar distance .
previous sbf work has entailed individuals hand selecting regions in galaxy images for the analysis . to make the results as impartial as possible and data reduction more efficient
we are developing a rapid , semi - automatic sbf analysis package named sapac that can process large numbers of galaxies .
sapac is a software package that carries out a semi - automatic sbf analysis of any early - type galaxy for which ccd data meets the requirements as discussed above . for a detailed description of the fluctuation magnitude calibration and the individual reduction steps such as the modelling of the galaxy , foreground star removal , selection of sbf fields etc .
we refer the reader to jerjen ( 2003 ) .
sapac consists of perl scripts using and iraf module and uses a sophisticated graphical user interface , also written in perl .
the average processing time for 10 sbf fields in a galaxy and measuring a distance is approximately 20 minutes .
initially we have concentrated the pipeline on @xmath14 , @xmath15 images , but the implementation of calibration information for a wider range of commonly used filter sets for sbf work like @xmath16 of the sdss @xmath17 filters is in process .
potential users of sapac who are interested in testing this package for calculating accurate distances of early - type dwarfs are welcome to contact laura dunn .
this software package will be made available to the astronomical community soon . | large volumes of ccd imaging data that will become available from wide - field cameras at telescopes such as the cfht , subaru , vst , or vista in the near future are highly suitable for systematic _ distance surveys of early - type galaxies _ using the surface brightness fluctuation ( sbf ) method . for the efficient processing of such large data sets
, we are developing the first semi - automatic sbf analysis pipeline named sapac .
after a brief description of the sbf method we discuss the image quality needed for a successful distance measurement and give some background information on sapac . |
last time the interest has sharply increased for searching the conditions for realization supersolidity phenomenon in solid @xmath1he @xcite , when the crystalline order combines with superfluidity . in spite of the great number of experimental and theoretical investigations in this area , the consensus has not been attained yet . for the present , it has been determined well that observing effects strongly depend on the growing conditions and annealing degree of helium crystals .
the special modeling which was conducted from the first principles by monte - carlo method , showed that in the perfect hcp @xmath1he crystal the supersolidity effects can not appear @xcite .
the most authors connect such effects in solid @xmath1he at low temperatures with the disorder in helium samples .
possible kinds of the disorder may be the defects , grain boundaries @xcite , glass phase , or liquid inclusions @xcite .
also , the possible interpretation @xcite of the experiments on flow the superfluid helium through the solid helium @xcite show the essential role of the liquid channels , which may exist in the solid helium up to the ultralow temperatures . in this connection , the experiments which allow to identify the kind of the disorder , for example , in rapidly grown helium crystals , interesting .
these data can be obtained by nuclear magnetic resonance ( nmr ) .
whereas for its realization the nuclei of @xmath0he are necessary , we deal hereafter with the samples of not pure @xmath1he but with dilute @xmath0he-@xmath1he mixture .
since nmr technique allows to measure diffusion coefficient in different coexisting phases and difference of diffusion coefficients in liquid and solid helium are several orders of the magnitude then such an experiment may answer the question whether liquid inclusions are formed in solid helium under very rapid crystal growing .
the aim of present work is to elucidate this problem .
we detect , by nmr technique , the presence of liquid phase in solid helium samples grown in different conditions and also establish the influence of annealing effect on character of diffusion processes .
the crystals were grown by the capillary blocking method from initial helium gas mixture with a 1% of @xmath0he concentration .
the copper cell of cylindrical form with inner diameter of 8 mm and length of 18 mm has the nmr coil glued to the inner surface of the cell . the pressure and temperature variations of the sample in the cell were controlled by two capacitive pressure gauges fixed to the both cylinder ends and by two resistance thermometers attached to the cold finger of the cell with sensitivities about 1 mbar and 1 mk , respectively . two series of crystals under the pressure above 33 bar were studied .
the first one ( `` low quality crystals '' ) was prepared by quick step - wise cooling from the melting curve down to the lowest temperature ( 1.27 k ) without any special thermal treatment . to improve the crystal quality of the second series ( `` high quality crystals '' )
a special three - stage thermal treatment was used : annealing at the melting curve , thermocycling in single phase regions and annealing in the hcp single phase region near the melting curve @xcite .
the criterions of crystal quality are , first , constancy of the pressure with time under constant temperature which is closed to melting and , second , reaching the pressure minimum under thermal cycling .
the spin diffusion coefficient was determined with the help of the pulsed nmr technique at a frequency of @xmath2 mhz .
the carr - purcell ( @xmath3 ) spin - echo method @xcite was used with a 90@xmath4-@xmath5 - 180@xmath4 sequence of probe pulses as well as the method of stimulated echo ( @xmath6 ) with the sequence of three probes pulses 90@xmath4-@xmath7 - 90@xmath4-@xmath8 - 90@xmath4 were applied to the nuclear system of the sample . generally , if a few phases do coexist in the sample , the echo amplitude @xmath9 for @xmath3 is given by @xmath10 and for @xmath6 @xmath11 \label{2}\ ] ] where @xmath12 is the maximal amplitude of a echo amplitude at @xmath13 , @xmath14 is the magnetic field gradient , @xmath15 is a gyromagnetic ratio , index @xmath16 numerates coexisting phases with the diffusion coefficients @xmath17 , @xmath18 is the relative content of the @xmath16-th phase in the sample
. one can choose duration parameters @xmath5 , @xmath7 , and @xmath8 in order to get the strongest @xmath19 dependence and to single out @xmath17 fitting parameter .
it should be emphasized that spin - diffusion coefficient @xmath20 measurement was just the method to identify a thermodynamical phases by their typical @xmath20 value .
neither contribution of @xmath0he atoms in a phase transition processes nor even the dynamics of different phase s ratio could be tracking because of too long spin - lattice relaxation times .
the typical results of nmr measurements for diffusion coefficients in two - phase sample on the melting curve are presented in fig .
[ fig_mc ] in @xmath19 scale .
there are two slopes for the data obtained which correspond to two different diffusion coefficients .
experimental data analysis according to eq .
( [ 1 ] ) gives for curve piece with sharp slope @xmath21
@xmath22/s which corresponds to diffusion in liquid phase @xcite and for curve piece with mildly slope @xmath23 @xmath22/s which corresponds to diffusion in hcp phase @xcite .
the phase ratio is @xmath24 .
then this sample was rapidly cooled down to 1.3 k in the hcp region .
the results of nmr measurements are shown in fig .
[ fig_quenched ] .
the presence of significant contribution ( @xmath25 ) of phase with fast diffusion coefficient ( @xmath26 @xmath22/s ) was unexpected .
this fact can be interpreted as existence of liquid - like inclusions in hcp matrix which were apparently quenched from the melting curve .
such a situation was visually observed in pure @xmath1he in refs .
[ 1,4,15,16].the liquid droplets formation was also observed by nmr technique in 1% @xmath0he-@xmath1he mixture under bcc and hcp phases coexistence @xcite .
note that this effect was observed in all three low - quality samples studied .
after that this crystal was heated up to melting curve and , after annealing procedure described above ( sec .
[ method ] ) , to avoid a thermal shock , was slowly cooled down to 1.3 k ( the hcp region ) .
the results are presented in fig .
[ fig_good ] . both the absence of visible @xmath19 functional dependence ( see eq .
( [ 1 ] ) ) which should be characteristic feature for @xmath27 @xmath22/s under @xmath28 ms at @xmath29 gs/@xmath22 and the position ( 0 ; 0 ) of the intersection point of @xmath3 and @xmath6 data curves are the evidences of the liquid - like diffusion absence in the crystal .
it also should be noted that monotonous pressure decrease was observed in low - quality samples with fast diffusion coefficient .
the typical pressure relaxation times were about @xmath30 hour .
after annealing of such samples along with fast diffusion process disappearing , monotonous pressure decreasing was also stopped .
this relaxation indirectly confirms our speculation about liquid - like inclusions quenched from the melting curve in the samples without any annealing . detailed study of pressure relaxation in quenched samples is projected .
it is shown that under rapidly cooling from the melting curve ( without annealing ) solid helium samples contain liquid - like inclusions identified by additional fast diffusion decay of echo - signal .
subsequent annealing of these samples leads to fast diffusion disappearing which is connected with crystallization of liquid - like inclusions .
coming out of these defects is accompanied by pressure relaxation in the system .
we thank b.cowan for useful consultations and for applying of his nmr spectrometer .
this work has also been partially supported by grant stcu # 3718 , program of cooperation in research and education in science and technology for the 2008 ukrainian junior scientist research collaboration , and the ministry of education and science of ukraine ( project m/386 - 2009 ) . | the study of phase structure of dilute @xmath0he - @xmath1he solid mixture of different quality is performed by spin echo nmr technique .
the diffusion coefficient is determined for each coexistent phase .
two diffusion processes are observed in rapidly quenched ( non - equilibrium ) hcp samples : the first process has a diffusion coefficient corresponding to hcp phase , the second one has huge diffusion coefficient corresponding to liquid phase .
that is evidence of liquid - like inclusions formation during fast crystal growing .
it is established that these inclusions disappear in equilibrium crystals after careful annealing .
pacs numbers : 61.72.cc , 66.30.ma , 61.50.-f , 64.70.d- keywords : nmr , @xmath0he-@xmath1he solid mixture , diffusion , defects * * + _ ye.o .
vekhov , a.p .
birchenko , n.p .
mikhin , and e.ya .
rudavskii _ + _ _ |
sciboone @xcite is a muon neutrino scattering experiment located at the boone neutrino beam at fermilab .
the 0.8 gev mean energy neutrino beam is produced with a 8 gev proton beam .
protons hit a beryllium target producing charged pions that are selected and focused using a magnetic horn .
the ability to switch the horn polarity allows to select @xmath1 to produce neutrino beam or @xmath2 to produce anti - neutrino beam .
only neutrino beam is currently used in this analysis .
sciboone detector consists in three sub - detectors : the main detector scibar , the electromagnetic calorimeter ec , and the muon range detector mrd. * scibar@xcite is a fully active and fine grained scintillator detector that consists in 14,336 bars arranged in vertical and horizontal planes .
scibar is capable to detect all charged particles and perform de / dx based particle identification . *
the electron catcher ( ec)@xcite , is a lead - scintillator calorimeter consisting in two planes , one vertical and one horizontal , with a width corresponding to 11 @xmath3 . *
the mrd@xcite , consists in 12 steel plates sandwiched between vertical and horizontal planes of scintillator .
the mrd has the capability to stop muons with momentum up to 1.2 gev .
the mrd detector is used in this analysis to define charged current events by tagging the outgoing muon .
the current analysis is covering scibar contained events , which means that events with particles other than muons escaping from scibar detector are not being considered .
ec detector will be introduced in the analysis in the near future allowing us to use events with particles escaping from scibar in the forward direction and reaching the ec .
neut @xcite event generator is used in this analysis .
the rein - sehgal model is implemented to simulate charged current resonant pion production with an axial mass @xmath4 gev/@xmath5 .
all resonances up to 2 gev are taken into account .
however @xmath6 is the resonance that more largely contributes to the @xmath0 production .
a cc-@xmath0 event is defined in this analysis as such event that contains at least a muon and a neutral pion coming out from the interaction vertex .
this definition includes neutral pions generated by secondary interactions inside the target nucleus as , for instance , charge exchanges .
though the @xmath0 decays almost immediately to two photons , and those produce em cascades with an average flight distance of 25 cm , topologically a cc-@xmath0 scibar contained event contains a muon reaching the mrd and two or more tracks contained in scibar ( see fig . [
fig : event ] ) .
the non - muon tracks are considered gamma candidates and are used to , at the end , reconstruct the neutral pion
. event .
muon track in green , reconstructed em showers in yellow and blue . ]
given the signal definition we can use some event topology and track property based cuts in order to reduce the background events in the sample ( see table [ tab : summary ] for summary ) .
the chosen filters are applied sequentially as follows : * scibar uses a cc event definition based on the muon tagging using the mrd .
then , the first applied selection is over events that contains a track reaching the mrd tagged as a muon . because we do nt expect any other particle to reach the mrd
, we also require only one tagged muon in the event . *
given that we are selecting scibar contained events , we use a veto filter to dismiss events with outgoing tracks .
the veto filter applies to events with outgoing tracks either from the upstream or the sides of the detectors .
the veto filter does not apply on tracks pointing to the ec because those tracks will be fully reconstructed once the ec information will be used .
the veto filter is also useful in order to remove events with in - going tracks originated in interactions outside the detector ( called dirt interactions ) . * as discussed before , we expect events with 3 tracks in scibar , the muon and the 2 electromagnetic cascades from the pion decay .
we thus use a filter to meet this topology .
* we also use a time based filter in order to avoid cosmic rays and dirt generated tracks in our selected events .
this filter requires that the photon candidates should match the muon time with a difference of 20 ns or less . *
as commented before , we use the scibar de / dx capability in order to separate minimum ionizing particles as muons or photons from protons .
most protons are rejected using this filter . * finally ,
a cut is placed requiring that the photon tracks should be disconnected from the event vertex taking advantage of the larger photon flight distance .
this cut is particularly useful to reject protons and charged pions , which track starts always from the event vertex .
.event selection summary .
[ cols= " < , > , > , > , > " , ] after the above commented cuts , we get reconstructed photons with a typical energy between 50 and 200 mev ( see fig . [
fig : photone ] ) . also , for correctly associated photon candidates , the energy is reconstructed with 100 mev resolution and small bias .
the photons are reconstructed at all angles .
once we have the 2 reconstructed gammas , we are able to reconstruct also the @xmath0 observables . in particular we reconstructed the invariant mass and also the momentum and angle . as you can see in fig .
[ fig : angle ] neutral pions are produced at all angles with a momentum in 50 - 300 mev / c range .
it is also visible a peak in the invariant mass plot near the @xmath0 mass ( fig .
[ fig : mass ] ) . from the plots we can see that our neut - based mc reproduces well the @xmath0 observables . reconstructed mass .
mc background broken in events with neutral pion and events without neutral pion .
mc normalized to cc - inc events . ]
[ fig : angle ]
since the poster was presented , some reconstruction improvements have been performed , in this section we are going to discuss them .
the track reconstruction in scibar is performed by a cellular automaton which essentially travels among the beam direction connecting hits to create tracks .
the first reconstruction improvement was to implement in the code a second run of the automaton but this time traveling in the transversal direction , that is perpendicular to the beam , and using the hits that are not associated to any track from the first processing . in this way we found abut a 10% more events containing 3 or more tracks and also we got the ability to reconstruct tracks at larger angle , close to 90 degrees like in fig .
[ fig : sbtcat_event ] .
this has been an important upgrade given the low statistics of the analysis mainly due to the lack of events with 3 or more reconstructed tracks .
a second improvement is to use a new algorithm that improves the reconstruction performance of the em cascades .
the em cascades in scibar are characterized by disconnected track segments and isolated hits , making difficult to recover and correctly associate all the photon visible energy .
the new algorithm seeks for those disconnected track segments and merge them into a single extended track via an energy - flow algorithm .
it also seeks for hits around the gamma candidate track in order to add the energy coming from those hits to the gamma track .
i this way , the photon energy reconstruction is improved and so is the @xmath0 observables . by using the new algorithm we find a narrower invariant mass peak with less low mass @xmath0 than in the fig .
[ fig : mass ] . also , the bias in the @xmath0 momentum is reduced and it can be observed an increment of the high momentum pions .
the sciboone collaboration gratefully acknowledges support from various grants and contracts from the department of energy ( u.s . ) , the national science foundation ( u.s . ) , the mext ( japan ) , the infn ( italy ) and the spanish ministry of education and science . | sciboone , located in the booster neutrino beam at fermilab , collected data from june 2007 to august 2008 to accurately measure muon neutrino and anti - neutrino cross sections on carbon below 1 gev neutrino energy .
sciboone is studying charged current interactions . among them , neutral pion production interactions will be the focus of this poster . the experimental signature of neutrino - induced neutral pion production
is constituted by two electromagnetic cascades initiated by the conversion of the @xmath0 decay photons , with an additional muon in the final state for cc processes . in this poster
, i will present how we reconstruct and select charged - current muon neutrino interactions producing @xmath0 s in sciboone address = ific ( u. valencia / csic ) |
the cherenkov telescope array ( cta , acharya et al .
2013@xcite ) is the project of a new array of several imaging atmospheric cherenkov telescopes ( iacts ) for very high - energy ( vhe ) astronomy .
the array shall be composed by three different types of telescopes , in order to maximize the performance in three different energy ranges : the large size telescope ( lst ) for the low energy range ( e @xmath1 20 gev 1 tev ) , the medium size telescope ( mst ) for the core energy range ( e @xmath1 0.110 tev ) , and the small size telescope ( sst ) for the high energy range ( e @xmath2 1 tev ) . the astri project ( ` astrofisica con specchi a tecnologia replicante italiana ' ) is included in this framework : it is a ` flagship project ' of the italian ministry of education , university and research , which , under the leadership of the italian national institute of astrophysics ( inaf ) , aims to realize and test an end - to - end prototype of the sst .
the astri sst-2 m prototype is characterized by two special features which will be adopted for the first time on a cherenkov telescope ( pareschi et al .
2013@xcite ) : a dual - mirror schwarzschild
couder ( sc ) optical design ( vassiliev et al .
2007@xcite ) , which is characterized by a wide field of view ( fov ) and a compact optical configuration , and a light and compact camera based on silicon photo - multipliers , which offer high photon detection sensitivity and fast temporal response .
figure [ fig1 ] ( left panel ) shows the telescope layout , whose mount exploits the classical altazimuthal configuration . the proposed layout ( canestrari et al .
2013@xcite ) is characterized by a wide - field aplanatic optical configuration : it is composed by a segmented primary mirror made of three different types of segments , a concave secondary mirror , and a convex focal surface .
the design has been optimized in order to ensure , over the entire fov , a light concentration higher than 80 % within the angular size of the pixels .
the telescope design is compact , since the primary mirror ( m1 ) and the secondary mirror ( m2 ) have a diameter of 4.3 m and 1.8 m , respectively , and the primary - to - secondary distance is 3 m. the sc optical design has an f - number f/0.5 , a plate scale of 37.5 mm/@xmath3 , a logical pixel size of approximately 0.17@xmath3 , an equivalent focal length of 2150 mm and a fov of 9.6@xmath3 in diameter ; the mean value of the active area is @xmath0 6.5 m@xmath4 .
the primary mirror is composed by 18 hexagonal segments , with an aperture of 849 mm face - to - face ; the central segment is not used because it is completely obstructed by the secondary mirror . according to their distance from the optical axis ,
there are three different types of segments , each having a specific surface profile . in order to perform the correction of the tilt misplacements ,
each segment will be equipped with a triangular frame with two actuators and one fixed point .
the secondary mirror is monolithic and has a curvature radius of 2200 mm and a diameter of 1800 mm .
it will be equipped with three actuators , where the third actuator will provide the piston / focus adjustment for the entire optical system . for both the segments of the primary mirror and the secondary mirror the reflecting surface
is obtained with a vapor deposition of a multilayer of pure dielectric material ( bonnoli et al .
2013@xcite ) .
the sc optical configuration allows us designing a compact and light camera .
in fact , the camera of the astri sst-2 m prototype has a dimension of about 56 cm @xmath5 56 cm @xmath5 56 cm , including the mechanics and the interface with the telescope structure , for a total weight of @xmath0 50 kg ( catalano et al .
2013@xcite ) . such small detection surface , in turn , requires a spatial segmentation of a few square millimeters to be compliant with the imaging resolving angular size .
in addition , the light sensor shall offer a high photon detection sensitivity in the wavelength range between 300 and 700 nm and a fast temporal response . in order to be compliant with these requirements , we selected the hamamatsu silicon photomultiplier ( sipm ) s11828 - 3344 m .
the ` unit ' provided by the manufacturer is the physical aggregation of 4 @xmath5 4 pixels ( 3 mm @xmath5 3 mm each pixel ) , while the logical aggregation of 2 @xmath5 2 pixels is a ` logical pixel ' ( figure [ fig1 ] , lower right ) ; its size of 6.2 mm @xmath5 6.2 mm corresponds to 0.17@xmath3 . in order to cover the full fov
, we adopt a modular approach : we aggregate 4 @xmath5 4 units in a photon detection module ( pdm ) and , then , use 37 pdms to cover the full fov .
the advantage of this design is that each pdm is physically independent of the others , allowing maintenance of small portions of the camera . to fit the curvature of the focal surface , each pdm
is appropriately tilted with respect to the optical axis .
the camera is also equipped with a light - tight two - petal lid ( figure [ fig1 ] , upper right ) in order to prevent accidental sunlight exposure of its sipm detectors . the astri sst-2 m prototype
will be placed at the ` m. g. fracastoro mountain station ' , the observing site of the inaf catania astrophysical observatory ; it is at serra la nave , on the etna mountain , at an altitude of 1735 m a.s.l .
( maccarone et al .
2013@xcite ) .
the prototype is currently under construction and it will be tested on field : it is scheduled to start data acquisition in 2014 . although the astri sst-2 m prototype will mainly be a technological demonstrator , it should be able to perform also scientific observations .
based on the foreseen sensitivity ( @xmath1 0.2 crab unit at 0.8 tev ) , a source flux of 1 crab at e @xmath2 2 tev should be detectable at 5 @xmath6 confidence level in some hours , while a few tens of hours should be necessary to obtain a comparable detection at e @xmath2 10 tev ( bigongiari et al .
2013@xcite ) .
in this way we would obtain the first crab observations with a cherenkov telescope adopting a schwarschild couder optical design and a sipm camera ; in addition , also the brightest agns ( mkn 421 and mkn 501 ) could be detected .
beside the prototype , the astri project aims to realize , in collaboration with cta international partners , a mini - array of a few sst dual - mirror ( sst-2 m ) telescopes .
thanks to the array approach , it will be possible to check the trigger algorithms and the wide fov performance , to compare the mini - array performance with the monte carlo expectations and to validate the performance predictions for the full sst array .
the astri / cta mini - array shall constitute the first seed of the cta observatory at its southern site and shall perform the first cta science , starting operation in 2016 . considering 7 telescopes at an optimized distance of 250 - 300 m
, preliminary monte carlo simulations yield a minimal improvement in sensitivity compared to the current iacts ( di pierro et al .
2013@xcite ) : starting from e = 10 tev , the mini - array expected sensitivity is slightly better at few tens of tev ; moreover , the astri / cta mini - array sensitivity is still competitive up to 100 tev , where the performance of the present generation of iacts drops dramatically . in this energy regime
the mini - array will operate as the most sensitive iact array
. the astri / cta mini - array will be able to study in great detail sources with a flux of a few 10@xmath7 erg @xmath8 s@xmath9 at 10 tev , with an angular resolution of a few arcmin and an energy resolution of about 10 - 15 % .
the astri / cta mini - array will observe prominent sources such as extreme blazars ( 1es 0229 + 200 ) , nearby well - known bl lac objects ( mkn 421 and mkn 501 ) and radio - galaxies , galactic pulsar wind nebulae ( crab nebula , vela - x , hess 1825 - 137 ) , supernovae remnants ( vela - junior , rx j1713.7 - 3946 , kepler ) and microquasars ( ls 5039 ) , as well as the galactic center . in this way it will be possible to investigate the electron acceleration and cooling , to study the relativistic and non relativistic shocks , to search for cosmic - ray ( cr ) pevatrons , to study the cr propagation and the impact of the extragalactic background light on the spectra of the nearby sources ( vercellone et al .
2013@xcite ) .
this work was partially supported by the astri flagship project financed by the italian ministry of education , university , and research ( miur ) and lead by the italian national institute of astrophysics ( inaf ) .
we also acknowledge partial support by the miur bando prin 2009 . | the astri project aims to develop , in the framework of the cherenkov telescope array , an end - to - end prototype of the small - size telescope , devoted to the investigation of the energy range @xmath0 1100 tev .
the proposed design is characterized by two challenging but innovative technological solutions which will be adopted for the first time on a cherenkov telescope : a dual - mirror schwarzschild couder configuration and a modular , light and compact camera based on silicon photo - multipliers . here
we describe the prototype design , the expected performance and the possibility to realize a mini array composed by a few such telescopes , which shall be placed at the final cta southern site . |
the concept of gpds @xcite has led to completely new methods of `` spatial imaging '' of the nucleon .
the mapping of the nucleon gpds , and a detailed understanding of the spatial quark distribution of the nucleon , have been widely recognized are a key objectives of nuclear physics of the next decade , and is a key justification for the jlab energy upgrade to 12 gev .
gpds also allow to quantify how the orbital motion of quarks in the nucleon contributes to the nucleon spin
a question of crucial importance for our understanding of the `` mechanics '' underlying nucleon structure .
this requires a comprehensive program , combining results of measurements of a variety of processes in electron
nucleon scattering with structural information obtained from theoretical studies , as well as with expected results from future lattice qcd simulations .
it is well recognized @xcite that exclusive processes can be used to probe the gpds and construct 2-dimensional and 3-dimensional images of the quark content of the nucleon . deeply virtual compton scattering and deeply virtual meson production are identified as the processes most suitable to map out the twist-2 vector gpds @xmath1 and the axial gpds @xmath2 in @xmath3 , where @xmath4 is the momentum fraction of the struck quark , @xmath5 the longitudinal momentum transfer to the quark , and @xmath6 the momentum transfer to the nucleon . having access to a 3-dimensional image of the nucleon ( two dimensions in transverse space , one dimension in longitudinal momentum ) opens up completely new insights into the complex structure of the nucleon .
for example , the nucleon matrix element of the energy - momentum tensor contains 3 form factors that encode information on the angular momentum distribution @xmath7 of the quarks with flavor @xmath8 in transverse space , their mass - energy distribution @xmath9 , and their pressure and force distribution @xmath10 .
these form factors also appear as moments of the vector gpds @xcite , thus offering prospects of accessing these quantities through detailed mapping of gpds .
the quark angular momentum in the nucleon is given by @xmath11~,\ ] ] and the mass - energy and pressure distribution @xmath12 the mass - energy and force - pressure distribution of the quarks are given by the second moment of gpd @xmath13 , and their relative contribution is controlled by @xmath5 .
the separation of @xmath14 and @xmath10 requires measurement of these moments in a large range of @xmath5 .
dvcs has been shown @xcite to be the cleanest process to access gpds at the kinematics accessible today .
it is also a relatively rare process and requires high luminosities for the required high statistics measurements .
the beam helicity - dependent cross section asymmetry is given in leading twist as @xmath15d\phi~,\]]where @xmath16 and @xmath17 are the dirac and pauli form factors , @xmath18 is the azimuthal angle between the electron scattering plane and the hadronic plane . the kinematically suppressed term with gpd @xmath19 is omitted .
for not too large @xmath5 the asymmetry is mostly sensitive to the gpd @xmath20 .
the asymmmetry with a longitudinally polarized target is given by @xmath21~.\ ] ] the combination of @xmath22 and @xmath23 allows a separation of gpd @xmath20 and @xmath24 .
using a transversely polarized target the asymmetry @xmath25\ ] ] can be measured , which depends in leading order on gpd @xmath19 and is highly sensitive to orbital angular momentum contributions of quarks . clearly , determining moments of gpds for different @xmath6 will require measurement in a large range of @xmath4 , in particular at large @xmath4 .
the reconstruction of the transverse spatial quark distribution requires measurement in a large range in @xmath6 , and the separation of the @xmath10 and @xmath14 form factors requires a large span in @xmath5 .
to meet the requirements of high statistics measurements of relatively rare exclusive processes such as dvcs at high photon virtuality @xmath26 , large @xmath6 and @xmath5 , the clas detector will be upgraded and modified to clas12 @xcite .
the main new features of clas12 over the current clas detector include a high operational luminosity of @xmath27@xmath28sec@xmath29 , an order of magnitude increase over clas @xcite .
improved particle identification will be achieved with additional threshold gas cerenkov counter , improved timing resolution of the forward time - of - flight system , and a finer granularity electromagnetic preshower calorimeter that , in conjunction with th existing clas calorimeter will provide much improved @xmath30 separation for momenta up to 10 gev .
in addition , a new central detector will be built that uses a high - field solenoid magnet for particle tracking and allows the operation of dynamically polarized solid state targets . with these upgrades clas12
will be the workhorse for exclusive electroproduction experiments in the deep inelastic kinematics .
the 12 gev upgrade offers much improved capabilities to access gpds .
figure [ fig : dvcs_alu_12gev ] shows the expected statistical precision of the beam dvcs asymmetry for some sample kinematics . at the expected luminosity of @xmath27@xmath28sec@xmath29 and for a run time of 2000 hours ,
high statistics measurements in a very large kinematics range are possible . using a dynamically polarized @xmath31 target we can also measure the longitudinal target spin asymmetry @xmath23 with high precision .
the projected results are shown in fig .
[ fig : aul ] .
the statistical accuracy of this measurement will be less than for the @xmath22 asymmetry due to the large dilution factor in the target material , but it will still be a very significant measurement .
polarizing the target transverse to the beam direction will access a different combination of gpds , and provide different sensitivity for the y- and x - components of the target polarization . the expected accuracy for one of the polarization projections is shown in fig .
[ fig : dvcs_aut_12gev ] . here
the target is assumed to be a frozen hd - ice target , which has different characteristics from the @xmath31 target .
a measurement of all 3 asymmetries will allow a separate determination of gpds @xmath32 and @xmath19 at the above specified kinematics . through a fourier transformation
the t - dependence of gpd @xmath33 can be used to determine the @xmath34quark distribution in transverse impact parameter space .
figure [ fig : gpd_h ] shows projected results for such a transformation assuming a model parameterization for the kinematical dependences of gpd @xmath33 .
knowledge of gpd @xmath19 will be particularly interesting as it is directly related to the orbital angular momentum distribution of quarks in transverse space .
we thank the members of the clas collaboration who contributed to the development of the exciting physics program for the jlab upgrade to 12 gev , and the clas12 detector .
much of the material in this report is taken from the clas12 technical design report version 3 , october 2007 @xcite .
this work was supported in part by the u.s .
department of energy and the national science foundation , the french commisariat lenergie atomique , the italian instituto nazionale di fisica nucleare , the korea research foundation , and a research grant of the russian federation .
the jefferson science associates , llc , operates jefferson lab under contract de - ac05 - 060r23177 .
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the complete technical design report document may be obtained from the authors . | an overview is given about the capabilities provided by the jlab 12 gev upgrade to measure deeply virtual exclusive processes with high statistics and covering a large kinematics range in the parameters that are needed to allow reconstruction of a spatial image of the nucleon s quark structure .
the measurements planned with clas12 will cross section asymmetries with polarized beams and with longitudinally and transversely polarized proton targets in the constrained kinematics @xmath0 .
in addition , unpolarized dvcs cross sections , and doubly polarized beam target asymmetries will be measured as well . in this talk
only the beam and target asymmetries will be discussed . |
the shape of the stellar velocity ellipsoid , defined by @xmath5 , @xmath6 , and @xmath7 , provides key insights into the dynamical state of a galactic disk : @xmath7:@xmath5 provides a measure of disk heating and @xmath6:@xmath5 yields a check on the validity of the epicycle approximation ( ea ) .
additionally , @xmath5 is a key component in measuring the stability criterion and in correcting rotation curves for asymmetric drift ( ad ) , while @xmath7 is required for measuring the disk mass - to - light ratio .
the latter is where the diskmass survey focuses ( verheijen et al .
2004 , 2005 ) ; however , in anything but face - on systems , @xmath7 must be extracted via decomposition of the line - of - sight ( los ) velocity dispersion .
below , we present such a decomposition for two galaxies in the diskmass sample : ngc 3949 and ngc 3982 . previous long - slit studies ( e.g. , shapiro et al . 2003 and references therein ) acquired observations along the major and minor axes and performed the decomposition via the ea and ad equations ; using both dynamical equations overspecifies the problem such that ad is often used as a consistency check .
here , use of the sparsepak ( bershady et al .
2004 , 2005 ) integral field unit ( ifu ) automatically provides multiple position angles , thereby increasing observing efficiency and ensuring signal extraction along the desired kinematic axes .
long - slit studies have also used functional forms to reduce the sensitivity of the above decomposition method to noise . here , only measures of the los velocity dispersions within a 40@xmath0 wedge about the major axis are used to perform the decomposition by incorporating both the ea and ad equations under some simplifying assumptions .
velocities and radii within the wedge are projected onto the major axis according to derived disk inclinations , @xmath8 , and assuming near circular motion . in the end
, our method requires neither fitted forms nor error - prone interpolation between the major and minor axes . future work will compare this decomposition method with the multi - axis long - slit method and investigate effects due to use of points off the kinematic axes .
following derivations in binney & tremaine ( 1987 ) and assuming ( 1 ) ea holds , ( 2 ) the velocity ellipsoid shape and orientation is independent of @xmath9 ( @xmath10 ) , ( 3 ) both the space density , @xmath11 , and @xmath5 have an exponential fall off radially with scale lengths of @xmath12 and @xmath13 , respectively , and ( 4 ) the circular velocity is well - represented by the gaseous velocity , @xmath14 , the equation for the ad of the stars becomes @xmath15 , where @xmath16 is the mean stellar rotation velocity ; hence , @xmath5 is the only unknown .
the third assumption requires mass to follow light , @xmath17 , and constant velocity ellipsoid axis ratios with radius ; @xmath18 is the surface density .
the major - axis dispersion is geometrically given by @xmath19 , where @xmath20 is constant with radius .
finally , ea , @xmath21 , completes a full set of equations for decomposition of the velocity ellipsoid .
data for testing of the above formalism was obtained during sparsepak commissioning ( bershady et al .
2005 , see table 1 ) .
both ngc 3949 and ngc 3982 were observed for @xmath22s at one ifu position with @xmath23 nm and @xmath24 or 26 km s@xmath25 .
the velocity distribution function ( vdf ) of both gas and stars is parameterized by a gaussian function . in each fiber with sufficient signal - to - noise
, the gaseous vdf is extracted using fits to the [ oiii ] emission line ; the stellar vdf is extracted using a modified cross - correlation method ( tonry & davis 1979 ; statler 1995 ) with hr 7615 ( k0iii ) as the template ( westfall et al . 2005 ) .
the pointing of the ifu on the galaxy is determined _ post factum _ to better than 1 " by minimizing the @xmath26 difference between the fiber continuum flux and the surface brightness profile .
subsequent galactic coordinates have been deprojected according to the kinematic @xmath8 and position angle .
figure 1 shows los dispersions for both the gas , @xmath27 , and stars , @xmath28 ; data points are given across the full field of the ifu with points along the major and minor axes and in between having different symbols ( see caption ) . from this figure note ( 1 )
there is no significant difference in @xmath29 along the major and minor axes for ngc 3949 and ( 2 ) the large gas dispersion within @xmath30 " for ngc 3982 is a result of poor single gaussian fits to the multiple dynamical components of its liner nucleus .
figure 2 gives the folded gaseous and stellar rotation curves and compares the measured @xmath1 from figure 1 with that calculated using the formalism from 1 .
the value of @xmath31 used in figure 2 provides the minimum difference between the two sets of data ( as measured by @xmath32 ; see figure 3a ) .
we find @xmath33 and @xmath34 for ngc 3949 and ngc 3982 , respectively ; errors are given by 68% confidence limits .
a comparison of these values to the summary in shapiro et al .
( 2003 ) is shown in figure 3b .
the disk of ngc 3982 is similar to other sb types studied ; however , ngc 3949 seems to have an inordinately hot disk .
the latter , while peculiar , is also supported by the indifference between its major and minor axis @xmath29 from figure 1 and the same indifference seen in the caii data presented by bershady et al .
our streamlined velocity - ellipsoid decomposition method appears accurate , as seen by comparison with ( 1 ) galaxies of a similar type for ngc 3982 , and ( 2 ) data in a different spectral region for ngc 3949
. 1 bershady , m. , verheijen , m. , andersen , d. 2002 , in disks of galaxies : kinematics , dynamics and perturbations , eds .
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2004 , pasp , 116 , 565 bershady , m. a. et al . 2005 , apjs , 156 , 311 binney , j. & tremaine , s. 1987 , _ galactic dynamics _ ( princeton university press : princeton , nj ) shapiro , k. l. , gerssen , j. , & van der marel , r. p. 2003 , aj , 126 , 2707 staler , t. 1995 , aj , 109 , 1371 tonry , j. & davis , m. 1979 , aj , 84 , 1511 verheijen , m. a. w. et al .
2004 , an , 325 , 151 verheijen , m. et al .
2005 , these proceedings westfall , k. b. et al .
2005 , in prep . | we present the decomposition of the stellar velocity ellipsoid using stellar velocity dispersions within a 40@xmath0 wedge about the major - axis ( @xmath1 ) , the epicycle approximation , and the asymmetric drift equation .
thus , we employ no fitted forms for @xmath1 and escape interpolation errors resulting from comparisons of the major and minor axes .
we apply the theoretical construction of the method to integral field data taken for ngc 3949 and ngc 3982 .
we derive the vertical - to - radial velocity dispersion ratio ( @xmath2 ) and find ( 1 ) our decomposition method is accurate and reasonable , ( 2 ) ngc 3982 appears to be rather typical of an sb type galaxy with @xmath3 despite its high surface brightness and small size , and ( 3 ) ngc 3949 has a hot disk with @xmath4 . |
one of the main ingredients necessary to study few - body nuclear systems is a realistic description of the nuclear interaction .
a number of nucleon - nucleon ( @xmath1 ) potentials has been determined in the recent years . they all reproduce the deuteron binding energy and fit a large set of @xmath1 scattering data below the pion - production threshold with a @xmath2/datum of about 1 . among these potentials
, we will consider in the present study only the `` phenomenological '' model of ref .
@xcite ( av18 ) , and a model based on chiral symmetry derived in ref .
@xcite ( n3lo - idaho ) . among the many features of these two models , we note only that the av18 is a local @xmath1 potential model , with a strong short - range repulsion and tensor component , while the n3lo - idaho is a non - local @xmath1 potential model , with a softer short - range repulsion and tensor component than the av18 . as a consequence of these differences , it is interesting to test these potential models studying light nuclear systems . in these systems , a further contribution to the realistic nuclear hamiltonian model comes from the three - nucleon interaction ( tni ) .
several models of tni s have been proposed .
they are mainly based on the exchange of pions among the three nucleons , as the urbana ix ( uix ) tni @xcite , which will be considered in the present study .
the more recent tni models studied within the chiral approach @xcite and the extension of the uix model known as the illinois tni @xcite will be considered in a near future .
a second crucial ingredient in the study of light nuclear systems is the technique used to solve the @xmath0-body schrdinger equation .
several methods have been developed in the past years ( see refs .
@xcite for a review ) . among them
, we consider in the present study the technique known as the hyperspherical harmonics ( hh ) method , which will be briefly described in the following section . in sec .
[ sec : res ] , the results for the @xmath3 and @xmath4 scattering lengths will be presented and compared with the available experimental data .
the nuclear wave function for an @xmath0-body system can be written as @xmath5 where @xmath6 is a suitable complete set of states , and @xmath7 is an index denoting the set of quantum numbers necessary to completely determine the basis elements . in the present work ,
the functions @xmath6 have been written in terms of hh functions both in configuration - space or in momentum - space @xcite .
the unknown coefficients @xmath8 of eq .
( [ eq : psi ] ) are obtained applying the rayleigh - ritz ( kohn ) variational principle for the bound ( scattering ) state problem .
then , the matrix elements of the different operators of the hamiltonian are calculated , working in coordinate- or in momentum - space depending on what is more convenient .
thus , the problem is reduced to an eigenvalue - eigenvector problem ( system of algebraic linear equations ) , which can be solved with standard numerical techniques @xcite .
the @xmath3 and @xmath4 doublet and quartet scattering lengths obtained with the non - local n3lo - idaho @xcite @xmath1 interaction , with or without the inclusion of the uix tni @xcite , are given in table 1 , and compared with the available experimental data @xcite .
also shown are the results obtained with the local av18 @xcite @xmath1 interaction and the av18/uix potential model for a comparison @xcite .
note that in the case of the n3lo - idaho / uix model , the parameter in front of the spin - isospin independent part of the uix tni has been rescaled by a factor of 0.384 to fit the triton binding energy . in this way , the triton , @xmath9he , and @xmath10he binding energies are 8.481 mev , 7.730 mev , and 28.534 mev , respectively .
furthermore , the n3lo - idaho and n3lo - idaho / uix results shown in the table are accurate at the 10@xmath11 fm level .
in fact , the convergence of the hh expansion has been tested with a procedure similar to the one used in ref .
@xcite for the @xmath0=3 and 4 bound states observables .
from inspection of the table we can conclude that : ( i ) both the @xmath3 and @xmath4 quartet scattering lengths are very little model - dependent . also , they are not affected by the inclusion of the tni .
the trend shown by the av18 and av18/uix results has been found also in the case of the non - local n3lo - idaho and n3lo - idaho / uix potential models .
( ii ) the @xmath3 doublet scattering length is very sensitive to the choice of the @xmath1 potential model , when no tni is included .
however , once the tni is included , and therefore the triton binding energy is well reproduced , @xmath12 becomes model - independent .
this is a well - known feature , related to the fact that @xmath12 and the triton binding energy are linearly correlated ( the so - called phillips line @xcite ) .
( iii ) the @xmath4 doublet scattering length is positive and quite model - dependent , if only the two - nucleon interaction is included .
once the tni is added , @xmath13 becomes very little and negative .
some model - dependence remains , but the problem of extrapolating to zero energy the experimental results makes impossible any meaningful comparison between theory and experiment . in conclusion , the application of the hh method to treat the low - energy scattering problem using non - local @xmath1 interactions has been found successful .
both @xmath3 and @xmath4 systems have been considered , with the full inclusion of the coulomb interaction , in the second case .
a similar investigation for the @xmath0=4 scattering lengths has been reported in ref .
. further work at higher energies is currently underway . | the structure of @xmath0=3 low - energy scattering states is described using the hyperspherical harmonics method with realistic hamiltonian models , consisting of two- and three - nucleon interactions . both coordinate and momentum space
two - nucleon potential models are considered . |
all the well - established particles can be categorized using the constituent quark model which describes light mesons as bound states of @xmath2 pairs , and baryons as bound 3-quarks states . on the other hand ,
high energy experiments have shown a more complicated internal structure of mesons and baryons made of a swarms of quarks , anti - quarks and gluons .
it is then natural to ask wether particles with more complex configurations exists , like for example 5-quarks ( @xmath3 ) states , where the @xmath4 has different flavor than the others quarks .
these states , with quark content other than @xmath2 or @xmath5 are termed as _
exotics_. + the idea of exotics has in fact been proposed since the early 70 s but the experimental signals for exotic baryons were so controversial that never rised to a level of certainty sufficient for the particle data group s tables @xcite . till ,
in its 1988 review the particle data group officially put the subject to sleep @xcite .
+ although the lack of clear evidence of exotic particles , theoretical work on this subject was continued by several authors on the basis of quark and bag models @xcite and on the skyrme model @xcite . using the latter one ,
praszalowicz @xcite provided the first estimate of the mass of the lightest exotic state , @xmath6 mev , and in 1997 diakonov , petrov and polyakov @xcite , in the framework of the chiral quark soliton model , predicted an antidecuplet of 5-quarks baryons , with spin and parity @xmath7 illustrated in fig .
[ fig : decupletto ] .
the lowest mass member is an isosinglet state , dubbed @xmath1 , with quark configuration ( @xmath8 ) giving s=+1 , with mass @xmath9 gev and width of around 15 mev .
+ invariant mass measured by the leps collaboration @xcite in @xmath10 events.,title="fig:",width=275 ] + invariant mass measured by the leps collaboration @xcite in @xmath10 events.,title="fig:",width=275 ] experimental evidence for a s=+1 baryon resonance with mass 1.54 gev and width less than 25 mev has been reported for the first time by the leps collaboration at spring-8 @xcite in the photoproduction on neutron bound in a carbon target .
immedialely after , several other experimental groups analyzing previously obtained data , have found this exotic baryon in both his decaying channels @xmath11 and @xmath12 @xcite .
the properties of the observed candidate pentaquark signals obtained studying different reactions with different experimental methods , are summarized in table [ table:1 ] .
.summary table of the experimental results of the different @xmath1 experiments ( first column ) .
the @xmath1 decay channels studied are reported in the second column ; mass , width and statistical significance of the measured signals in columns 3 to 5 .
[ cols= " < , < , < , < , < " , ] + the g11 experiment run soon after the _
g10 _ one and finished to take data at the end of july 2004 .
data were taken using a 40 cm length liquid hydrogen target and tagged photons in the enrgy range ( 0.8 - 3.8 ) gev .
the new longer target , necessary to achieve the goal of this experiment , needed a new start counter detector around the target itself to improve event triggering and particle identification . under this
conditions an integrated luminosity of 80 @xmath13 was achieved .
the detector calibration is underway and the data quality check of the clas setup is shown in fig .
[ fig : g11 ] where the @xmath14 invariant mass spectrum , based on a small fraction of the statistics , in the @xmath15 reaction clearly shows the @xmath16 peak .
the reaction channels under study are : @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 , @xmath22 , and @xmath23 .
+ while the goal of the _ g11 _ experiment is primarly to check the existence of the @xmath1 and possible excited states on a proton target , the _ super - g _ experiment will be a comprehensive study of exotic baryons from a proton target with a maximum photon energy of about 5.5 gev . due to the broad kinematic coverage for a variety of channels , it will measure spin , decay
angular distributions and reaction mechanism of the produced particles .
another goal of the _ super g _
experiment is to try to verify the existence of exotic cascades reported by na49 @xcite .
the experiment is scheduled to run in the @xmath24 half of 2005 .
+ invariant mass spectrum in the @xmath15 reaction , showing the @xmath16 peak .
( preliminary clas data.),title="fig:",width=279 ] + invariant mass spectrum in the @xmath15 reaction , showing the @xmath16 peak .
( preliminary clas data.),title="fig:",width=260 ] as mantioned above , observation of other 5-quarks states belonging to the antidecuplet of fig .
[ fig : decupletto ] , came from na49 @xcite which found the @xmath25 and the @xmath26 at a mass of 1.86 gev .
nevertheless , up to date , no other experiments have been able to confirm these observations .
+ the goal of the _ eg3 _ experiment is to measure the production of pentaquark cascade states using a 5.7 gev electron beam incident on a thin deuterium target ( 0.5 cm length ) but without detecting the scattered electron .
this untagged virtual photon beam is necessary to achieve sufficient sensitivity to the expected small cross sections . in this case , missing mass technique can not be used and the method requires the direct reconstruction of the cascades using their decay products .
the sequence of weakly decaying daughter particles provides a powerful tool to pick out the reactions of interest .
the main goal of the experiment will be to search for @xmath27 , @xmath28 and @xmath29 .
other decay mode are detectable with lower sensitivity . using the available theoretical estimate for the production cross section of 10 nb , the detection of 460 @xmath30 particles is expected during a 20 day run .
together with the estimation for the background levels , this represents a statistical significant result of @xmath31 .
the experiment is schedule to start to take data in november 2004 .
a key question in non - perturbative qcd is the structure of hadrons .
the existence of baryon states beyond the minimal @xmath32 configuration is one of the open questions of strong interaction physics .
while such states are not prohibited by qcd , no experimental evidence had been found until recently .
the first evidence of a narrow resonance with a quark content ( @xmath33 ) and so with strangeness s=+1 , named @xmath1 , was reported by the leps collaboration .
this observation has been confirmed by another nine experimental groups , with various projectiles and targets .
there are however other experiments where @xmath1 has not been seen .
in addition , all the signals have rather low statistical precision and there are inconsistencies in the measured masses and widths .
thus , at this time the existence of a narrow pentaquark state is not fully confirmed . + the question of whether pentaquarks exist
can only be solved by a second generation high statistics experiments .
the clas collaboration at jafferson lab is currently pursuing this goal .
high statistics searches for exotic baryons on hydrogen and deuterium target and in various final states have been started in march 2004 and will going on till next year .
data for two of these experiments are already in hand and results are expected by the end of the year .
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92 , ( 2004 ) 042003 . | the existence of an anti - decuplet of pentaquark particles has been predicted some year ago within the chiral soliton model . in the last year , several experimental groups have reported evidence for a s=+1 baryon resonance , with mass ranging from 1.52 and 1.55 gev and width less than 25 mev , by looking at the invariant mass of the @xmath0 system .
this resonance , has been identified with the lowest mass of the anti - decuplet , the @xmath1 . at the same time
, there are a number of experiment , mostly at high energies , that report null results .
+ an overview of the experimental results so far obtained will be given here together with a review of the second generation experiments currently ongoing and planned at jefferson lab hall b. |
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* 60 * 73 ] ; cruise a m 2000 _ class . quantum grav . _ * 17 * 2525 ; url ` http://www.sr.bham.ac.uk/research/gravity ` | we present a proposal for a gravitational wave detector , based on the excitation of an electromagnetic mode in a resonance cavity .
the mode is excited due to the interaction between a large amplitude electromagnetic mode and a quasi - monochromatic gravitational wave .
the minimum metric perturbation needed for detection is estimated to the order @xmath0 using current data on superconducting niobium cavities . using this value together with different standard models predicting the occurrence of merging neutron star or black hole binaries ,
the corresponding detection rate is estimated to 120 events per year , with a ` table top ' cavity of a few meters length .
[ [ section ] ] during the last decades the quest for detecting gravitational waves has intensified .
the efforts have been inspired by the indirect evidence for gravitational radiation @xcite , advances in technology and the prospects of obtaining new useful astrophysical information through the development of gravitational wave astronomy @xcite .
a number of ambitious detector projects are already in operation or being built all over the world , for example ligo and allegro in usa , virgo , auriga and geo 600 in europe , tama 300 in japan , aigo and niobe in australia @xcite .
furthermore , there are well developed plans to use space based gravitational wave detectors , i.e. , the lisa project @xcite .
the detection mechanisms are basically of a mechanical nature in the cases above , but there have also been several proposals for electromagnetic detection mechanisms @xcite . in the present paper
we will investigate a detection mechanism based on the interaction of electromagnetic modes and gravitational radiation in a cavity with highly conducting walls
. the main feature of our proposed gravitational wave detector is that it supports two electromagnetic eigenmodes with nearby eigenfrequencies , a possibility that has previously been discussed in refs
. @xcite .
if one eigenmode is excited initially ( called the pump - mode ) , and a quasi - monochromatic gravitational wave with a frequency equal to the eigenmode frequency difference reaches our system , a new electromagnetic eigenmode can be excited due to the gravitational - electromagnetic wave interaction .
the coupling mechanism is similar in principle to the wave interaction processes described in , e.g. , ref .
@xcite .
the low - frequency nature of the gravitational modes , as compared to the electromagnetic resonance frequencies , at first seem to greatly limit the efficiency of a cavity with nearby frequencies . to get a large gravitationally induced mode - coupling for a simple cavity geometry ,
the estimated cavity dimensions become prohibitively large , i.e. , comparable to the wavelength of the gravitational wave . solutions to this problem
has been found by refs .
@xcite , who has considered a gravitational wave detector consisting of two coupled cavities .
cavities based on these principles have been built , and experimental results are presented in refs .
@xcite . in this letter
we consider a single cavity with a variable crossection .
the main purpose of varying the crossection is the following . for a cavity with dimensions much smaller than the wavelength of the gravitational wave
, the suggested geometry greatly magnifies the gravitational wave induced mode - coupling . in our present work
we have simulated the effect of a varying crossection , by considering a cavity filled with three different dielectrics , in order to be able to perform most of the calculations analytically .
it is straightforward to make a semi - quantitative translation of our results to the case of a vacuum cavity with a varying crossection . using current data on the latter type of cavity @xcite
, we estimate the minimum detection level of the metric perturbation to the value @xmath1 , where we have considered an inspiraling neutron star or black hole pair as a gravitational wave source .
if such a level of sensitivity can be reached , neutron star or black hole binaries close to collapse could be detected at a distance @xmath2 .
adopting data from ref .
@xcite for the occurrence of compact binary mergers , we obtain the estimate 120 detection events per year . in vacuum
, a linearized gravitational wave can be represented by @xmath3 where @xmath4 , and @xmath5 in standard notation .
neglecting terms proportional to derivatives of @xmath6 and @xmath7 , the wave equation for the magnetic field is @xcite @xmath8{\boldsymbol{b } } = \left [ h_+\left ( \frac{\partial^2}{\partial y^2 } - \frac{\partial^2}{\partial z^2 } \right ) + h_{\times}\frac{\partial^2}{\partial y\partial z } \right]{\boldsymbol{b } } , \label{waveb}\ ] ] and similarly for the electric field . here
@xmath9 is the index of refraction . for the moment
, we will neglect mechanical effects , i.e. , effects which are associated with the varying coordinates of the walls due to the restoring forces of the cavity .
the coupling of two electromagnetic modes and a gravitational wave in a cavity will depend strongly on the geometry of the electromagnetic eigenfunctions .
we can greatly magnify the coupling , as compared to a rectangular prism geometry , by varying the cross - section of the cavity , or by filling the cavity partially with a dielectric medium .
the former case is of more interest from a practical point of view , since a vacuum cavity implies better detector performance , but we will consider the latter case since it can be handled analytically .
_ however _ , we will show how to make a semi - quantitative translation of our results to the case of a varying cavity cross - section . specifically , we choose a rectangular cross - section ( side lengths @xmath10 and @xmath11 ) , and we divide the length of the cavity into three regions .
region 1 has length @xmath12 ( occupying the region @xmath13 ) and a refractive index @xmath14 .
region 2 has length @xmath15 ( occupying the region @xmath16 ) , with a refractive index @xmath17 , while region 3 consists of vacuum and has length @xmath18 ( occupying the region @xmath19 ) .
the cavity is supposed to have positive coordinates , with one of the corners coinciding with the origin .
furthermore , we require that @xmath20 , and that the wave number in region 2 is less than in region 1 .
the reason for this arrangement is twofold .
firstly , we want to obtain a large coupling between the wave modes , and secondly we want an efficient filtering of the eigenmode with the lower frequency in region three . the first step is to analyze the linear eigenmodes in this system .
the simplest modes are of the type [ region1 ] @xmath21e^{-i\omega t } , \\ b_{z } = \widetilde{b}_{zj}\cos \left ( \frac{m\pi x}{x_0}\right ) \sin [ k_{j}z + \varphi_{j}]e^{-i\omega t } , \\ b_{x } = -\frac{k_{j}x_0}{m\pi } \widetilde{b}_{zj}\sin \left ( \frac{m\pi x}{x_0}% \right ) \cos [ k_{j}z + \varphi_{j}]e^{-i\omega t } , \end{aligned}\ ] ] in regions @xmath22 , @xmath23 and @xmath24 , respectively , where the wave in region 3 is a standing wave , and @xmath25 is the mode number . in region 3 we may also have a decaying wave [ region2b ] @xmath26e^{-i\omega t } , \\ b_{z } = \widetilde{b}_{z3}\cos \left ( \frac{m\pi x}{x_0}\right ) \sinh [ k_{3}z+\varphi _ { 3}]e^{-i\omega t } , \\ b_{x } = -\frac{k_{3}x_0}{m\pi } \widetilde{b}_{z3}\sin \left ( \frac{m\pi x}{x_0}% \right ) \cosh [ k_{3}z+\varphi _ { 3}]e^{-i\omega t } .
\end{aligned}\ ] ] using standard boundary conditions , the wave numbers are calculated for an eigenmode , and the relation between the amplitudes in the three regions is found , and thereby the mode profile .
we are interested in the shift from decaying to oscillatory behavior in region 3 .
denote the highest frequency mode which is decaying in region 3 with index @xmath27 , and the wave number and decay coefficient with @xmath28 , @xmath29 and @xmath30 respectively .
similarly , the next frequency , which is oscillatory in both regions , is denoted by index @xmath31
. if we have @xmath32 ( and @xmath25 the same ) these two frequencies will be very close , and a gravitational wave which has a frequency equal to the difference between the electromagnetic modes causes a small coupling between these modes .
an example of two such eigenmodes is shown in fig . 1 . , @xmath33 , @xmath34 , @xmath35 and @xmath36 .
@xmath37 is the solid line and @xmath38 is the dotted line , and @xmath39 . ]
we define the eigenmodes to have the form @xmath40 , where @xmath41 is a time - dependent amplitude and the normalized eigenmodes @xmath42 satisfy @xmath43 .
we let all electromagnetic field components be of the form @xmath44 , where c.c
. stands for complex conjugate , and the indices stand for the eigenmodes discussed above .
the gravitational perturbation can be approximated by @xmath45 , where we neglect the spatial dependency , since the gravitational wavelength is assumed to be much longer than all of the cavity dimensions . during a certain interval in time ,
the frequency matching condition @xmath46 will be approximately fulfilled .
given the wave equation ( [ waveb ] ) , and the above ansatz we find after integrating over the length of the cavity @xmath47 where @xmath48 and we have added a phenomenological linear damping term represented by @xmath49 .
thus we note that for the given geometry , only the @xmath50-polarization gives a mode - coupling .
calculations of the eigenmode parameters show that @xmath51 may be different from zero when @xmath52 , and generally @xmath51 of the order of unity can be obtained , see fig . 1 for an example .
from eq .
( [ excitation - eq ] ) , we find that the saturated value of the gravitationally excited mode is @xmath53 in fig .
1 it is shown that we can get an appreciable mode - coupling constant @xmath51 for a cavity filled with materials with different dielectric constants , and it is of interest whether or not this can be achieved in a vacuum cavity . as seen by eq .
( [ coupling - int ] ) , the coupling is essentially determined by the wave numbers of the modes , given by @xmath54 . thus by adjusting the width @xmath10 in a vacuum cavity , we may get the same variations in the wave numbers as when varying the index of refraction @xmath9 .
the translation of our results to a vacuum cavity with a varying width is not completely accurate , however . when varying @xmath10 , the mode - dependence on @xmath55 and @xmath56 does not exactly factorize , in particular close to the change in width .
moreover , the contribution to the coupling @xmath57 in each section becomes proportional to the corresponding volume , and thereby also to the cross - section .
however , since most of the contribution to the integral in eq .
( [ coupling - int ] ) comes from region 1 , our results can still be approximately translated to the case of a vacuum cavity , by varying @xmath10 instead of @xmath9 such as to get the same wavenumber as in our above example .
we denote the minimum detection level of the excited mode with @xmath58 and the maximum allowed field in the cavity with @xmath59 .
the magnetic field @xmath58 is related to the minimum number of photons @xmath60 needed for detection by @xmath61 .
furthermore , we have @xmath62 @xmath63 , where @xmath64 is the quality factor of the cavity , and thus we obtain , using eq .
( [ saturation - eq ] ) , @xmath65 before giving estimates of the parameter values , we will investigate certain other effects that may limit the detection efficiency .
massive binaries produce monochromatic radiation to a good approximation , but close to merging , the frequency will be increasing rather rapidly which means that the phase matching will be lost .
the cavity is designed to detect the frequency @xmath66 , and we have assumed that the signal varies as @xmath67 , but in reality we have @xmath68 , where for simplicity we assume @xmath69 , @xmath70 at @xmath71 .
the coherence time @xmath72 is roughly defined by @xmath73 .
thus , @xmath74^{1/2}$ ] provided @xmath75 .
using newtonian calculations of two masses @xmath76 in circular orbits around the center of mass , complemented by the quadrupole formula for gravitational radiation , we find @xmath77 close to binary merging , the time of coherent interaction will be shorter than the photon life time , and in that regime the growth of the excited mode is limited by decoherence rather than the damping due to a finite quality factor of the cavity .
however , formula ( [ hplus ] ) can still be applied if we simply replace @xmath78 by @xmath79 . to be able to estimate the number of photons needed for detection
, we must study various sources of noise .
the simplest effect is direct thermal excitation of photons in mode @xmath31 .
since each mode has a thermal energy level of order @xmath80 , the number of such photons is @xmath81 .
however , we will also have a contribution associated with thermal variations in the length of the cavity .
a standard model for the variations in length @xmath82 is @xcite @xmath83 where @xmath84 is the eigenfrequency of longitudinal oscillations ( of the order of the acoustic velocity in the cavity divided by the length ) , @xmath85 is the mechanical quality factor associated with these oscillations , and @xmath86 is the stochastic acceleration due to the thermal motion , giving rise to a random walk in the oscillation amplitude .
first we note that the amplitude of the length variations with the gravitational frequency is @xmath87 .
we will consider the case when @xmath88 , which implies that _ the amplitude _ of the gravitational length perturbation is essentially unaffected by the restoring force of the cavity , as is the number of gravitationally generated photons . the thermal fluctuation contribution to the right hand side of eq.([excitation - eq
] ) , via the coupling to the pump wave , becomes proportional to @xmath89 $ ] .
since @xmath90 , the longitudinal oscillations give rise to slightly off - resonant ( i.e. , driven ) fields with a frequency difference @xmath91 compared to mode @xmath31 .
however , due to the stochastic changes in amplitude and/or phase of the longitudinal oscillation ( where the time - scale for significant changes is given by @xmath92 ) , a contribution to mode @xmath31 of the order @xmath93 is also made during a single oscillation period @xmath94 . here
@xmath25 is the mass taking part in the longitudinal oscillation . during a time of the order @xmath95
, this contribution adds up to approximately @xmath96 by a random walk process . using @xmath97 , the condition for the gravitational contribution @xmath98 to be larger than that of the thermal fluctuations
can be written @xmath99 assume that we want to reach a sensitivity @xmath100 .
we let @xmath101 , @xmath102 , @xmath103 , and @xmath104 which gives @xmath105 . furthermore , we take @xmath106 and let @xmath107 .
we assume @xmath108 together with @xmath109 . from ( [ h_therm_cond ] )
, we then find that we need a mechanical quality factor @xmath110 to reach the desired sensitivity .
moreover , assuming the necessary number of photons for detection to be @xmath111 ( well above the direct electromagnetic noise level of a few photons ) , @xmath112 and @xmath113 @xcite , we need an electromagnetic quality factor @xmath114 to reach the desired sensitivity @xmath115 .
note that the coherence time is slightly longer than the photon life - time , as needed .
following the example given above for calculating the coherence time , i.e. , a binary consisting of two compact objects , each of one solar mass @xmath116 , separated by a distance @xmath117 , the amplitude of the metric perturbation at a distance @xmath118 is given by @xmath119 . for definiteness
we choose @xmath120 corresponding to @xmath106 , and thus for @xmath121 of the order of @xmath122 we obtain the maximum observational distance @xmath123 . using data from ref .
@xcite , we deduce that the number of galaxies within the observational distance @xmath2 is of the order @xmath124 . combining these figures with the expected number of compact binary mergers per galaxy and million years @xcite
, we obtain a detection rate in the interval @xmath125 events per year ( the uncertainty is due to different models used for the birth of compact binaries ) .
our proposal for a gravitational wave detector is to a large extent based on currently available technology @xcite , and our requirements are moderate given the performance of some existing microwave cavities .
for example , values of @xmath126 has been reported in ref .
@xcite and quantum non - demolition measurements of single microwave photons have been made in ref.@xcite .
furthermore , the key performance parameters of the superconducting niobium cavities , i.e. , the quality factor and the maximum allowed field strength before field emission , have been improving over the years , suggesting that the detection sensitivity can be increased even further .
a sensitivity @xmath127 seems extremely good , but , on the other hand , idealizations have been made when making the estimate .
in addition to any effects induced by the gravitational wave , the walls generally vibrate slightly due to the electromagnetic forces exerted by the large pump field . while these later oscillations clearly will be larger than the variations in length that are directly due to the gravitational wave
, the associated nonlinearities will be harmonics of the pump frequency , and thus such effects do not couple to the other eigenmodes of the cavity .
furthermore , we have assumed that the detection of the excited mode is not much affected by the presence of the pump signals .
even though mode @xmath27 is partially filtered out in region 3 , the small frequency shift between the two electromagnetic modes may pose a certain difficulty in this respect : in particular , a very narrow bandwidth ( pump ) antenna signal must be used , in order to exclude the slightest initial perturbation at the gravitationally excited frequency @xmath128 .
however , although there are technical difficulties in constructing an electromagnetic detector , the real advantage is the possibility to reduce the size of the devise . in the example
presented above , the length of the cavity has been taken to be @xmath129 , and the cross section roughly @xmath130 .
this alone could prove to be useful when trying to set up new gravitational wave observatories .
we thank ulf jordan for helpful discussions . |
classification of networked data is a quite attractive field with applications in computer vision , bioinformatics , spam detection and text categorization . in recent years
networked data have become widespread due to the increasing importance of social networks and other web - related applications .
this growing interest is pushing researchers to find scalable algorithms for important practical applications of these problems .
+ in this paper we focus our attention on a task called _ node classification _ , often studied in the semi - supervised setting @xcite .
recently , different teams studied the problem from a theoretic point of view with interesting results . for example @xcite
developed on - line fast predictors for weighted and unweighted graphs and herbster et al . developed different versions of the perceptron algorithm to classify the nodes of a graph ( @xcite ) .
@xcite introduced a game - theoretic framework for node classification .
we adopt the same approach and , in particular , we obtain a scalable algorithm by finding a nash equilibrium on a special instance of their game . the main difference between our algorithm and theirs
is the high scalability achieved by our approach .
this is really important in practice , since it makes possible to use our algorithm on large scale problems .
given a weighted graph @xmath0 , a labeling of @xmath1 is an assignment @xmath2 where @xmath3 .
+ we expect our graph to respect a notion of regularity where adjacent nodes often have the same label : this notion of regularity is called _
homophily_. most machine learning algorithms for node classification ( @xcite ) adopt this bias and exploit it to improve their performances .
+ the learner is given the graph @xmath1 , but just a subset of @xmath4 , that we call training set .
the learner s goal is to predict the remaining labels minimizing the number of mistakes .
@xcite introduce also an irregularity measure of the graph @xmath1 , for the labeling @xmath4 , defined as the ratio between the sum of the weights of the edges between nodes with different labels and the sum of all the weights . intuitively , we can view the weight of an edge as a similarity measure between two nodes , we expect highly similar nodes to have the same label and edges between nodes with different labels being `` light '' .
based on this intuition , we may assign labels to non - training nodes so to minimize some function of the induced weighted cut . in the binary classification case , algorithms based on min - cut have been proposed in the past ( for example @xcite ) .
generalizing this approach to the multiclass case , naturally takes us to the _ multi - way cut _ ( or multi - terminal cut see @xcite ) problem .
given a graph and a list of terminal nodes , find a set of edges such that , once removed , each terminal belongs to a different component .
the goal is to minimize the sum of the weights of the removed edges .
+ unfortunately , the multi - way cut problem is max snp - hard when the number of terminals is bigger than two ( @xcite ) . furthermore , efficient algorithms to find the multi - way cut on special instances of the problem are known , but , for example , it is not clear if it is possible to reduce a node classification problem on a tree to a multi - way cut on a tree .
in this section we describe the game introduced by @xcite that , in a certain sense , aims at distributing over the nodes the cost of approximating the multi - way cut .
this is done by expressing the labels assignment as a nash equilibrium .
we have to keep in mind that , since this game is non - cooperative , each player maximizes its own payoff disregarding what it can do to maximize the sum of utilities of all the players ( the so - called social welfare ) .
the value of the multi - way cut is strongly related to the value of the social welfare of the game , but in the general case a nash equilibrium does not give any guarantee about the collective result . + in the graph transduction game ( later called gtg ) , the graph topology is known in advance and we consider each node as a player .
each possible label of the nodes is a pure strategy of the players . since we are working in a batch setting
, we will have a train / test split that induces two different kind of players : * * determined players*(@xmath5 ) those are nodes with a known label ( train set ) , so in our game they will be players with a fixed strategy ( they do not change their strategy since we can not change the labels given as training set ) * * undetermined players*(@xmath6 ) those that do not have a fixed strategy and can choose whatever strategy they prefer ( we have to predict their labels ) the game is defined as @xmath7 , where @xmath8 is the set of players , @xmath9 is the joint strategy space ( the cartesian product of all strategy sets @xmath10 ) , and @xmath11 is the combined payoff function which assigns a real valued payoff @xmath12 to each pure strategy profile @xmath13 and player @xmath14 . a mixed strategy of player @xmath14 is a probability distribution @xmath15 over the set of the pure strategies of @xmath16 .
each pure strategy @xmath17 corresponds to a mixed strategy where all the strategies but the @xmath17-th one have probability equals to zero .
we define the utility function of the player @xmath16 as @xmath18 where @xmath19 is the probability of @xmath20 .
we assume the payoff associated to each player is additively separable ( this will be clear in the following lines ) .
this makes gtg a member of a subclass of the multi - player games called polymatrix games . for a pure strategy profile @xmath21 ,
the payoff function of every player @xmath14 is : @xmath22 where @xmath23 means that @xmath16 and @xmath24 are neighbors , this can be written in matrix form as @xmath25 where @xmath26 is the partial payoff matrix between @xmath16 and @xmath24 , defined as @xmath27 , where @xmath28 is the identity matrix of size @xmath29 and @xmath30 represent the element of @xmath31 at row @xmath15 and column @xmath4 .
the utility function of each player @xmath32 can be re - written as follows : [ cols= " > , < " , ] the results of our experiments , shown in table [ t : multi ] , are not conclusive , but we can observe some interesting trends : * it is not really clear which one between gtg - ess and labprop is the most accurate algorithm , but anyway @xmath33 is always competitive with them .
* @xmath33 is always much better than wmv .
as expected wmv works better on `` not too sparse '' graphs such ghgraph , but even in this case it is outperformed by @xmath33 .
* gtg - ess and labprop s time complexity did not permit us to run them in a reasonable amount of time with our computational resources .
we introduced a novel scalable algorithm for multiclass node classification in arbitrary weighted graphs .
our algorithm is motivated within a game theoretic framework , where test labels are expressed as the nash equilibrium of a certain game . in practice ,
mucca works well even on binary problems against competitors like label propagation and shazoo that have been specifically designed for the binary setting .
several questions remain open .
for example , committees of mucca predictors work well but we do not know whether there are better ways to aggregate their predictions .
also , given their common game - theoretic background , it would be interesting to explore possible connections between committees of mucca predictors and gtg - ess . | we introduce a scalable algorithm , mucca for multiclass node classification in weighted graphs . unlike previously proposed methods for the same task , mucca works in time linear in the number of nodes .
our approach is based on a game - theoretic formulation of the problem in which the test labels are expressed as a nash equilibrium of a certain game .
however , in order to achieve scalability , we find the equilibrium on a spanning tree of the original graph .
experiments on real - world data reveal that mucca is much faster than its competitors while achieving a similar predictive performance . |
we congratulate marek jeabek for organizing an excellent conference . we thank maria krawczyk for several useful discussions .
this research was partially supported by the polish state committee for scientific research grants 2 p03b 184 10 , 2 p03b 89 13 and by the eu fourth framework programme `` training and mobility of researchers '' , network quantum chromodynamics and the deep structure of elementary particles , contract fmrx - ct98 - 0194 .
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* c53 * ( 1992 ) 219 . | the parametrisation of the photon structure function in the low @xmath0 region is formulated .
it includes the vmd contribution and the qcd improved parton model component suitably extrapolated to the low @xmath0 region .
the parametrisation describes reasonably well existing experimental data on @xmath1 for real photons and the low @xmath0 data on @xmath2 .
predictions for @xmath1 and for @xmath2 for energies which may be accesssible in future linear colliders are also given .
* @xmath3 at low @xmath0 + and @xmath1 at high energies * + , j. kwieciski @xmath4 and a. m. stato @xmath4 + @xmath5 _ department of physics , uppsala university , p.o.box 530 , 751 21 uppsala , sweden _
+ _ and institute of experimental physics , warsaw university , hoa 69 , 00 - 681 warsaw , poland _
+ @xmath4 _ department of theoretical physics , h. niewodniczaski institute of nuclear physics , + radzikowskiego 152 , 31 - 342 cracow , poland _
+ the structure function of the photon is described at large scales @xmath0 by the qcd improved parton model @xcite .
it is expected however that in the low @xmath0 region the vector meson dominance ( vmd ) contribution @xcite may also become important . here , as usual , @xmath6 where @xmath7 denotes the four momentum of the virtual photon probing the real photon with four momentum @xmath8 .
the cm energy squared @xmath9 of the @xmath10 system is @xmath11 .
+ in this talk we wish to present the representation of the photon structure function which includes both the vmd contribution together with the qcd improved parton model term suitably extrapolated to the low @xmath0 region .
this representation of the photon structure function is based on the extension of similar representation of the nucleon structure function to the case of the photon `` target '' @xcite .
possible parametrization of the photon structure function which extends to the low @xmath0 region has also been discussed in ref .
@xcite .
there do also exist several microscopic models describing the energy dependence of the total @xmath12 cross - section @xcite .
+ our representation of the structure function @xmath13 is based on the following decomposition : @xmath14 where in what follows we shall consider the structure function of the photon , i.e. @xmath15 . the terms @xmath16 and @xmath17 denote the vmd and partonic contributions respectively .
the vmd part is given by the following formula : @xmath18 where @xmath19 is the mass of the vector meson @xmath20 and @xmath21 denotes the @xmath22 total cross - section .
the parameters @xmath23 can be determined from the leptonic widths @xmath24 @xcite : @xmath25 the partonic contribution is expressed in terms of the structure function @xmath26 obtained from the qcd improved parton model analysis of the photon structure function in the large @xmath0 region @xcite : @xmath27 where @xmath28 with @xmath29 denoting the bjorken variable , i.e. @xmath30 .
the parameter @xmath31 should have its magnitude greater than the mass squared of the heaviest vector meson included in the vmd part and its value will be taken to be the same as in ref .
@xcite , i.e. @xmath32 gev@xmath33 .
+ the @xmath34 total cross - section @xmath2 is related in the following way to the photon structure function : @xmath35 after taking in equation ( [ sigma ] ) the limit @xmath36 ( for fixed @xmath37 ) we obtain the total cross - section @xmath38 corresponding to the interaction of two real photons .
the representation ( [ dec ] ) and equations ( [ vmd ] ) and ( [ partons ] ) give the following expression for this cross - section : @xmath39 in the large @xmath0 region the structure function given by eq .
( [ dec ] ) becomes equal to the qcd improved parton model contribution @xmath40 .
the vmd component gives the power correction term which vanishes as ( @xmath41 ) for large @xmath0 .
the modifications of the qcd parton model contribution ( i.e. replacement of the parameter @xmath29 by @xmath42 defined by equation ( [ xbar ] ) , the shift of the scale @xmath43 and the factor @xmath44 instead of 1 ) are also negligible at large @xmath0 and introduce the power corrections which vanish as @xmath41 .
+ in the quantitive analysis of @xmath45 and of @xmath38 we have taken the @xmath26 from the lo analysis presented in ref .
@xcite .
+ the vmd part was estimated using the following assumptions : 1 .
the numerical values of the couplings @xmath46 are the same as those used in ref .
@xcite .
they were estimated from relation ( [ gammav ] ) which gives the following values : @xmath47 2 .
the cross - sections @xmath48 are represented as the sum of the reggeon and pomeron contributions : @xmath49 where @xmath50 @xmath51 with @xmath52 and @xmath53 @xcite .
+ 3 .
the pomeron couplings @xmath54 are related to the corresponding couplings @xmath55 controlling the pomeron contributions to the total @xmath56 cross - sections assuming the additive quark model and reducing the total cross - sections for the interaction of strange quarks by a factor equal 2 .
this gives : @xmath57 + @xmath58 4 .
the reggeon couplings @xmath59 are estimated assuming additive quark model and duality ( i.e. dominance of planar quark diagrams ) .
we also assume that the quark couplings to a photon are proportional to the quark charge with the flavour independent proportionality factor .
this gives : @xmath60 + @xmath61 5 .
the couplings @xmath55 and @xmath62 are taken from the fit discussed in ref .
@xcite which gave : @xmath63 in fig.1 we compare our predictions with the data on @xmath64 @xcite .
we show experimental points corresponding to the `` low '' energy region ( @xmath65 10 gev ) @xcite and the recent preliminary high energy data obtained by the l3 and opal collaborations at lep @xcite .
we can see that the representation ( [ sgamgam ] ) for the total @xmath12 cross - section describes the data reasonably well . it should be stressed that our prediction is essentially parameter free .
the magnitude of the cross - section is dominated by the vmd component yet the partonic part is also non - negligible .
the latter term is in particular responsible for generating steeper increase of the total cross - section with increasing @xmath37 than that embodied in the vmd part which is described by the soft pomeron contribution .
the decrease of the total cross - section with increasing energy in the low @xmath37 region is controlled by the reggeon component of the vmd part ( see eqs .
( [ rpgv ] ) , ( [ rgv ] ) and ( [ lambda ] ) ) and by the valence part of the partonic contribution .
[ fig : fig1 ] in fig .
2 we show predictions for the total @xmath12 cross - section as the function of the total cm energy @xmath37 in the wide energy range which includes the energies that might be accessible in future linear colliders . we also show in this figure the decomposition of @xmath64 into its vmd and partonic components . we see that at very high energies these two terms exhibit different energy dependence .
the vmd part is described by the soft pomeron contribution which gives the @xmath66 behaviour with @xmath67 = 0.0808 ( [ lambda ] ) .
the partonic component increases faster with energy since its energy dependence reflects increase of @xmath68 with decreasing @xmath42 generated by the qcd evolution @xcite .
[ fig : fig2 ] this increase is stronger than that implied by the soft pomeron exchange . as the result the total @xmath12 cross - section , which is the sum of the vmd and partonic components does also exhibit stronger increase with the increasing energy than that of the vmd component .
it is however milder than the increase generated by the partonic component alone , at least for @xmath69 gev .
this follows from the fact that in this energy range the magnitude of the cross - section is still dominated by its vmd component .
we found that for sufficiently high energies @xmath37 the total @xmath70 cross - section @xmath64 described by eq .
( [ sgamgam ] ) can be parametrized by the effective power law dependence @xmath71 with @xmath72 slowly increasing with energy within the range @xmath73 for 30 gev @xmath74 10@xmath75 gev .
+ [ fig : fig3 ] in fig .
3 we compare our predictions for @xmath76 based on equations([dec ] , [ vmd ] , [ partons ] ) and ( [ sigma ] ) with the experimental data in the low @xmath0 region @xcite .
we can see that in this case the model is also able to give a good description of the data .
+ finally in fig .
4 we show our results for @xmath76 plotted as the function of @xmath0 for different values of the total cm energy @xmath37 .
we notice that for low values @xmath0 the cross - section does only weakly depend upon @xmath0 . in the large @xmath0 region
it follows the @xmath41 scaling behaviour modulated by the logarithmic scaling violations implied by perturbative qcd .
+ [ fig : fig4 ] to sum up we have presented an extension of the representation developed in refs .
@xcite for the nucleon structure function @xmath77 for arbitrary values of @xmath0 , onto the structure function of the real photon .
this representation includes both the vmd contribution and the qcd improved parton model component suitably extrapolated to the region of low @xmath0 .
we showed that it is fairly succesful in describing the experimental data on @xmath38 and on @xmath76 at low @xmath0 .
we also showed that one can naturally explain the fact that the increase of the total @xmath12 cross - section with increasing cm energy @xmath37 is stronger than that implied by soft pomeron exchange .
the calculated total @xmath12 cross - section was found to exhibit approximate power - law increase with increasing energy @xmath37 , i.e. @xmath78 with @xmath72 slowly increasing with energy within the range @xmath73 for 30 gev @xmath74 10@xmath75 gev . |
itamp is supported in part by a grant from the nsf to the smithsonian institution and harvard university .
vmm and glk were partially supported by faperj ( proceess nos .
e26/170.132 and 170.409/2004 ) and by the russian foundation for basic research ( grant no .
050818119a ) .
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* 59 * 357 mahanty j and ninham b w 1976 _ dispersion forces _ ( new york : academic press ) | the casimir - polder and van der waals interactions between an atom and a flat cavity wall are investigated under the influence of real conditions including the dynamic polarizability of the atom , actual conductivity of the wall material and nonzero temperature of the wall .
the cases of different atoms near metal and dielectric walls are considered .
it is shown that to obtain accurate results for the atom - wall interaction at short separations , one should use the complete tabulated optical data for the complex refractive index of the wall material and the accurate dynamic polarizability of an atom . at relatively large separations in the case of a metal wall ,
one may use the plasma model dielectric function to describe the dielectric properties of wall material .
the obtained results are important for the theoretical interpretation of experiments on quantum reflection and bose - einstein condensation .
[ [ section ] ] recently the study of dispersion interactions between an atom and a wall has assumed a new significance in connection with bose - einstein condensates of ultracold atoms [ 13 ] .
the van der waals and casimir - polder forces acting between dilute individual atoms , confined in a magnetic trap , and a wall may influence the stability of a condensate and the effective size of the trap @xcite . as was shown in ref .
@xcite , the study of the collective oscillations of the bose - einstein condensate can provide a sensitive test of dispersion forces .
this prediction was later supported both theoretically @xcite and experimentally @xcite .
dispersion interaction between an atom and a wall is also taken into account in quantum reflection of cold atoms on a surface @xcite and in dynamical interaction effects of fast atoms and molecules with solid surfaces @xcite .
currently the new asymptotic behavior of the surface - atom interaction out of thermal equilibrium has been advanced @xcite .
below we use the generic name casimir - polder " for all atom - wall interactions of dispersion nature because the pure nonretarded regime occurs at separations from zero to a few nanometers only .
the theoretical basis for the description of the casimir - polder interaction between an atom at a separation @xmath0 from a flat wall at temperature @xmath1 in thermal equilibrium is given by the lifshitz - type formula for the free energy [ 1012 ] @xmath2 \vphantom{\sum\limits_{l=1}^{\infty}}\right\}. \nonumber\end{aligned}\ ] ] here @xmath3 is the atomic dynamic polarizability , @xmath4 is the boltzmann constant , @xmath5 are the dimensionless matsubara frequencies , @xmath6 is the characteristic frequency of the casimir - polder interaction , and the reflection coefficients for two independent polarizations of electromagnetic field are defined as @xmath7 where @xmath8 is the permittivity of wall material computed at imaginary matsubara frequencies . for dielectrics @xmath9/[\varepsilon(0)+1]$ ] and for metals
. in most calculations of the atom - wall interaction previously performed only the limiting cases of large and short separations were considered .
the polarizability of the atom was taken into account in the static approximation @xcite or in the framework of the single - oscillator model @xcite , and the dielectric properties of the wall material were oversimplified ( for example , by considering a metal wall to be made of ideal metal ) .
the present experimental situation requires precise ( 1% accuracy ) computations of the casimir - polder interaction in a wide separation range from about 3 nm ( where the lifshitz formula becomes applicable ) to 10@xmath11 m . in this paper
we present the results of such computations clarifying the atomic and material properties which are essential to attain the required accuracy .
we have performed numerical computations of the free - energy ( [ eq1 ] ) , ( [ eq1a ] ) for metastable he@xmath12 , na , and cs atoms in ground state located near metal ( au ) , semiconductor ( si ) and dielectric ( sio@xmath13 ) walls at @xmath14k .
( the modification on account of walls in the spontaneous emission of rydberg atoms , obtained , e.g. , by means of two lasers , is discussed in refs .
. however , thermal quanta at @xmath14k are too small to excite atom from the ground state to some other states . )
three different descriptions for the dielectric properties of a metal were used : _
i _ ) as an ideal metal , _ ii _ ) using the dielectric permittivity from the free - electron plasma model @xmath15 ( where @xmath16 is the plasma frequency ) , and _
iii _ ) with @xmath17 obtained by means of dispersion relation using the tabulated optical data for the complex index of refraction @xcite .
the dielectric permittivity of a semiconductor or dielectric was described either by their static permittivity @xmath18 or by means of their tabulated optical data and the dispersion relation .
the polarizability of an atom was represented by its static value @xmath19 or by means of the highly accurate @xmath20-oscillator model @xcite @xmath21 where @xmath22 and @xmath23 are the electron mass and charge , @xmath24 and @xmath25 are the oscillator strength and frequency of the @xmath26th excited - state to ground - state transition , respectively . a more simplified single - oscillator model [ eq . ( [ eq2 ] ) with @xmath27 was also used .
@rccccccc & & + & & + @xmath28 @xmath29(nm)@xmath30 & ( a)&(b)&(c)&(d ) & ( a)&(b)&(c ) + 3@xmath31 & 3.80@xmath32 & 1.16 & 0.956 & 0.937 & 1.61@xmath32 & 1.78 & 0.949 + 10@xmath31 & 9.95@xmath33 & 1.14&0.961&0.948 & 4.18@xmath33 & 1.73 & 0.958 + 20@xmath31 & 1.18@xmath33 & 1.14&0.973&0.959 & 4.94@xmath34 & 1.68 & 0.967 + 50@xmath31 & 6.62@xmath35 & 1.13&0.984&0.976 & 2.71@xmath35 & 1.64 & 0.983 + 100@xmath31 & 6.98@xmath36 & 1.11&0.991&0.981 & 2.76@xmath36 & 1.60 & 0.993 + 150@xmath31 & 1.77@xmath36 & 1.10&0.997&0.992 & 6.93@xmath37 & 1.57 & 0.994 + computations show that at short separations ( from 3 nm to about 150 nm ) it is necessary to use the complete tabulated optical data for the complex index of refraction in order to find the most accurate results . for the dynamic polarizability of an atom , at shortest separations
the highly accurate data for it should be used . with increasing atom - wall distance up to several tens of nanometers
the single - oscillator model becomes applicable .
these calculations are illustrated in table 1 by the example of a metastable he@xmath12 atom near au and sio@xmath38 walls ( the analogous results for na and cs atoms near au , si , and sio@xmath38 walls can be found in refs .
@xcite ) . the tabulated optical data for au and sio@xmath13 were taken from ref .
@xcite , and the values of au plasma frequency and sio@xmath13 static permittivity are @xmath39rad / s and @xmath40 .
the accurate data for the dynamic polarizability of metastable he@xmath12 ( with a relative error of order @xmath41 ) were taken from ref .
@xcite and the parameters of a single - oscillator model from ref .
@xcite were used .
as is seen in table 1 , the use of the ideal metal or the static dielectric permittivity approximations leads to errors up to 16% for metal and 78% for dielectric
. these errors slowly decrease with increasing separation between the atom and the wall .
the plasma model is a better approximation than the ideal metal approximation .
it results in errors of about 5% at the shortest separations and becomes sufficiently exact when the separation approaches 150 nm .
the use of the static atomic polarizability would result in much greater errors and for this reason it is omitted from table 1 . at large separations , from 150 nm to a few micrometers ,
the effects of the atomic dynamic polarizability play a more important role than the effects of the finite conductivity of the metal . the single - oscillator model , however , is sufficient to achieve the required accuracy . the dielectric properties of a metal
can be approximated by the plasma model . for dielectrics and semiconductors both tabulated optical data and the ninham - parsegian representation for the dielectric permittivity @xcite are suitable for obtaining accurate results .
for sufficiently large separations one can use the static dielectric permittivity of the wall .
we illustrate these features using the example of a he@xmath12 atom near an au wall . due to the strongly nonmonotonous dependence of the free energy on separation , we plot along the vertical axis the ratio of the free energy to the casimir - polder energy @xmath42 of an atom near a wall made of ideal metal at @xmath43 . as is seen from fig . 1 , at separations @xmath44
m all approaches lead to approximately equal values of the free energy . to conclude , results such as those presented in the columns labeled ( a ) in table 1 and by line 1 in fig .
1 can be used in interpretation of precision experiments on atom - surface interactions . |
jet observables , event shapes and jet rates , revealed themselves as one of the richest laboratories to explore qcd .
being infrared and collinear safe ( irc ) , they can be predicted with perturbative ( pt ) techniques , but their high sensitivity to low energy emissions allows us to investigate the fairly unknown non - perturbative regime .
most discriminatory studies make use of distributions . in integrated distributions
@xmath0 one requires that the value of the observable @xmath1 a function of all secondary final state momenta @xmath2 and of the born momenta after recoil from the emissions @xmath3 be less than a fixed value @xmath4 @xmath5 the inclusive phase space region , where @xmath6 , is dominated by events with hard jets , which move the value of the observable far away from its born value , @xmath7 .
these events can be described with fixed order pt expansions , however they are quite rare , every additional jet being suppressed by an additional factor of @xmath8 .
more common events are characterised by a large number of soft - collinear emissions which modify only slightly the value of the observable from its born value , so that @xmath9 . here
fixed order predictions fail since every power of @xmath8 is accompanied by up to two large logarithms @xmath10 of the value of the observable . a reorganization of the pt expansion is then needed in order to resum all leading ( ll , @xmath11 ) and next - to - leading ( nll , @xmath12 ) logarithmic terms .
in the past few years the analytical resummation for a variety of observables have been presented in @xmath13-collision@xcite and dis@xcite .
the matching of resummed predictions with fixed order results allowed tests of qcd , measures of the coupling constant and studies of non - perturbative corrections@xcite .
however , the need for a separate analytical calculation for every observable has limited the experimental use of resummed predictions .
when dealing with multi - jet observables , analytical calculations become quite unfeasible , involving many integral transforms in order to write the distribution in a factorized form@xcite . also in some cases it turns out not to be possible to resum the observable analytically@xcite .
we present then here a general approach to resummation based on a preliminary automated analysis of the observable , to establish its relevant properties with respect to soft - collinear emissions ; in a subsequent step this information is used as an input of a general master formula .
we start by considering a born event consisting of @xmath14 hard partons ( ` legs ' ) , @xmath15 of which are incoming , with momenta @xmath16 .
we resum @xmath17-jet observables in the @xmath14-jet limit .
the ( positive defined ) observable should then 1 .
vanish smoothly as a single extra ( @xmath14+@xmath18 ) parton of momentum @xmath19 is made soft and collinear to a leg @xmath20 , with the functional dependence @xmath21 here @xmath22 is a hard scale of the process and the secondary emission @xmath19 is defined in terms of its transverse momentum @xmath23 and rapidity @xmath24 with respect to leg @xmath20 , and where relevant , by an azimuthal angle @xmath25 relative to a born event plane . by requiring the functional form ( in practise , almost always valid ) , the problem of analyzing the observable reduces in part to identifying , for each leg @xmath20 , the coefficients @xmath26 , @xmath27 , @xmath28 and the function @xmath29 .
irc safety demands @xmath30 .
2 . be _ recursively _ irc safe , i. e. given an ensemble of arbitrarily soft and collinear emissions , the addition of a relatively much softer or more collinear emission should not significantly alter the value of the observable , condition required for exponentiation of the leading logarithms .
observables like jet - rates in the jade algorithm are then excluded , and many other examples of non - exponentiating irc safe observables exist@xcite .
3 . be continuously global@xcite this means that for a single soft emission , the observable s parametric dependence on the emission s transverse momentum ( with respect to the nearest leg ) should be independent of the emission direction . in practice
this is perhaps the most restrictive of the conditions .
it implies @xmath31 . to enable our computer program caesar ( computer automated expert semi - analytical resummation ) to establish these properties with the desired degree of reliability and precision ,
we have found it useful to make use of multiple - precision arithmetic@xcite . given the above conditions
, one can derive the following nll master resummation formula for the distribution @xmath0@xcite
\nonumber \\ & & + \sum_{\ell=1}^{n_i } \ln \frac{f_\ell(x_\ell , v^{\frac{2}{a+b_\ell } } { \mu_\textsc{f}}^2)}{f_\ell(x_\ell , { \mu_\textsc{f}}^2 ) } + \ln s\left(t(l / a\right ) ) + \ln { { \cal{f}}}(c_1 r_1',\ldots , c_n r_n ' ) , \end{aligned}\ ] ] where @xmath33 is the color factor associated with born leg @xmath20 , and @xmath34 is its energy , @xmath35 is @xmath36 for quarks and @xmath37 for gluons , @xmath38 , and for incoming legs , @xmath39 are the parton densities .
we note that is independent of the frame in which one determines the @xmath28 and ( to nll accuracy ) of the choice of hard scale @xmath22 . the functions @xmath40 , which contain all the ll ( and some nll ) terms , are @xmath41 here @xmath8 , in the bremsstrahlung scheme@xcite , runs at two - loop order .
@xmath42 and @xmath43 are relevant only at nll level @xmath44 the process dependence associated with large - angle soft radiation is described by @xmath45 , whose form depends on the number @xmath14 of legs . for @xmath46 @xmath47
\,,\ ] ] where @xmath48 and @xmath49 , @xmath50 and @xmath51 denote the ( anti)-quarks and gluon .
the simpler case @xmath52 can be read from setting @xmath53 .
the @xmath54 formulae apply then to @xmath13 , dis and drell - yan production , while a process such as @xmath55 involves simply different color factors .
the ( more involved ) @xmath56 case needed to describe hadronic dijet production can be found in@xcite .
we examine now the factor @xmath57 . without it ,
. corresponds essentially to the probability of vetoing all emissions @xmath19 with @xmath58 .
however at nll subtle effects enter : a simple veto on _ single emissions _ turns out to be insufficient , since events might have @xmath59 though all emissions separately had @xmath60 , or vice versa .
this _ multiple emission _ effect , encoded in @xmath57 , is connected to how all secondary emission coherently determine the value of the observable and can be computed in a general way in@xcite . while this talk concentrates on the method ,
new results obtained with it were presented at this conference in@xcite ( and other results can be found in@xcite ) .
this project started with the development of an algorithm to numerically compute the non - trivial nll terms associated with multiple emissions .
it was initially applied by hand to three new observables [ 6 ] .
progress since then includes the derivation of a general master formula , together with a precise , automatically verifiable list of conditions on the observable for the resummation to be valid at nll and the full numerical implementation of this . though no human intervention is needed , results have the quality of analytic nll predictions , so that any hadronisation model can be applied , studies of renormalization and factorization scale dependence can be carried out and a matching with fixed order is feasible .
the most import results obtained up to now are the first resummations in hadronic dijet production , for a variety of observable at a time .
we now aim at automating the matching with fixed order results@xcite , this will open up the possibility to carry out a vast amount of phenomenological studies .
i thank the organizers of dis2003 , in particular yuri dokshitzer , for the friendly atmosphere at the conference , and for the opportunity to visit a wonderful town .
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a. banfi , g. p. salam and g. zanderighi , arxiv : hep - ph/0304148 and in preparation . | we present a master formula , with applicability conditions , which allows us to automate the resummation of infrared and collinear logarithms appearing in distributions of jet observables in qcd at next - to - leading logarithmic accuracy . |
structure growth via mergers is one of the main predictions of cdm type cosmologies .
however , what is predicted is the merger rates of dark matter halos , which are not directly observable .
using dark matter halo merger rates to predict galaxy merger rates requires a theory of galaxy formation or at least a model of how galaxies populate dark matter halos . in a similar way ,
what can actually be observed are close galaxy pairs , disturbed galaxies , or morphological differences between galaxies , all of which can only be indirectly tied to galaxy mergers using theoretical models . thus connecting theory to observations
poses a number of difficulties which are often not given enough attention .
in particular the halo merger rate is often used as an indicator of galaxy merger rates .
if galaxy mass scaled linearly with dark matter halo mass then this could possibly be true .
but differences in the shapes of the galaxy stellar mass and halo mass functions imply that galaxy formation is much less efficient in low and high mass halos .
thus we should expect that galaxy merger statistics should differ from halo merging statistics .
the majority of theoretical studies of merger rates analyze mergers of dark matter halos in n - body simulations ( * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* and references therein ) .
while there has been no study comparing the results of different analysis , differing treatments at least show qualitative agreement .
a summary of the results from these studies for halos associated with galaxy are : + 1 . halos rarely have major ( greater than 1:3 ) mergers .
minor mergers ( of order 1:10 ) are very common .
the merger rate shows weak dependance on halo mass . +
these results are displayed in the left panel of figure [ fig : time ] taken from @xcite which shows the fraction of halos that have accreted an object of a given mass as a function of lookback time .
only about a third of halos have had a major merger event involving a sizable amount of the halos final mass ; however , @xmath0 of halos have had a merger with an object with a mass one tenth of the halo s final mass . creating this plot for different final halo masses results in almost no change aside from a very slight increase in the likelihood of a merger for all merger ratios .
to go from dark matter halo merger rates to galaxy merger rates requires a theory of galaxy formation .
unfortunately at this time we have no theory that matches all the observed properties of galaxies , so the best that can be done is to explore the predictions of a given model of galaxy formation .
one possibility is to study the merger rates of galaxies in hydrodynamical simulations @xcite .
however , one must keep in mind , that hydrodynamical simulations at this time do not produce the observed galaxy stellar mass function .
mergers in a hydrodynamical simulation are in most ways similar to the results of dark matter halos .
major mergers are rare .
however , the merger rate does seem to show a much stronger dependance on galaxy mass then it does on halo mass ( see * ? ? ?
* figure 9 ) .
there is some small difference in the kinematics of galaxies compared to dark matter halos , most notably in their dynamical friction time scales , but this is unlikely to be the primary source of this mass dependance .
a much more important effect is that stellar mass does not scale linearly with halo mass .
this means that the mass ratio of a galaxy merger may vary greatly from the mass ratio of the halos in which the galaxies reside .
this understanding can explain why hubble type is such a strong function of galaxy mass .
a 1:3 merger in halo mass could result in a 1:10 or a 1:1 merger in galaxy mass depending on how galaxies inhabit dark matter halos .
we do nt know exactly how to assign galaxies to halos , but we know that galaxy formation must be very inefficient for high and low mass galaxies .
this can be seen in the right panel of figure [ fig : time ] , which shows the fraction of halo mass in the central galaxy using equation 7 of @xcite , which is obtained from a sdss galaxy group catalogue . while one can argue about the details of this result , the generic shape of the function in the plot
is well established . just from the shape of this function
we can understand why hubble type is a strong function of galaxy or halo mass . for low mass halos the efficiency of galaxy formation increases with halo mass
; so if two low mass halos merge the ratio of the stellar masses will be less than that of the halos .
but for high mass halos the efficiency of galaxy formation decreases with increasing mass , which leads to more nearly equal mass galaxy mergers .
this is illustrated in figure [ fig : comp ] which shows the mean number of objects accreted above a certain mass for different mass halos .
the left panel shows the dark matter case and simply plots equation 3 from @xcite for four different halo masses . in comparison
the right panel shows the same results for galaxy mass where the function from @xcite has been used to convert halo mass to central galaxy mass .
the point of this figure is just to show the striking difference in the two cases .
while there is almost no mass dependence in the dark matter halo case , for galaxies the expected number of events can differ by almost two orders of magnitude .
thus we would expect galaxy morphology to show dependance on mass . in conclusion , mergers of dark matter halos
are largely independent of halo mass , but galaxy mergers are most likely very dependent on mass .
measurements of galaxy merger statistics can be used as direct tests of galaxy formation models .
while major mergers between halos are rather rare they can be relatively common between galaxies of certain masses depending on how galaxies inhabit dark halos . | in the cdm cosmological framework structures grow from merging with smaller structures
. merging should have observable effects on galaxies including destroying disks and creating spheroids .
this proceeding aims to give a brief overview of how mergers occur in cosmological simulations . in this regard
it is important to understand that dark matter halo mergers are not galaxy mergers ; a theory of galaxy formation is necessary to connect the two .
mergers of galaxies in hydrodynamical simulations show a stronger dependence on mass than halo mergers in n - body simulations .
if one knows how to connect galaxies to dark matter halos then the halo merger rate can be converted into a galaxy merger rate . when this is done
it becomes clear that major mergers are many times more common in more massive galaxies offering a possible explanation of why hubble type depends on galaxy mass . |
the arecibo oh megamaser ( ohm ) survey selects candidates from the pscz redshift catalog ( saunders et al .
2000 ) with the criteria : ( 1 ) @xmath0 jy , ( 2 ) @xmath1 , and ( 3 ) @xmath2 ( darling & giovanelli 2000 ) . with a detection rate of 1 ohm in 6 candidates ,
the complete survey will double the sample of ohms to roughly 100 objects .
the survey has identified 35 new ohms in luminous infrared galaxies to add to the sample of 55 found in the literature .
there is a strong bias for the most fir - luminous galaxies to host ohms , and a weak fir color dependence ( see figure 1 ) .
ohms are detectable out to @xmath35 with modern instruments , and can thus be used to measure the high luminosity tail of the luminous ir galaxy luminosity function for redshifts spanning the epoch of major galaxy mergers ( @xmath4 ) .
blank field surveys for ohms at various redshifts can also measure the galaxy merger rate as a function of cosmic time ( briggs 1998 ) .
variability has been detected in several ohms , and is currently under investigation .
the variability appears over time scales of months in individual spectral features rather than in broad - band modulation which could be attributed to antenna calibration or pointing errors .
variability in ohms constrains the sizes of the variable and quiescent spectral features , regardless of the source of modulation ( intrinsic to the source or due to propagation effects ) .
intrinsically variable regions would have sufficiently small angular sizes that they would also be expected to scintillate ( see walker 1998 ) .
we thus attribute the variability to interstellar scintillation , which gives a weaker constraint on the sizes of emission regions than intrinsic variability .
variability in ohms , particularly those with @xmath5 , will provide a powerful tool for understanding the small - scale physical settings and mechanisms of masers which can be observed at cosmological distances .
briggs , f. 1998 , , 336 , 815 darling , j. & giovanelli , r. 2000 , , 119 , 3003 saunders , w. , et al .
2000 , in cosmic flows : towards an understanding of the large - scale structure in the universe , ed .
s. courteau , m. strauss & j. willick ( san francisco : asp ) , in press walker , m. a. 1998 , , 294 , 307 | we present the current results of a survey for oh megamasers ( ohms ) underway at the arecibo observatory .
the survey is 2/3 complete and has produced a high ohm detection rate ( 1 in 6 ) from a redshift - selected sample of _ iras _ galaxies .
the survey will relate the ohm luminosity function to the galaxy merger rate , allowing subsequent blind ohm surveys to measure the galaxy merger rate as a function of cosmic time .
the survey has also made the first detection of strong variability in ohms .
variability will provide a powerful tool for understanding the small - scale physical settings and mechanisms of ohms . |
at the 14th of september 2015 , the advanced ligo detectors registered for the first time a gravitational wave ( * ? ? ?
* ( abbott 2016 ) ) .
according to the analysis of the waveform , this wave testified the event of two merging black holes ( bhs ) of @xmath2 and @xmath3 at a distance of about 400mpc .
the immediate conclusion , and even the prediction prior to the measurement , was that such heavy bhs can only form by stellar evolution at low metallicity , where the mass - loss due to stellar winds is low and hence the stellar remnants can be more massive ( * ? ? ? * ( belczynski 2016 ) ) .
still heavily debated is whether such bhs form separately in dense clusters and then combine into a close pair by dynamical interactions , or whether they evolve as close binaries all the time .
since both scenarios have their problems , a primordial origin has also been suggested ( see postnov , these proceedings ) .
massive stars may end their life in a gravitational collapse while being in the red - supergiant ( rgs ) phase or as wolf - rayet ( wr ) stars .
the sample of putatively single and optically un - obscured galactic wr stars has been comprehensively analyzed with increasing sophistication ( cf.fig.[fig:hrd-galwr ] ) .
it became clear that the wn stars ( i.e. the wr stars of the nitrogen sequence ) actually form two distinct groups .
the very luminous wns with @xmath4 are slightly cooler than the zero - age main sequence and typically still contain hydrogen in their atmosphere ( often termed wnl for late ) .
in contrast , the less luminous wne stars are hotter ( `` early '' wn subtypes ) and typically hydrogen free .
the wr stars of the carbon sequence ( wc ) are composed of helium - burning products and share their location in the hertzsprung - russell diagram ( hrd ) with the wne stars . from this empirical hrd
one can deduce the evolutionary scenario ( * ? ? ? * ( sander 2012 ) ) .
the wnl stars evolve directly from o stars of very high initial mass ( @xmath5 ) . in the mass range
@xmath6 the o stars first become rsgs and then wne stars and finally wcs . stars with initially less then @xmath7 become rsgs and explode there as type ii supernova before having lost their hydrogen envelope .
evolutionary tracks still partly fail to reproduce this empirical hrd quantitatively , despite of all efforts , e.g. with including rotationally induced mixing .
the wne and wc stars are observed to be much cooler than predicted ; this is probably due to the effect of `` envelope inflation '' ( * ? ? ?
* ( grfener 2012 ) ) .
moreover , the mass ( and luminosity ) range of wne and wc stars is not covered by the post - rsg tracks .
evolutionary calculations depend sensitively on the mass - loss rates @xmath8 that are adopted as input parameters .
empirical @xmath8 suffer from uncertainties caused by wind inhomogeneities : when clumping on small scales ( `` microclumping '' ) is taken into account , lower values for @xmath8 are derived from observed emission - line spectra .
large - scale inhomogeneities ( `` macroclumping '' ) , on the other hand , can lead to underestimating mass - loss rates ( * ? ? ?
* ( oskinova 2007 ) ) . due to the open questions of mixing and the true @xmath8 , it is still uncertain which is the highest bh mass that can be produced from single - star evolution at galactic metallicity .
for instance , the luminosities of the two wo stars included in fig.[fig : hrd - galwr ] would correspond to masses as high as @xmath9 if they were chemically homogeneous , while the displayed evolutionary track for initially @xmath10 ends with only @xmath11 at core collapse .
the population of massive stars depends critically on their metallicity @xmath12 .
this becomes obvious , e.g. , from the wr stars in the small magellanic cloud ( smc ) where @xmath12 is only about 1/7 of the solar value .
in contrast to the galaxy , _ all _ putatively single wn stars in the smc show a significant fraction of hydrogen in their atmosphere and wind , like the galactic wnl stars . however , the wn stars in the smc are all hot and compact , located in the hrd ( fig.[fig : hrd - smc - wn ] ) between the zero age main sequence for helium stars ( he - zams ) and the h - zams ( or at least , in two cases , close the latter ) .
such parameters can not be explained with standard evolutionary tracks , unless very strong internal mixing is assumed which makes the stars nearly chemically homogeneous .
corresponding tracks are included in fig.[fig : hrd - smc - wn ] .
quantitatively , they still do not reproduce the observed hydrogen mass fractions .
stellar winds from hot massive stars are driven by radiation pressure intercepted by spectral lines .
the literally millions of lines from iron and iron - group elements , located in the extreme uv where the stellar flux is highest , play a dominant role .
hence a metallicity dependence is theoretically expected . for o stars ,
such @xmath12 dependence is empirically established ( * ? ? ?
* ( e.g. mokiem 2007 ) ) . for wn stars
, @xcite found a surprisingly steep dependence , probably due to the multiple - scattering effect ( see also hainich , these proceedings ) .
colors code in both cases for the hydrogen mass fraction ( see inlet ) . from @xcite , width=326 ]
hence , the lower mass - loss for massive o stars in the smc , compared to the galaxy , might reduce the angular - momentum loss and thus maintain the rapid rotation which causes the mixing and quasi - homogeneous evolution to the wr regime .
alternatively , one might speculate that the low @xmath8 in the smc is insufficient to remove the hydrogen envelope , and thus prevents the formation of single wr stars .
this would imply that the observed single wns have all formed through the binary channel , possibly as merger products .
but what happens with smc stars of slightly lower mass ? we have analyzed about 300 ob stars in the region of the supergiant shell sgs1 ( ramachandran in prep . ) .
their hrd positions are included in fig.[fig : hrd - smc - massivestars ] , together with `` normal '' tracks with less rotational mixing .
as the comparison shows , the o and b - type stars with initial masses below @xmath13 are consistent with `` normal '' evolution to the rsg stage .
only the more massive of stars might also be consistent with quasi - homogenous evolution , as are the wn stars discussed above .
, as are the quasi - homogeneous evolutionary tracks .
the `` normal '' tracks are also from @xcite but with slower initial rotation ( @xmath14km / s ) .
, width=326 ]
in their majority , massive stars are born in binary systems .
@xcite suggested a scenario of `` massive overcontact binary ( mob ) evolution '' that could lead to a tight pair of massive black holes as observed in the gw events .
two massive stars which are born as tight binary would evolve fully mixed due to their tidally induced fast spin and interaction .
they would swap mass several times , making their masses about equal , but under lucky circumstances they might avoid early merging .
figure[fig : hrd - pablo ] shows two such evolutionary tracks from marchant ( priv . comm . ) . in both examples ,
the tracks end at core collapse with a pair of @xmath15 objects .
we have calculated synthetic spectra for representative points along the evolutionary tracks ( marked by asterisks in fig.[fig : hrd - pablo ] ) and found that such spectra would look unspectacular if observed ; in the advanced stages , the stars would appear as wn - type ( with hydrogen , like those in the smc discussed above ) or , towards the end of the track for @xmath16 , as a hot wc type , always with otherwise weak metal lines due to the low abundances .
the only characteristic differences compared to single stars would be the doubled luminosity and , if the orbital inclination is favorite , the radial - velocity variation in the double - lined spectrum with short period . and
metallicity of 1/20 solar , and the another one for @xmath17 and metallicity of 1/10 solar .
the asterisks mark positions for which we calculated representative synthetic spectra ( hainich in prep . ) .
, width=326 ] | the recent discovery of a gravitational wave from the merging of two black holes of about 30 solar masses each challenges our incomplete understanding of massive stars and their evolution .
critical ingredients comprise mass - loss , rotation , magnetic fields , internal mixing , and mass transfer in close binary systems .
the imperfect knowledge of these factors implies large uncertainties for models of stellar populations and their feedback . in this contribution
we summarize our empirical studies of wolf - rayet populations at different metallicities by means of modern non - lte stellar atmosphere models , and confront these results with the predictions of stellar evolution models . at the metallicity of our galaxy , stellar winds are probably too strong to leave remnant masses as high as @xmath030m@xmath1 , but given the still poor agreement between evolutionary tracks and observation even this conclusion is debatable . at the low metallicity of the small magellanic cloud , all wn stars which are ( at least now ) single are consistent with evolving quasi - homogeneously .
o and b - type stars , in contrast , seem to comply with standard evolutionary models without strong internal mixing .
close binaries which avoided early merging could evolve quasi - homogeneously and lead to close compact remnants of relatively high masses that merge within a hubble time . |
the hall sensor array resides in the center of a printed circuit board ( pcb ) .
there is a hole in the pcb and the hall sensor is glued directly on a copper plate cold finger , which extends from the dr mixing chamber .
gold wire bonding connects the sensors and the leads on the pcb .
all wires are thermally connected to the mc .
typical sample dimensions are 3 @xmath18 2 @xmath71 1 mm@xmath31 .
the samples have clear facets and are oriented with the easy axis parallel to the applied field .
they are covered by a thin layer of super glue and placed directly on the surface of the hall sensor with apizon - n grease , which is used to protect the sample from disintegration and hold it in place .
the array backbone has a resistance of @xmath72 k@xmath73 at our working temperatures , and is excited with a 10@xmath74a dc current .
no effect of the sensors excitation on the dr - mixing chamber temperature was detected .
the hall voltage from each sensor is filtered with a 30 hz low - pass filter for hysteresis measurements and a 200 hz high - pass filter for the avalanche measurements .
the voltage is amplified @xmath75 times by a differential amplifier .
it is digitized with an ni usb 6251 a / d card at a rate of @xmath76 hz and @xmath77 khz for the hysteresis and avalanche measurements respectively .
the thermal diffusivity measurements are performed using two thermometers mounted on opposite sides of the sample and a heater on the hot side of the sample , whose configuration is shown in fig.[fig7 ] .
the hot side is attached to the cold finger and is hot only after the heat pulse .
the thermometers are ruo@xmath82 films .
the heater is a 2.2k@xmath73 resistor .
the hot side thermometer is between the heater and the sample .
the cold side thermometer is between the sample and a teflon plate .
it has a weak thermal link to the cold plate via the measurement wires only .
a heat pulse is generated by applying @xmath81 v to the 2.2k@xmath73 resistor using a function generator , which also gives the trigger for the ruo@xmath82 voltage measurement .
the system has been tested by repeating the measurement without the sample to ensure that the recorded heat on the cold side flows through the sample and not through the wires .
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matter phys . 1 , 109 ( 2010 ) | we report spatially resolved , time - dependent , magnetization reversal measurements of an fe@xmath0 single molecular magnet using a microscopic hall bar array . we found that under some conditions the molecules reverse their spin direction at a resonance field in the form of an avalanche .
the avalanche front velocity is of the order of @xmath1 m / sec and is sensitive to field gradients and sweep rates .
we also measured the propagation velocity of a heat pulse and found that it is much slower than the avalanche velocity .
we therefore conclude that in fe@xmath0 , the avalanche front propagates without thermal assistance .
single molecular magnets ( smm ) are an excellent model system for the study of macroscopic quantum phenomena and their interplay with the environment . in recent years , the focus of these studies shifted from single molecule to collective effects . while there are two famous smm that show quantum behavior , namely , fe@xmath0 and mn@xmath2 , most of the work on collective effects has been focused on mn@xmath2 .
indeed , in mn@xmath2 intriguing effects were found , such as deflagration @xcite , quantum assisted deflagration @xcite , and detonation @xcite .
in all these cases , a spin reversal front propagates through the sample as an avalanche .
although showing some signs of quantum behavior hernandez2005 , these processes are based on over - the - barrier magnetization reversal . here , we focus on the spin avalanche phenomena in fe@xmath0 , where pure quantum effects exist at dilution refrigerator ( dr ) temperatures .
we measure the avalanche velocity @xmath3 for various sweep rates and applied field gradients .
we also determine the thermal diffusivity .
we find that @xmath4 is much faster than the velocity at which heat or matching field propagates through the sample .
moreover , @xmath3 is affected by field gradients .
therefore , the avalanche in fe@xmath0 is a quantum effect sometimes called cold deflagration @xcite .
fe@xmath0 provides the first experimental manifestation of such cold deflagration .
the fe@xmath0 smm has spin @xmath5 ground state , as does mn@xmath2 .
the magnetic anisotropy correspoding to an energy barrier between the spin projection quantum number @xmath6 and @xmath7 is @xmath8 k worensdorferscience99,mukhin2001,barra1996,caciuffo1998,park2002 ; in mn@xmath9 this anisotropy is @xmath10 k @xcite .
fe@xmath0 molecules show temperature - independent hysteresis loops at @xmath11 mk , with magnetization jumps at matching fields that are multiples of @xmath12 twernsdorfer2000,wernsdorfer1999 . however , when tunneling is taking place from state @xmath13 to @xmath14 , where @xmath15 , the excited state can decay to the ground state @xmath16 , releasing energy in the process . in a macroscopic sample
, this energy release can increase the temperature and support a deflagration process by assisting the spin flips .
spontaneous deflagration in mn@xmath2 takes place at various and not necessarily matching fields higher than @xmath1 t. the deflagration velocity starts from @xmath1 m / sec and increases with an increasing ( static ) field up to @xmath17 m / sec suzuki2005 .
our avalanche velocity measurements are based on local and time - resolved magnetization detection using a hall sensor array .
the array is placed at the center of a magnet and gradient coils . a schematic view of the array and coils is shown in the inset of fig . [ fig1 ] .
the array is made of hall bars of dimensions 100@xmath18100 @xmath19m@xmath20 with 100 @xmath19 m intervals ; the active layer in these sensors is a two - dimensional electron gas formed at the interface of gaas / algaas heterostructures .
the surface of the hall sensors is parallel to the applied field .
consequently , the effect of the applied field on the sensor is minimal and determined only by the ability to align the array surface and field . the sample and sensors
are cooled to @xmath21 mk using a dr .
more details on the hall measurements can be found in the supplemental material .
a magnetic field gradient could also be produced by two superconducting coils wound in the opposite sense .
they are placed at the center of the main coil and produce @xmath22 mt / mm per ampere .
since there is no option of adjusting the sample position after it has been cooled it is reasonable to assume that the sample is not exactly in the center of the main magnet .
in addition , the sample has corners and edges .
therefore , a field gradient is expected even when the gradient coils are turned off . in the experiments ,
the molecules are polarized by applying a magnetic field of @xmath23 t in the @xmath24 direction .
afterwards , the magnetic field is swept to @xmath25 t. the sweep is done at different sweep rates and under various applied magnetic field gradients . during the sweep ,
the amplified hall voltage from all sensors and the external field are recorded . from the raw field - dependent voltage of each sensor ,
a straight line is subtracted .
this line is due to the response of the hall sensor to the external field .
the line parameters are determined from very high and very low fields where no features in the raw data are observed . in our experiments , we found that fe@xmath0 samples can be divided into two categories : those that do not show avalanches , which have multiple magnetization steps regardless of the sweep rate , and those that show avalanches where the number of magnetization steps depends on the sweep rate . in fig .
[ fig1 ] , we present the normalized hall voltage as detected by one of the hall sensors from a sample of the first category .
the normalization is by the voltage at a field of 1 t where the molecules are fully polarized .
thus , the normalized voltage provides @xmath26 , where m is the magnetization and @xmath27 is the saturation magnetization .
the bottom abscissa is for a sweep where the field decreases from @xmath1 t. the top abscissa is for a sweep where the field increases from @xmath28 t. the magnetization shows typical steps at intervals of 0.225 t. no step is observed near zero field . in addition , the hysteresis loop s coercivity increases as the sweep rate increases .
these results are in agreement with previous measurements on fe@xmath0 @xcite .
they are presented here to demonstrate that the hall sensors are working properly , that their signals indeed represent the fe@xmath0 magnetization , and that in some samples all magnetization steps are observed .
the hysteresis loop of a sample from the second category is plotted in the bottom inset of fig .
[ fig1 ] . in this case
, there is a small magnetization jump at zero applied field , followed by a nearly full magnetization reversal at a field of @xmath29 t in the form of an avalanche . in all samples tested in this and other experiments in our groupleviantphotons ,
avalanches occurred only at the first matching field .
we could not tell in advance whether a sample was of the first or second category .
we always worked with samples of approximately the same dimensions ( @xmath30 mm@xmath31 ) .
this is in contrast to mn@xmath2 , where avalanches are associated with large samples @xcite .
avalanche velocity measurements in fe@xmath0 should be done with extra care . in an avalanche
there is , of course , a propagating front where spins flip .
but since our measurement in fe@xmath0 are done by sweeping the field through resonance , there is a similar front even without avalanche .
this is demonstrated in the inset of fig .
[ fig2 ] . in this inset , a sample placed off the symmetry point of a symmetric field profile
is shown .
thus , the sample experiences a field gradient . due to this gradient ,
tunneling of molecules will start first at a particular point in the sample where the local field is at matching value .
the spin reversal front will then propagate from that point to the rest of the sample as the external field is swept . in this case , pausing the field sweep will stop the magnetization evolution .
this is demonstrated in fig .
[ fig2 ] for an avalanche free sample .
the left ordinate is the normalized hall voltage ( solid symbols ) from three different sensors on the array .
each symbol represents a different sensor .
the right ordinate is the applied magnetic field ( line ) .
the voltage and field are plotted as a function of time .
we focus on fields before , near , and after the third transition in fig .
[ fig1 ] . for the most part
, the magnetization changes only when the field changes , even in the middle of a magnetization jump .
this means that the sample is subjected to some field gradients and a tunneling front propagates through the sample even without an avalanche .
it is possible to estimate the matching field front velocity of @xmath32 m / sec from a typical transition width ( @xmath33 t ) , a typical sweep rate ( @xmath34 mt / sec ) and the sample length ( @xmath35 mm ) . in fig .
[ fig3 ] , we zoom in on the magnetization jump of samples from the second category at a @xmath29 t field . in this figure , we show the time - resolved hall voltage from five different sensors along the array .
the three middle sensors show a peak in the hall voltage , which is experienced by each sensor at different times .
the two outer sensors experience a smoother variation of the hall voltage , in the form of cusps , also at different times .
this type of behavior is a clear indication of a magnetization reversal avalanche propagating from one side of the sample to the other .
the peaks and cusps are due to a zero magnetization front , where the magnetization @xmath36 changes sign due to tunneling . at the same front
, the magnetic induction @xmath37 from the sample is forced to point outward and toward the sensors , to maintain zero divergence friedman2010 .
this is demonstrated in the inset of fig .
[ fig2 ] . by following the time evolution of the peaks and cusps
, we can determine the front velocity .
since the sensors are spaced by parts of a millimeter and the peaks are spaced by parts of a millisecond , the avalanche velocity @xmath38 is of the order of @xmath1 m / sec , which is much higher than @xmath39 .
we found that the avalanche propagation direction can be affected by applying field gradients as long as the sweep rate is low .
this is demonstrated in fig .
[ fig4 ] . in this figure
, we show for each detector location the time at which it experiences a peak or a cusp .
the slope of each line is the avalanche velocity . for the lowest sweep rate of 0.83
mt / sec with no gradient , the velocity is negative .
it becomes positive as the gradient is switched on to 0.14 mt / mm , but becomes slower as the gradient increases to 0.69 mt / mm .
the effect of the gradient is opposite and weaker for our highest sweep rate of 8.3 mt / sec . in this case , all velocities are positive and increase as the gradient increases . only at the intermediate sweep rate of @xmath40
mt / sec does the gradient have no effect on the velocity .
although we find it challenging to explain the gradient dependence of the avalanche velocity , we do learn from this experiment that the safest sweep rate from which one can estimate the avalanche velocity is around @xmath41 mt / sec . in this case
, the external gradient does not affect the velocity .
the ratio between sweep rates and gradient ( when it is on ) is a quantity with units of velocity of the order of tens of millimeters per second .
this is much lower than @xmath3 .
therefore , the gradient experiment is another indication , but with an avalanching sample , that the propagation of the external magnetic field does not determine the avalanche velocity , and that @xmath4 is an internal quantity of the molecules .
in addition , our ability to affect @xmath3 with the gradient field rules out the possibility that the avalanche is due to over - the - barrier spin flips . finally , in fig .
[ fig5 ] we depict the avalanche velocities @xmath3 as a function of sweep rate with zero applied gradient .
the field was swept from positive to negative and vice versa .
the sample used in this experiment was of the second category and produced avalanches only for sweep rates higher than 3 mt / sec .
slower sweep rates generated the usual magnetization jumps , as shown in fig .
[ fig1 ] .
although there is some difference between the velocity for different sweep directions , it is clear that the velocity tends to increase with increasing sweep rate , and perhaps saturate . in light of the gradient experiment , the most representative avalanche velocity of fe@xmath42 is @xmath43 m / sec . to clarify the role of heat propagation in the avalanche process of fe@xmath0
, we also measured the thermal diffusivity @xmath44 between @xmath45 mk and @xmath1 k. this is done by applying a heat pulse on one side of the sample for a duration of @xmath46 msec , and measuring the time - dependent temperature on the hot side ( @xmath47 ) and on the cold side ( @xmath48 ) of a sample of length @xmath49 mm .
more experimental details are provided in the supplemental material .
the results are shown in fig .
[ fig6 ] .
the thermal diffusivity is defined via the heat equation @xmath50 where @xmath51 is the location and time dependent temperature along the sample . for a long rod @xmath52
, one has that @xmath53we fit this expression to our @xmath54 data with @xmath55 and @xmath44 as fit parameters .
@xmath55 accounts for the coupling of the two thermometers to the sample .
the fit is shown by the solid line in fig .
[ fig6 ] .
although the fit is not perfect , it does capture the data quite well .
the @xmath44 obtained with this method at a few different temperatures is depicted in the inset of fig.[fig6 ] .
@xmath44 and @xmath56 obey the long rod condition .
it is much smaller than @xmath44 of mn@xmath2 , which is estimated to be @xmath57 to @xmath58 m@xmath20/sec @xcite .
now , we can generate a heat velocity @xmath59 where @xmath60 is the sample cross section . at @xmath61
mk we find that @xmath62 m / sec .
this is roughly @xmath63 divided by the time between the peak of @xmath64 and that of @xmath65 .
our experiments show that @xmath66 .
this means that the spin reversal front outruns the matching field as it crosses the sample .
more important , the avalanche outruns the heat generated in its wake .
every new molecular spin that tunnels does so at the dr temperature .
although heat is produced in the process , this heat does not propel the tunneling front forward .
moreover , the avalanche starts only at the first matching field and it s velocity is affected by a field gradient .
therefore , the avalanche properties are sensitive to the resonance conditions .
all these observations render the avalanche in fe@xmath0 a quantum mechanical phenomena .
the open question is then what sets its velocity . a natural guess , of tunnel splitting @xmath67 sec@xmath68 times
unite cell size of @xmath69 nm , namely , @xmath70 m / sec is too slow @xcite . therefore , to address this question , more profound considerations have to be taken into account .
this study was partially supported by the russell berrie nanotechnology institute , technion , israel institute of technology . |
we thank g. kohring , d. stauffer and c. tsallis for interesting discussions .
this work was performed within the sfb 341 kln
aachen jlich supported by the dfg .
[ fig2 ] time - dependence of the activity for @xmath42 and various values of @xmath13 .
the system size is @xmath72 . concerning the statistical error we observe that all runs using different random numbers yield curves that are indistinguishable on this scale .
[ fig3 ] determination of @xmath43 : the system size is @xmath73 , @xmath42 and @xmath68 ( lower curve ) , @xmath57 ( middle curve ) and @xmath74 ( upper curve ) .
the straight line in the middle is the function @xmath75 .
we conclude that @xmath76 .
[ fig5 ] time - dependence of the distance for @xmath77 and @xmath78 ( lower curve ) , @xmath69 ( upper curve ) .
the system size is @xmath79 .
the curve for @xmath69 shows that @xmath80 is well inside the chaotic region , whereas @xmath81 lies within the frozen phase .
this fact stronly supports reentrance .
the emerging phase diagram in the vicinity of the tricritical point is depticted in the insert the two black dots represent the parameter values for the two curves shown . | we present numerical and analytical results for a special kind of one - dimensional probabilistic cellular automaton , the so called domany - kinzel automaton .
it is shown that the phase boundary separating the active and the recently found chaotic phase exhibits reentrant behavior .
furthermore exact results for the @xmath0=0-line are discussed .
pacs numbers : 87.10.+e , 02.50.+s , 89.80.+h cellular automata have been an intensive research field in recent years @xcite due to their computational simplicity and the wide range of applications in various areas . even in one dimension
a particular probabilistic variant ( domany - kinzel automaton ) of the originally deterministic cellular automata shows a rich phase diagram including directed percolation and other critical phenomena @xcite . only recently
a new phase in this model has been explored numerically exhibiting chaotic behavior @xcite .
this region of the diagram , up to a deterministic corner - point , is not accessible to exact treatments up to now .
nevertheless sophisticated approximation - methods , which systematically go beyond mean - field theory , have been applied successfully @xcite . in the so called tree - aproximation @xcite one
finds reentrant behavior in two directions , which is not fully understood yet .
this phenomenon has never been observed in numerical simulations up to now @xcite .
therefore one might ask , whether this reentrant behavior is a real feature of the model or just an artifact of the tree - approximation .
this issue is the main topic of the present paper , where we try to clearify this point with an alternative approximation method ( the cluster - approximation ) as well as with large scale monte - carlo simulations ( up to @xmath1 sites ) . to state the final results already at this place : the cluster - approximation again yields reentrant behavior in two directions and the simulations show clear evidence for reentrance near the tricritical point .
the model we consider is defined as follows : the domany - kinzel pca consists of a one - dimensional chain of @xmath2 binary variables , @xmath3 , @xmath4 taking on the values @xmath5 ( empty , occupied ) .
all sites are updated simultaneously ( i.e.parallel ) at discrete time steps and the state of each site at time @xmath6 depends only upon the state of the two nearest neighbors at time @xmath7 according to the following rule : @xmath8 \right\ } \end{aligned}\ ] ] where @xmath9 is the ( time - independent ) conditional probability that site @xmath10 takes on the value @xmath4 given that its neighbors have the values @xmath11 and @xmath12 at the previous time step .
@xmath13 ( @xmath0 ) is the probability that site @xmath10 is occupied if exactly one ( both ) of its neighbors is ( are ) occupied .
if neither neighbor is occupied , the site @xmath10 will also become empty , therefore the state with all sites empty is the absorbing state of the pca . the @xmath14-phase diagram , as it is known up to now , consists of three different phases .
most of it ( small enough @xmath13 ) is dominated by the _ frozen _
phase , where all initial conditions eventually lead into the absorbing state .
with other words , the activity @xmath15 tends to zero for @xmath16 within the frozen phase . for large enough @xmath13
one enters the @xmath17 phase , where , starting from a random initial condition , the system ends up in a state with a finite density of active sites . within this active phase
one can distinguish between a chaotic and a non - chaotic part .
this difference can be seen by starting with two slighly different ( random ) initial conditions @xmath18 and
@xmath19 subjected to the same external noise ( local updating rules ) . calculating the normalized distance @xmath20 of these two systems @xmath21 during the update of the replicated systems according to the rule displayed in equation ( 2 ) of reference @xcite one
observes a sharp transition from the chaotic phase , characterized by @xmath22 , to the active phase with @xmath23 ( in the following we call the active / non - chaotic phase simply the active phase ) .
the underlying picture is that in the latter case the system is characterized by only one attractor , which nevertheless depends strongly on the external noise . with other words , in this phase the noise ( and not the initial condition ) dominates the dynamics completely .
this is not true for the chaotic phase , where the system memorizes the initial state even after infinite time .
first we present analytical results obtained by the application of the so - called cluster - approximation already known in different contexts @xcite as probability path method @xcite or local structure theory @xcite . in this way we check earlier results @xcite derived with a different approximation scheme ( the tree - approximation ,
see @xcite ) .
the problem with the dynamical rules defined above is that one can not write down the probability distribution of the stationary state since no simple detailed balance condition can be derived .
therefore , in principle , it is necessary to solve the dynamics completely in order to obtain the equilibrium properties .
this is not possible in general .
one way out of this dilemma is to take into account systematically all possible correlations between @xmath24 neighboring sites ( @xmath24-cluster approximation ) and to treat interactions over longer distances by conditional probabilities .
more formally , given the probability @xmath25 for the configuration @xmath26 in an @xmath24-cluster - approximation the probabilitiy for configuration @xmath27 with @xmath28 is approximated to be : @xmath29 here @xmath30 denotes the conditional probability to find site @xmath31 in state @xmath32 given that the @xmath33 sites to the left are in the state @xmath34 .
a factorisation of this kind can describe the stationary state exactly only if the interactions extend over not more than @xmath24 sites .
a natural choice for the conditional probaility @xmath35 is @xmath36 with @xmath37 simple examples of one - dimensional systems which can be described exactly by a finite value of @xmath24 are the @xmath38-spin - ising - model where one needs @xmath39 for the exact equilibrium distribution ( @xmath40 being the standard one - dimensional ising model with next - neighbour interactions only ) @xcite .
another example is the the parallel asymmetric exclusion process where again @xmath41 leads to the exact result for the stationary state @xcite the phase diagram resulting from a calculation based on the cluster approximation with @xmath41 is shown in figure 1 .
since during one update step according to the rules equation 1 the even ( odd ) sites only depend on the odd ( even ) sites at the timestep before we performed two timesteps at once to deal with sites of only one fixed parity .
one firstly observes that @xmath41 is still far from the exact solution for the stationary state .
unfortunately higher approximations are very hard to obtain due to the exponentially growing number of equations to be analysed simultaneously ( especially for the distance @xmath20 with two replicated systems ) .
furthermore even for @xmath41 the resulting equations can not be solved analytically with final closed expressions but have to be iterated until one finds a fixed point of the system of equations . in order to obtain a better localisation of the phase boundaries we applied the same method described below to analyse the numerical data from the monte - carlo - simulations . as can be seen from the figure we find reentrant behaviour both in @xmath13- and @xmath0-direction comparable to the result from the tree approximation @xcite .
it seems that the tricritical point has moved upwards , but a detailed analysis of the results suggests that it remains on the @xmath42-line . for the frozen / active - phase boundary one can go to larger clusters with higher values of @xmath24 . in tabular 1 the critical values @xmath43 ( @xmath42 ) for of @xmath44
are given : @xmath45 a simple least square fit leads to a limiting value for @xmath43 of about @xmath46 which is significantly larger than the known values from the simulations @xcite . in order to test the predictions of both approximation schemes mentioned above we performed large - scale monte - carlo simulations of the domany - kinzel cellular automaton with probabilities @xmath13 and @xmath0 in the vicinity of the two end - points of the phase boundary of the chaotic phase ( i.e. : @xmath47 and @xmath48 ) , where reentrance could occur according to the above calculations .
the system - sizes were up to @xmath49 sites with periodic boundary conditions , and the number of iterations @xmath50 were maximally @xmath51 . in this way
one avoids self - correlations ( finite size effects ) , since after @xmath7 updates those sites separated by a distance smaller than @xmath7 are correlated .
therefore @xmath50 has to be smaller than @xmath2 . by choosing @xmath2 much larger than @xmath50 one improves the statistics significantly ( for obvious reasons , since one can devide the system into many statistically independent subsystems ) .
therefore no finite - size effects are present in our data ( which was checked by comparing results for different system sizes ) and we need not to perform a ( non - trivial ) extrapolation the infinite system @xmath52 .
furthermore the probability that the system gets trapped by the absorbing state ( @xmath53 ) after time @xmath7 increases with decreasing system size .
this renders the simultaneous limit @xmath52 and @xmath54 to a delicate point , which we also avoid by our approach .
looking at the data obtained from the simulations it turned out to be rather unreliable to try to discriminate between two phases by looking at the long - time limit of the order parameter ( activity @xmath55 or distance @xmath20 ) . apart from the two phase - boundaries we expect exponential decay of @xmath55 and @xmath20 to their asymptotic values .
exactly on the phase - boundary we expect the spectrum of relaxation times to extend to infinity and thus the decay to become algebraic .
this behavior is illustrated in figure 2 : the activity as a function of time is depicted in a log - log plot for increasing values of @xmath13 ( @xmath42 ) .
we see that below a certain value the curves are bended downwards , whereas above this value the curves are bended upwards reflecting exactly the behaviour explained above .
the curve just in the middle corresponding to @xmath56 is closest ( as defined quantitatively by a least square fit ) to a straight line . to determine @xmath43 more accurately we performed longer runs with larger system sizes and depict the result in figure 3 . the middle curve , corresponding to @xmath57 , is nicely approximated by an algebraic decay with an exponent @xmath58 .
this exponent agrees well with the universal order parameter exponent @xmath59 determined in reference @xcite . from figure 3
we determined @xmath43 to be @xmath60 .
this is the most accurate estimate of @xmath43 so far .
surprinsingly it is significantly larger than the value @xmath61 obtained with a different method but with system sizes of around @xmath62 @xcite .
it seems that in the latter reference the long transient times ( @xmath63 ) together with the small system sizes lower the critical value due to larger correlations in the system as known from similar systems @xcite . as we have mentioned above the finite size scaling analysis of small systems
is by no means straightforward and can not be done without further ad hoc assumptions , from which our method is free .
hence , from our point of view , the results we quote seem to be more reliable .
note that there is no overlap even of the error bars of the two critical values . in figure 4
we show the same scenario for @xmath64 . by the same arguments as above we now locate the critical value of @xmath13 ( i.e.the value at which the transition from vanishing to finite activity takes place ) to be @xmath65 , which is significantly lower than @xmath43 . for larger increasing values of @xmath0
the phase boundary between frozen and active phase bends down monotonically to smaller values of @xmath13 terminating at the point ( @xmath66 , @xmath67 ) which is exactly known since the whole @xmath67-line is exactly solvable . in figure 5
a comparison of the two curves for @xmath20 at @xmath68 , which is below @xmath43 , for @xmath42 and @xmath69 is shown .
note that ( 0.8090,0 ) lies within the frozen phase .
the upper curve bends upwards , which means that ( 0.8090,0.03 ) lies within the chaotic phase .
this is indicated by the schematic phase diagram depicted in the insert of figure 5 and which has been supported by simulations of various parameters @xmath14 in this region .
the two black dots represent the two curves shown and along the arrow connecting them one finds clear evidence for reentrant behavior .
the phase boundary of the chaotic phase therefore bends to the left up to values around @xmath69 and for larger values of @xmath0 it bends monotonically to the right until it terminates at the point @xmath48 .
one reason for the fact that this phenomenon was not seen in earlier simulations is that it is in fact a marginal effect observable only in high - precision simulation - data .
we also performed large scale simulations around the other endpoint of the chaotic / active phase boundary . here
it is quite evident that the reentrant behaviour parallel to the @xmath13-axis at @xmath48 is in fact an artifact of the approximation schemes and not existent in the actual system . concerning the question of the conjugate field for the order - parameter of the chaotic phase posed in reference @xcite one can make on the @xmath0=0-line exact statements .
since both the activity and the chaos order parameter obey exactly the same evolution equations @xcite it is easy to conclude that the conjugated fields also should be equivalent . for the activity one chooses independent random numbers at each site and each timestep ( on the @xmath0=0-line
this is just the role of @xmath13 ) .
accordingly one chooses for the chaotic order parameter independant random numbers at each site and each timestep ( rule @xmath70 in ref.@xcite ) .
the absorbing state now corresponds to identical variables states in the two replicas yielding the same update since the same noise has to be applied for equal configurations in the two systems .
this picture remains valid for @xmath71 although the evolution equations are no longer identical , but the absorbing state has the same properties .
note that on the line @xmath42 the critical exponents of the order - paramater are also the same .
if universality holds away from this line this statement should be true also for @xmath71 ( for @xmath67 it is known , that the critical exponents are different @xcite ) . in summary
we have shown in this letter that , in contradiction to previous findings , the chaotic phase in fact shows reentrant behaviour in the vicinity of the tricritical point as predicted by approximative analytical methods .
the effect was not seen before since it is relatively small and large scale simulations have to be made to detect it . on the other hand in the near of the @xmath13=1-line the predicted reentrant behaviour
is absent .
furthermore one can see that simulations of small systems with long transient times can lead to erroneous conclusions about the locations of the critical point as well as the shape of the phase boundary since it is difficult to estimate the error due to self correlations .
therefore the error - bars in reference @xcite seem to neglect these systematic errors and should be larger ( which could lead to an agreement with our results ) .
finally we have seen that the conjugate field to the chaotic order parameter can directly be identified from the equivalence to the activity order parameter on the @xmath0=0-line . |
[ sec:1 ] * remark .
* notation @xmath0 is equivalent to @xmath1 where @xmath2 } _ { n\times 1 } \ , & \rho & = & \rho_{ij } & = & \underbrace { \left [ \begin{array}{c } \rho_{1j } \\ \vdots \\ \rho_{nj } \\ \end{array } \right ] } _ { n \times 1 } \ . \end{array}\ ] ] notation @xmath3 is equivalent to @xmath4 where @xmath5}_{n \times n } } \ .
\end{array}\ ] ] let us consider ( e.g. for @xmath6 ) variance of the difference @xmath7 of two random variables @xmath8 and @xmath9 , where @xmath10 , in terms of covariance @xmath11 introducing the estimation statistics @xmath12 @xmath13 in terms of correlation function @xmath14 @xmath15 if @xmath16 and @xmath17 or @xmath18 if @xmath19 and @xmath20 the unbiasedness constraint ( i condition ) @xmath21 is equivalent to @xmath22 the minimization constraint @xmath23 where @xmath24 produces @xmath25 equations in the @xmath26 unknowns : kriging weights @xmath27 and a lagrange parameter @xmath28 ( ii condition ) @xmath29}_{n\times(n+1 ) } } & \cdot & \underbrace { \left [ \begin{array}{c } \omega_j^1
\\ \vdots \\ \omega_j^n \\ \mu_j \\ \end{array } \right ] } _ { ( n+1)\times 1 } & = & \underbrace { \left [ \begin{array}{c } \rho_{1j } \\ \vdots \\ \rho_{nj } \\ \end{array } \right ] } _ { n \times 1 } \end{array}\ ] ] multiplied by @xmath30 @xmath31 and substituted into @xmath32 @xmath33 ^ 2\}-\underbrace{e^2\{v_j-\hat{v}_j\}}_0 \\ & = & e\{[(v_j - m)-(\hat{v}_j - m)]^2\ } \\ & = & e\{[v_j - m]^2\}-2(e\{v_j\hat{v}_j\}-m^2)+e\{[\hat{v}_j - m]^2\ } \\ & = & \sigma^2 -2 \sigma^2 |\omega^i_j \rho_{ij}| + \sigma^2 |\omega^i_j \rho_{ii } \omega^i_j| \\ & = & \sigma^2 \pm 2 \sigma^2 \omega^i_j \rho_{ij } \mp \sigma^2 \omega^i_j \rho_{ii } \omega^i_j \end{array}\ ] ] give the minimized variance of the field @xmath8 under estimation @xmath34 ^ 2\ } = \sigma^2 ( 1 \pm ( \omega^i_j \rho_{ij } + \mu_j ) ) \ ] ] and these two conditions produce @xmath26 equations in the @xmath26 unknowns @xmath35}_{(n+1)\times(n+1 ) } } & \cdot & \underbrace { \left [ \begin{array}{c } \omega_j^1 \\ \vdots \\ \omega_j^n \\ \mu_j \\ \end{array } \right ] } _ { ( n+1)\times 1 } & = & \underbrace { \left [ \begin{array}{c } \rho_{1j } \\ \vdots \\ \rho_{nj } \\ 1 \\ \end{array } \right ] } _ { ( n+1 ) \times 1 } \ . \end{array}\ ] ]
since @xmath36 then @xmath37 and ( since ) @xmath38 then @xmath39 the minimized variance of the field @xmath8 under estimation @xmath34 ^ 2\ } = \sigma^2 ( 1\pm(\omega^i_j \rho_{ij } + \mu_j))\ ] ] has known asymptotic property @xmath40 ^ 2\ } = \lim_{n \rightarrow \infty } e\{[v_j-\omega^i_j v_i]^2\ } = e\{[v_j - m]^2\ } = \sigma^2 \ .\ ] ]
let us consider the field @xmath8 under estimation @xmath41 where for auto - estimation holds @xmath42 with minimized variance of the estimation statistics @xmath43 ^ 2\ } & = & cov\{(\omega^i_j v_i)(\omega^i_j v_i)\ } \\ & = & \sum_i\sum_l\omega^i_j \omega^l_j cov\{v_i v_l\ } \\ & = & \sigma^2 |\omega^i_j \rho_{ii } \omega^i_j| \\ & = & \mp\sigma^2(\omega^i_j \rho_{ij}-\mu_j ) \ , \end{array}\ ] ] where for auto - estimation holds @xmath44 ^ 2\ } = e\{[v_i - m]^2\ } = \sigma^2\ ] ] that means outcoming of input value is unknown for mathematical model , with minimized variance of the field @xmath8 under estimation @xmath45 ^ 2\ } & = & \sigma^2(1\pm(\omega^i_j \rho_{ij } + \mu_j ) ) \end{array}\ ] ] where for auto - estimation holds @xmath46 ^ 2\ } = \underbrace{e\{[v_i - m]^2\}}_{\sigma^2 } - \underbrace{2(e\{v_i\hat{v}_i\}-m^2)}_{2\sigma^2 } + \underbrace{e\{[\hat{v}_i - m]^2\}}_{\sigma^2 } = 0\ ] ] that means variance of the field is equal to variance of the ( auto-)estimation statistics ( not that auto - estimation matches observation ) .
for @xmath47 @xmath48 } _ { n \times 1 } = \xi \underbrace { \left [ \begin{array}{c } 1 \\
\vdots \\ 1 \\ \end{array } \right ] } _ { n \times 1 } \qquad \xi \rightarrow 0 ^ - ~(\mbox{or } ~\xi \rightarrow 0^+ ) \ ] ] and a disjunction of the minimized variance of the field @xmath8 under estimation @xmath49 ^ 2\ } - \underbrace{(e\{v_j\hat{v}_j\}-m^2)}_{\mp\sigma^2\xi } + \underbrace{e\{\hat{v}_j[\hat{v}_j - v_j]\}}_{\mp\sigma^2\xi } \quad \mbox{if } \quad \rho_{ij } \omega^i_j + \mu_j = \xi+ \mu_j=0\ ] ] which fulfills its asymptotic property the kriging system @xmath50}_{(n+1)\times(n+1 ) } } & \cdot & \underbrace { \left [ \begin{array}{c } \omega^1 \\ \vdots \\ \omega^n \\ - \xi \\ \end{array } \right ] } _ { ( n+1)\times 1 } & = & \underbrace { \left [ \begin{array}{c } \xi \\ \vdots \\ \xi \\ 1 \\ \end{array } \right ] } _ { ( n+1 ) \times 1 } & \end{array}\ ] ] equivalent to @xmath51 and @xmath52 where : @xmath53 , @xmath54 , @xmath55 , has the least squares solution @xmath56 and @xmath57 with a mean squared error of mean estimation @xmath58 ^ 2\ } = \mp\sigma^2 2\xi \ .\ ] ]
for white noise @xmath45 ^ 2\ } & = & e\{[v_j - m]^2\}+e\{[\hat{v}_j - m]^2\ } \\ * remark .
* precession of arithmetic mean can not be identical to @xmath62 cause a straight line fitted to high - noised data by ordinary least squares estimator can not have the slope identical to @xmath62 .
for this reason the estimator of an unknown constant variance @xmath63 in fact is the lower bound for precession of the minimized variance of the field under estimation @xmath34 ^ 2\ } = \sigma^2\left(1+\frac{1}{n}\right)\ ] ] to increase ` a bit ' the lower bound for @xmath64 we can effect on weight and reduce total counts @xmath25 by @xmath65 because @xmath65 is the closest positive integer number to @xmath62 so it is easy to find the closest weight such that @xmath66 then the so - called unbiased variance @xmath67 in fact is the simplest estimator of minimized variance of the field under estimation . | we present statistics ( s - statistics ) based only on random variable ( not random value ) with a mean squared error of mean estimation as a concept of error . |
here we show that if one uses an isotropic exchange interaction instead of the anisotropic interactions in the teleportation protocol one can also perform adiabatic teleportation . in this case
the initial hamiltonian is @xmath90\end{aligned}\ ] ] and the final hamiltonian is @xmath91\end{aligned}\ ] ] where we have expressed these hamiltonians in terms of the encoded operations given in eq . 1 of the main text .
these equations show that now instead of two decoupled encoded qubits , the encoded qubits are coupled .
however notice that the initial ground state is the @xmath92 eigenstate of @xmath23 and @xmath24 and the final ground state is the @xmath92 eigenstate of the @xmath27 and @xmath28 , just as in anisotropic exchange protocol , but with the signs flipped .
further there are no level crossing in a linear ramping between these two hamiltonians , and the gap is a constant @xmath93 occurring at the midpoint of this evolution .
thus the adiabatic teleportation protocol caries through for the isotropic exchange .
notice , importantly , that the coupling however must be antiferromagnetic .
here we provide more details on how to implement the hamiltonian in eq . 4 in the main text using the perturbation theory gadgets of bartlett and rudolph @xcite .
in these gadgets , one replaces one of the qubits in a three - qubit interaction by an _ encoded _
qubit across two qubits .
since we need two three - qubit interactions , this means that we require two extra qubits in this construction .
we label our logical qubits @xmath94 and @xmath95 ( for left and right ) , and encode each into four physical qubits labeled 1 4 . and @xmath95 , each encoded in three physical qubits @xmath96 , where the ancillas facilitate the teleportation as discussed in the main text .
blue bars represent @xmath97 couplings , while green triangles represent interactions of the form @xmath98 ( and similarly with @xmath99 ) as in eq .
( [ e : ideal ] ) .
] let s recall eq .
4 , relabeled here as in fig .
[ f : ideal ] .
the ideal initial hamiltonian is @xmath100 , \end{aligned}\ ] ] where @xmath101 $ ] just means to add the terms which exchange the qubits @xmath94 and @xmath95 .
now let s add the ancilla qubits and move to the encoded subspace .
the encoded subspaces we are working in are the subspaces spanned by @xmath102 and @xmath103 on qubits @xmath104 and @xmath83 .
we can force the joint state of qubits 3 and 4 to lie in this subspace by adding a strong @xmath105 coupling term to the ideal hamiltonian .
thus , eq . ( [ e : ideal ] ) can be realized using encoded operators as the following target hamiltonian @xmath106 . \end{aligned}\ ] ] here the encoded operators ( with bars on top ) are @xmath107 for both the left and right qubits and we are assuming that the coupling strengths satisfy @xmath108 .
we are free to choose either @xmath109 or @xmath110 for the encoded @xmath111 operation because these operators act equivalently up to multiplication by the stabilizer of the encoded subspace . writing this out in terms of the pauli operators on the physical qubits , we find ( for one such choice of encoded @xmath5 ) @xmath112 .\end{aligned}\
] ] following bartlett and rudolph , we use the following initial hamiltonian .
it is a two - body gadget hamiltonian that simulates the low energy behavior of the above target hamiltonian , and is given by @xmath113 .\end{aligned}\ ] ] the @xmath9 term in this hamiltonian by itself would force the ground state of qubits @xmath104 and @xmath83 to be in the subspace spanned by @xmath102 and @xmath103 as discussed above .
the @xmath71 term is now a two - qubit interaction which simulates the four - body term in the target hamiltonian .
our desired final hamiltonian is given by @xmath114 .\end{aligned}\ ] ] notice , importantly , that we leave on the interaction which forces qubits @xmath104 and @xmath83 into the encoded subspace during the entire evolution . as usual , our total evolution is given in terms of the scaled time @xmath19 by @xmath115 this evolution is depicted in fig .
[ f : gadget ] .
we must show that the above adiabatic evolution has high fidelity with the ideal evolution and that the gap is not too small .
the fidelity is governed by the overlap of the ground state of @xmath10 with the ground state of the ideal ( encoded ) hamiltonian @xmath116 . .
the simulation gadget uses one additional ancilla qubit ( labeled @xmath83 ) per logical qubit .
qubits @xmath104 and @xmath83 are bound by strong @xmath117 couplings for the duration of the evolution , as shown by the broad green bars .
blue bars represent two - body interactions @xmath118 , while the red horizontal bar represents a @xmath119 coupling .
when the coupling strengths are chosen so that @xmath120 , this adiabatic evolution simulates the ideal evolution of eq .
( [ e : ideal ] ) and fig .
[ f : ideal ] .
the fidelity of the simulation is @xmath121 and the energy gap governing the adiabatic condition is given by @xmath122 . ] in order to analyze this gadget it is useful to perform a change of basis .
in particular if one undoes the controlled - phase gate between the ancilla qubits @xmath123 and @xmath124 , then above hamiltonian becomes a sum of terms acting separately on @xmath94 and @xmath95 .
since this is a unitary conjugation it does nt change the gap , and we can also find the ground state in this basis and transform back . since the hamiltonian is now decoupled across @xmath94 and @xmath95 , we drop these subscripts now and write the transformed initial hamiltonian as @xmath125 note that the final hamiltonian is unaffected by this transformation , and so we need merely to drop the @xmath94 and @xmath95 superscripts to obtain @xmath126 let s first find the ground state of the initial hamiltonian so we can check the fidelity .
we can further simplify things by applying a controlled - not gate from qubit 3 to qubit 2 resulting in @xmath127 in this basis , qubits 1 and 2 completely decouple , and the fidelity depends only on the overlap of this ground state with the bell state @xmath128 on qubits 3 and 4 .
we can exactly diagonalize by first transforming to the bell basis .
let s define @xmath129 to be our small expansion parameter .
then the ground state of eq .
( [ e : twoprimes ] ) on qubits 3 and 4 is given by @xmath130 where the coefficient @xmath131 is @xmath132 expanding in powers of @xmath129 , the fidelity is @xmath133 which is corrected at second order in @xmath134
. now let s compute the gap to see what price we must pay to achieve high fidelity .
in the basis where we have applied a controlled - not from qubit 3 to qubit 2 , the final hamiltonian is @xmath135 note that @xmath136 and @xmath137 commute with both the initial and final hamiltonian , corresponding to the encoded quantum information .
suppose we work in a basis where this information is in the @xmath22 eigenstate of @xmath136 .
then the final hamiltonian simplifies to @xmath138 here we see that qubits @xmath88 and @xmath84 are decoupled from those of @xmath104 and @xmath83 .
if one linearly sweeps between these initial and final hamiltonians , one will obtain a minimal gap for each of these evolutions .
the smaller of these gaps comes from qubits @xmath104 and @xmath83 .
explicitly , the evolution to consider is @xmath139 -s [ \lambda z_3 + \omega ( z_3 z_4)].\ ] ] the gap between the lowest two eigenvalues of this evolution is @xmath140 where @xmath141 using the fact that @xmath142 for @xmath143 we can bound this as @xmath144 we can upper bound the lower equation by @xmath145 , and we can use @xmath146 for @xmath147 to express the gap as @xmath148 this obtains its max at @xmath149 for @xmath150 this yields a bound on the gap of @xmath151 thus we have shown that the initial fidelity with the proper ground state is high @xmath152 , and also that the energy scale which sets the adiabatic condition is set by the perturbative energy scale , @xmath153 . for fault - tolerance we require a fixed accuracy and our results imply that the gadget construction can achieve this , albeit at the cost of the energy gap shrinking and thus a slower adiabatic gate time . | the difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers . here
we introduce a simple universal primitive , adiabatic gate teleportation , which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space .
notably this construction allows for geometric robustness based upon the control of two independent qubit interactions .
further , our piecewise adiabatic evolution easily relates to the quantum circuit model , enabling the use of standard methods from fault - tolerance theory for establishing thresholds . building a quantum computer
is a daunting task , so much so that it is not even clear which of a plethora of architectures is the most physically viable .
in addition to the standard pulsed implementation of the circuit model of quantum computation ( qc ) , other possible architectures include measurement - based qc @xcite , universal adiabatic qc @xcite , and holonomic qc @xcite .
of these , adiabatic qc has recently drawn considerable attention , in part because of its deep connection to computational complexity problems @xcite , but also due to the advantages this model possesses with respect to decoherence and control @xcite .
similarly holonomic qc has attracted interest because of the geometric robustness of control in this scheme . motivated by some of the benefits of adiabatic and holonomic qc , we introduce a new model of qc which is a hybrid between the adiabatic , circuit , and holonomic models .
this model uses nothing but adiabatic quantum evolution , but instead of using a single interpolation between an initial and final hamiltonian , we use piecewise adiabatic evolutions whose individual parts implement a step in a quantum circuit .
we achieve this by introducing a new primitive : adiabatic gate teleportation ( agt ) .
our route to agt proceeds by merging two quantum computing protocols : teleportation and adiabatic qc .
quantum teleportation is the process of transferring the state of a qubit between two distant parties via the use of an initial shared entangled state and two bits of classical communication @xcite .
notably , while teleportation consumes a bell pair @xmath0 shared between the parties , it can end with a bell pair localized to the sender . in adiabatic qc @xcite one
adiabatically turns off one hamiltonian while turning on another hamiltonian , dragging the system from the ground state of the initial hamiltonian to that of the final hamiltonian .
the initial hamiltonian is chosen such that preparing the system in its ground state can be done efficiently , and the final hamiltonian is chosen so that its ground state is the solution to a computational problem .
motivated by teleportation and adiabatic quantum algorithms , we will attempt to adiabatically mimic teleportation .
this will lead us to an adiabatic protocol for swapping with a simple control scheme that we call adiabatic teleportation .
the main theme of this paper is to use variants on this adiabatic teleportation scheme and the analogy with gate teleportation @xcite to build a universal quantum computer from piecewise adiabatic evolutions .
constant - gap piecewise adiabatic evolution has previously been considered in the context of state preparation @xcite and in the context of producing geometric quantum gates from noncyclic adiabatic evolution @xcite .
our model is distinguished from these results by achieving universality and geometric robustness with separately controlled interactions , and by its explicit connection to gate teleportation . _ adiabatic teleportation _
our setup uses three qubits .
the first qubit is the qubit whose state we wish to transport ( swap ) to the third qubit .
the second qubit is merely a mediator , which ( we will see ) is necessary . at the beginning of the computation
we construct a system whose ground state has a single bell pair @xmath1 on the second and third qubit .
we then adiabatically drag the system to a new hamiltonian whose ground state has a bell pair on the first and second qubit ( again @xmath1 . ) throughout the evolution the lowest energy level , which is two - fold degnerate , remains degenerate .
if we encode a single qubit of information into this degeneracy , then after this adiabatic evolution the information in this first qubit will now reside in the third qubit .
we choose the initial hamiltonian for our three qubits to be @xmath2 and the final hamiltonian to be @xmath3 where @xmath4 and @xmath5 are single qubit pauli matrices , @xmath6 represents the operator @xmath7 acting on the @xmath8th qubit , and the identity acting on all other qubits and @xmath9 sets the energy scale .
the ground state of @xmath10 is two - fold degenerate : we can choose a basis for this space as @xmath11 and @xmath12 .
similarly , the ground state of @xmath13 is spanned by @xmath14 and @xmath15 . in other words , initially we can store a qubit of information in the first qubit and in the final system we can store it in the third qubit and both configurations are ground states of their respective hamiltonians .
now suppose we adiabatically drag the system between @xmath10 and @xmath13 .
for example , we may linearly turn off @xmath10 and turn on @xmath13 so that @xmath16 from time @xmath17 to @xmath18 and @xmath19 is a dimensionless scaled time with scale @xmath20 .
( other interpolation schemes are certainly possible , and indeed this is one of the benefits of using an adiabatic evolution . )
the above evolution moves the information stored in the first qubit to the third qubit , as we now show .
let s first define logical qubit operators @xmath21 initially we are in the @xmath22 eigenstate of @xmath23 and @xmath24 .
writing @xmath25 in this basis we find @xmath26 since this hamiltonian does not include the first logical qubit , it is untouched by the evolution .
this hamiltonian is nothing more than the time dependent sweeping of @xmath23 to @xmath27 and @xmath24 to @xmath28 .
evidently this means that if we perform the above evolution slow enough , then , since we start in the @xmath22 eigenstates of @xmath23 and @xmath24 , at the end of the evolution we will be in the @xmath22 eigenstates of @xmath27 and @xmath28 .
a minimum energy gap of @xmath29 occurs when @xmath30 .
can we figure out what happens to the first qubit under the above evolution ?
we can express the first qubit pauli operators in terms of the above logical qubits : @xmath31 and @xmath32 .
since we start off in the @xmath22 eigenspace of @xmath24 and @xmath23 , we see that the logical information is really encoded into the first logical qubit . as we have argued above , this qubit is untouched by the evolution .
thus when @xmath18 we must have the same logical information in the first qubit , but now be in the @xmath22 eigenvalue subspace of @xmath27 and @xmath28 . now notice that @xmath33 and @xmath34 .
thus we see that actually the information from the first qubit has been dragged to the information on the last qubit .
because the gap of the above adiabatic quantum evolution is constant , if we evolve the system sufficiently slowly and in a smooth enough manner , then the adiabatic theorem guarantees that we can achieve the above process with a high fidelity .
there are numerous adiabatic theorems that can be proven ( see for example @xcite ) which provide guarantees that by making @xmath20 sufficiently large we can increase the probability that the adiabatic evolution will act successfully ( meaning the probability that the system is excited out of the desired subspace is smaller than some constant ) .
choosing @xmath35 is sufficient to guarantee a constant error probability below the threshold for fault - tolerant qc @xcite .
_ three qubits are necessary _
we have shown that it is possible to swap quantum information between two qubits via a simple adiabatic interpolation between two fixed hamiltonians on three qubits .
is it possible to achieve a similar result without the ancilla qubit ? if we wish to simply interpolate between two two - qubit hamiltonians , then no .
this does not imply that it is impossible to adiabatically swap two qubits , only that a construction which behaves like the adiabatic quantum algorithm is not possible .
we will also see how this null result implies significant benefits over other adiabatic schemes such as holonomic qc .
suppose we have two qubits which we wish to swap by adiabatically ramping between an initial hamiltonian @xmath36 and a final hamiltonian @xmath37 .
the initial and final hamiltonians are required to be degenerate such that we can store a single qubit of information in these systems .
further the initial ( final ) hamiltonian must allow for this degeneracy to reside only in the first ( second ) qubit .
without loss of generality , we can pick a basis for the first and second qubit so that @xmath36 and @xmath37 are @xmath38 respectively .
now assume that we turn off @xmath36 while turning on @xmath37 .
this leads to the hamiltonian @xmath39 , where @xmath40 ( @xmath41 ) is a slowly decreasing ( increasing ) function with @xmath42 and @xmath43 ( @xmath44 and @xmath45 ) .
notice , however , that @xmath25 is always diagonal in the basis we picked , and therefore the system can not transform amplitude between these states as required for a swap .
it is crucial here that we assume a simple ramping on and off of the hamiltonians .
more complicated control schemes lead to holonomic qc which differs significantly from our approach
. _ adiabatic gate teleportation _
we have shown how to swap a qubit from the first qubit to the third qubit using adiabatic evolution and now we will show how this can be used to achieve universal qc .
first we will show how in the process of swapping we can also apply a single qubit gate by a simple modification of our initial hamiltonian .
we label this protocol adiabatic gate teleportation ( agt ) in analogy with how gates can be teleported in the quantum circuit model @xcite .
suppose , in analogy with the teleportation of quantum gates , that we apply a unitary rotation on the third qubit on the initial hamiltonian @xmath10 : i.e. consider the initial hamiltonian @xmath46 .
such an operation does not change the final hamiltonian , but does change the initial hamiltonian .
we can then carry the above analysis forward as before , but now in this changed basis . at the end of the evolution we end up with
the logical qubit dragged to the third physical qubit in a rotated basis .
the gap remains @xmath47 since the spectrum is unchanged by a unitary conjugation .
thus it is possible , using this construction , to perform any single - qubit unitary during the adiabatic teleportation .
notice that the rotated @xmath10 will still consist of two - qubit interactions .
for example , if we wish to perform a hadmard gate , we can use the same final hamiltonian , @xmath48 , but chang the initial hamiltonian to @xmath49 .
it is possible to make different assumptions about how the new , rotated @xmath50 hamiltonian arises physically .
we can just assume , for example , that a set of @xmath10 are available in order to perform the desired quantum gates .
a different assumption is that we start with only hamiltonians of the form @xmath51 between qubits @xmath52 and @xmath53 , but allows for one to adiabatically drag this hamiltonian to other `` gate teleporting '' hamiltonians . in this model
we must ensure that the total system remains in the ground space for the entire evolution , so we must also adiabatically transition from our canonical initial hamiltonian @xmath54 to a new hamiltonian @xmath55 which leaves the @xmath52 qubit untouched but prepares @xmath56 on the @xmath53 qubit for agt .
we call this adiabatic gate preparation ( agp ) . in general ,
such an evolution is nt directly possible for an arbitrary choice of @xmath57 .
( for example , consider @xmath58 . )
we can circumvent this by using a universal gate set for a single qubit where every member of the gate set yields an @xmath59 with a gap .
for instance , we can choose the unitaries @xmath60 which have the requisite properties .
the @xmath61 matrix is , up to a phase , a square root of the hadamard matrix , i.e. @xmath62 , while @xmath63 satisfies @xmath64 .
the minimum agp gaps are @xmath65 and @xmath66 , respectively , at @xmath30 .
together , @xmath61 and @xmath63 generate @xmath67 and hence are universal for single - qubit operations ( see pg .
196 of @xcite ) .
next consider how to achieve two - qubit gates during the swapping of two qubits . to do this
we follow as above , but instead of applying a single - qubit gate , we apply a two - qubit gate on the final two output qubits . for example , suppose that we wish to apply a controlled - phase between two logical qubits
. then we start with @xmath68 and end with the hamiltonian @xmath69 where @xmath70 is the controlled - phase between the the third and sixth physical qubit .
notice that the gap in this system is again the same constant @xmath65 , but now we require three - qubit interactions .
we can bypass the inconvenient three - qubit interactions by using perturbation theory gadgets @xcite , i.e. two - body hamiltonians whose low energy dynamics mimic three - qubit interactions .
the price is a reduction in the energy gap by a constant . in the appendix at the end of this paper we provide a detailed analysis of one such construction .
the crux of this analysis shows that we can use two ancilla qubits and interactions of strength @xmath9 and @xmath71 to produce an adiabatic evolution with energy gap @xmath72 with a gate fidelity of @xmath73 . , @xmath74 , and @xmath75 we can perform universal quantum computation .
here we diagram how this works for a single - qubit computation ( circuit below , the hamiltonians at different times diagramed from top to bottom . )
each circle represents a qubit , and a bar represents a two - qubit hamiltonian in our scheme , rotated by a labeled unitary @xmath76 . notice how in each step to the next hamiltonian , the qubit is swapped over two qubits ( the arrows ) and a gate is applied to this qubit .
thus the gates to be applied are encoded spatially across the the three hamiltonians .
the @xmath77th gate thus depends on the the hamiltonian @xmath78 with the gate being applied changing the interaction between qubits @xmath79 and @xmath80 in this hamiltonian .
generalizing to more than one qubit this proves that universal holonomic quantum computation can be done by interpolation between only three hamiltonians . ]
putting this all together we have shown how to use agt to perform one- and two - qubit gates by teleporting quantum information adiabatically between qubits .
given the ability to prepare fiducial initial single - qubit states and the ability to measure the qubits which contain the state of the final system , we then obtain a model equivalent in power to the standard circuit model of qc . _ relationship to holonomic qc _ in holonomic quantum computing ( hqc ) one uses a cyclic adiabatic evolution of a hamiltonian around a loop in parameter space to produce a quantum gate .
almost all hqc is cast within the context of cyclic evolutions , with the exception of kult _ et al .
_ @xcite who pointed out that noncyclic geometric gates are also possible .
agt is a example of a noncyclic geometric gate : so long as the evolution is adiabatic and we remain within the control manifold defined by the two interactions we are turning on and off , the desired gate is enacted independent of the actual time dependence of the path taken .
our construction is distinguished in two ways .
first , we achieve robustness by turning on and off interactions between two different subsystems ( as opposed to controlling interactions within the same system ) , and we expect that the separation of control needed to make geometric evolution robust will be much easier to achieve in this setting .
second , our explicit connection to gate teleportation leads directly to universal qc and enables methods from fault - tolerance theory .
_ possible architectures _
there are many different schemes for using the above agt primitives to build a universal quantum computer . using minimal resources ,
we can build a circuit on @xmath81 qubits using only @xmath82 qubits ( @xmath83 qubits for the two extra gates and @xmath84 for the ancillas in the perturbation gadgets ) assuming that we can move the qubits involved in the hamiltonians around at will .
more realistic and interesting architectures disallow such movement , but allow the parallel circuit elements required for fault - tolerant qc .
one very compelling architecture builds a circuit on @xmath81 qubits using @xmath85 qubits ( plus @xmath81 ancilla gadget qubits ) in a quasi - one - dimensional architecture .
the idea here is simply that one can perform alternating steps in a quantum circuit by gate teleportation from the first @xmath81 qubits to the third @xmath81 qubits and then back to the first @xmath81 qubits .
another possible architecture builds a quantum circuit of length @xmath86 on @xmath81 qubits onto teleportation across @xmath87 qubits by simply imprinting the quantum circuit being implemented spatially ( in a manner similar to what occurs in one - way quantum computing @xcite . )
thus we can perform universal qc by interpolating between just three different fixed hamiltonians ( see fig .
[ fig ] . ) _ fault tolerance _ a full analysis of fault - tolerance in the piecewise adiabatic scheme is beyond the scope of this letter , but here we argue that our system should show similar behavior to fault - tolerance in the standard quantum circuit model .
the reason for this is simply that agt , while using adiabatic evolution , essentially has the behavior of producing a gate on some ( teleported ) quantum information .
thus we could use the standard techniques for proving a threshold on this model .
that said , however , in practice this model may perform significantly better than the standard circuit model .
the reason is that the system is always performing adiabatic evolution with a constant energy gap ( unlike many other models which yield energy gaps which scale inversely as a polynomial in the number of qubits . )
thus we obtain two of the benefits of adibatic qc , ( 1 ) the system is separated by a constant energy barrier from , and thus at low temperature is robust to , excitation out of the ground state ( a form of leakage error ) and ( 2 ) considerable robustness exists with respect to varying the tunings which change the hamiltonian adiabatically .
_ comparison to other schemes _ using piecewise adiabatic quantum gate teleportations to build a quantum computer shares similarities with many other schemes , but differs in many respects as well .
like universal adiabatic qc , the scheme uses a smooth one way interpolation between an initial and final hamiltonian , but we use multiple such interpolations .
like holonomic qc , we rely on degenerate levels of a hamiltonian , but here our adiabatic evolution is not cyclic . along these lines ,
our scheme is related to a recent method to make holonomic qc fault - tolerant @xcite by using interpolations between encoded pauli operators .
in contrast to our proposal , these are done in a cyclic fashion and with three - qubit interactions .
further we achieve a gate by controlling interactions between separate subsystems , thus insuring that the geometric robustness depends only on the degree to which these independent controls can be manipulated .
finally the scheme is similar in spirit to recent proposals to use spin chains with adiabatic time - dependent interactions to transmit quantum information @xcite , where interpolation between two spin-@xmath88 hamiltonians was used to transmit quantum information down the chain with an energy gap that scaled ( at least numerically ) as @xmath89 where @xmath86 is the length of the chain .
by contrast , our scheme maintains a constant energy gap for the entire computation .
while both schemes require similar transmission times , the former @xcite has a small energy gap , which will be a problem when using this scheme at finite temperature .
furthermore , by explicitly connecting our scheme to gate teleportation , we achieved a universal qc .
_ discussion _ we have shown how to build a universal quantum computer using a series of piecewise adiabatic quantum evolutions related to teleportation .
this opens up a novel architecture for building a quantum computer based entirely on adiabatic quantum evolutions between two - qubit interactions and it considerably simplifies the control requirements for building a quantum computer . after completing this paper
we became aware of concurrent work done independently by oreshkov @xcite showing a similar result using cyclic two - qubit interpolations .
we thank d. gottesman for discussions .
db was supported by nsf grants 0803478 and 0829937 and darpa quest grant fa-9550 - 09 - 1 - 0044 .
stf was supported by the perimeter institute for theoretical physics .
research at perimeter is supported by the government of canada through industry canada and by the province of ontario through the ministry of research & innovation .
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decays of a bound state of a quark and its anti - quark , quarkonium , provide an excellent laboratory for studying qcd .
particularly , heavy quarkonia such as charmonium states are less relativistic , thus play a special role in probing strong interactions .
cleo recently has accumulated data taken at the @xmath5 resonance , providing a total of 27 m @xmath5 decays . with the combination of this large statistical sample and the excellent cleo detector , we will explore an unprecedented world of charmonia .
while many analyses are currently being carried out , in this note we present recent results on multi - body @xmath0 decays which employed the pre - existing 3 m @xmath5 sample .
we also present recent studies on decays of one of the exotic states , y(4260 ) , as well as precision measurement on @xmath2 that has an implication on properties of x(3872 ) . finally , based on the full sample of @xmath5 data
, we have results on properties of one of the light mesons , @xmath6 .
@xmath7 states , which have one unit of orbital angular momentum and total spin of j=0 , 1 , or 2 , can not be produced directly from @xmath8 collisions .
they can be reached from @xmath5 through radiative ( electric dipole ) transitions .
since @xmath9 , and @xmath10 for j=0 , 1 , and 2 respectively @xcite , 27 m @xmath5 decays of the new data provides @xmath112 m decays of each spin state of @xmath0 which should give us a greater understanding of the decay mechanisms of the @xmath0 mesons . in this section , we present recent results of studies of @xmath0
decays based on 3 m @xmath5 decays which should serve as the foundation for the future precision measurements by employing the full data sample of 27 m of @xmath5 decays .
we present results on @xmath0 decay into combinations of @xmath6 and @xmath12 mesons .
figure [ fig : etaetamass ] shows invariant masses of combinations of @xmath6 and @xmath12 .
no @xmath13 is seen as expected from conservation of spin - parity .
( a ) , @xmath14 ( b ) , and @xmath15 ( c),width=302 ] we measured @xmath16 to be @xmath17 @xcite where the first uncertainty is statistical , the second is systematic , and the third is systematic due to the uncertainty in @xmath18 .
this is slightly higher , but consistent with , the two previously published measurements .
the bes collaboration measured this branching ratio to be @xmath19 @xcite and the e-835 collaboration @xcite had @xmath20 .
we also measured @xmath21 to be @xmath22 for the first time .
we set upper limits for @xmath23 , @xmath24 , @xmath25 , and @xmath26 at @xmath27 confidence level .
our result can be compared to predictions based on the model of qiang zhao @xcite .
he translates these decay rates into a qcd parameter , @xmath28 , which is the ratio of doubly- to singly - ozi suppressed decay diagrams . in his model , our results indicate that the singly - ozi suppressed diagram dominates in these decays .
we have also looked at three - body decays of @xmath0 states ( one neutral and 2 charged hadrons ) @xcite .
they are @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35 , and @xmath36 . measured branching fractions
are summarized in table [ tab:3btab ] .
again , our results are consistent with the results from bes collaboration @xcite , with better precision . in three of the above modes we looked for , @xmath29 , @xmath33 , and @xmath35 ,
we observed significant signals of @xmath13 decays which are shown in figure [ fig : threebody ] .
[ cols="<,^,^,^",options="header " , ] [ tab : etabr ] further more , we also measured the mass of @xmath6 meson @xcite .
this was motivated by two recent precision measurements that were inconsistent with each other . in 2002 ,
the na48 collaboration reported @xmath37 mev @xcite , while in 2005 , gem collaboration reported @xmath38 mev @xcite which was 8 standard deviations below na48 s result .
we used the same @xmath6 sample described previously in this section but used only 4 decay modes , @xmath39 , @xmath40 , @xmath41 , and @xmath42 while , again , constraining masses of @xmath43 and @xmath5 .
our result , the average of the 4 @xmath6 decay modes , is @xmath44 mev which has comparable precision to both na48 and gem results , but is consistent with the former and 6.5 standard deviations larger than the later .
we note that the kloe collaboration also recently measured mass of the @xmath6 meson to be @xmath45 mev which was presented at the 2007 lepton - photon conference @xcite .
i have presented confirmation of babar s observation of y(4260 ) in di - pion transition to @xmath43 along with a new observation through neutral di - pion transition .
our precision measurement on @xmath2 calls for more precise measurement on @xmath46 . with 3 m @xmath5 sample
, we have results on two- , three- , and four - body decays of @xmath0 states in which many sub - structures were seen in three- and four - body modes .
dalitz plot analyses were done for the case of 3-body decays .
more detailed analyses can be done with the full 27 m @xmath5 sample . using the 27 m sample , we performed precision measurements on @xmath4 and @xmath3 .
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in vancouver a popular form of chinese luncheon is `` dim sum '' in which small quantities of a large variety of foods may be tasted .
this review is a `` dim sum '' of parity violation experiments . as with a luncheon ,
my selection is biased by my personal taste and experience .
i start with @xmath0 parity violation experiments , concentrating on the the triumf 221 mev @xmath0 experiment , then discuss @xmath3 parity violation experiments with details of the los alamos @xmath4 experiment now being installed at lansce .
finally , i discuss @xmath6 parity violation experiments , particularly the gzero experiment at jefferson lab .
i refer those interested in more background to specific reviews on nucleon - nucleon @xcite and @xmath6 @xcite experiments .
figure [ pptypes ] shows typical @xmath0 parity violation experiments .
they scatter a longitudinally polarized beam of protons from a hydrogen target and measure the difference in cross section for right - handed and left - handed proton helicities .
the intermediate and high energy experiments use transmission geometry in which the change in scattering cross section is deduced from the change in transmission through the target .
low energy experiments , where energy loss limits the target thickness , use scattering geometry , in which the detectors measure the scattered protons directly . both types of experiments measure the parity violating longitudinal analyzing power , @xmath9 , where @xmath10 and @xmath11 are the scattering cross sections for positive and negative helicity .
.summary of @xmath0 parity violation experiments .
the long times taken to achieve small uncertainties reflects the time taken to understand and correct for systematic errors . in cases where authors reported both statistical and systematic uncertainties ,
this table shows the quadrature sum of the two .
[ cols="<,<,^ , > " , ] [ epexp ] the gzero experiment completed a successful commissioning run of the forward angle configuration in fall 2002 and january 2003 and all major systems are now fully operational .
running will continue with an engineering run october to december , 2003 , and production running is scheduled to start in 2004 .
parity violation experiments provide a way to study effects of the weak interaction in the presence of the much stronger electromagnetic and strong nuclear interactions .
the polarized beam experiments i have described use similar experimental techniques and face similar problems controlling systematic errors .
the physics addressed by these experiments can , however be quite diverse .
@xmath3 experiments constrain the weak pion - nucleon coupling constant , @xmath5 .
@xmath0 parity violation experiments are sensitive to the shorter range part of the nucleon - nucleon force and constrain the combinations @xmath12 and @xmath13 .
finally , @xmath6 parity violation experiments , such as the jlab gzero experiment , offer the opportunity to measure the contribution of strange quark - antiquark pairs to the proton charge and magnetism .
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( trieste , 2003 ) , g0 report g0 - 03 - 075 , ( this report and others are available from http://www.npl.uiuc.edu/exp/g0/docs/ ) . | i start by reviewing existing @xmath0 measurements with particular emphasis on the recent 221 mev @xmath0 measurement at triumf which permitted the weak meson - nucleon coupling constants @xmath1 and @xmath2 to be determined separately for the first time .
i then review @xmath3 experiments , with specific details of the @xmath4 experiment now under preparation at los alamos national laboratory .
this experiment will provide a clean measurement of the weak pion nucleon coupling , @xmath5 .
finally , i discuss @xmath6 parity violation experiments , particularly the gzero experiment under way at jefferson lab in virginia .
this experiment will measure the weak form factors @xmath7 and @xmath8 , allowing the distribution of strange quarks in the quark sea to be determined . |
the off - shell three - gluon vertex has been under investigation for more than three decades . by an analysis of the nonabelian gauge ward identities , ball and chiu@xcite in 1980 found a form factor decomposition of this vertex which is valid at any order in perturbation theory , with the only restriction that a covariant gauge be used . at the one - loop level
, they also calculated the vertex explicitly for the case of a gluon loop in feynman gauge . later cornwall and
papavassiliou@xcite applied the pinch technique to the non - perturbative study of this vertex .
davydychev , osland and sax @xcite calculated the massive quark contribution of the one loop three - gluon vertex .
binger and brodsky@xcite calculated the one - loop vertex in the pinch technique and found the following susy - related identity between its scalar , spinor and gluon loop contributions , @xmath0 in this talk , i present a recalculation of the scalar , spinor and gluon loop contributions to the three - gluon vertex using the worldline formalism @xcite .
the vertex is shown in fig .
1 ( for the fermion loop case ) . following the notation of @xcite , we write @xmath1 the gluon momenta are ingoing , such that @xmath2 .
there are actually two diagrams differing by the two inequivalent orderings of the three gluons along the loop .
those diagrams add to produce a factor of two .
the ball - chiu decomposition of the vertex can be written as @xmath3 here the @xmath4 , @xmath5 and @xmath6 functions are symmetric in the first two arguments , @xmath7 antisymmetric , and h(s ) are totally ( anti)symmetric with respect to interchange of any pair of arguments .
note that the @xmath6 and @xmath8 functions are totally transverse , i.e. , they vanish when contracted with any of @xmath9 , @xmath10 or @xmath11 .
the path integral ( [ bk ] ) is gaussian so that its evaluation requires only the standard combinatorics of wick contractions and the appropriate green s function , @xmath20 in this formalism structural simplification can be expected from the removal of all second derivatives @xmath21 s , appearing after the wick contractions , by suitable integrations by part ( ibp ) .
after doing this we have ( see@xcite for the combinatorial details of the wick contraction and ibp procedure ) @xmath22)\int_{0}^{\infty } \frac{dt}{t^{\frac{d}{2}}}{\rm e}^{-m^2 t}\int_{0}^{t}d\tau_{1}\int_0^{\tau_{1}}d\tau_{2}\ , q_3 ^ 3\vert_{\tau_3=0}~ { \rm e}^{(g_{b12}p_{1}\cdot p_{2}+g_{b13}p_{1}\cdot p_{3}+g_{b23}p_{2}\cdot p_{3})}\nonumber\\ \gamma_{\rm scalar}^2 & = & \gamma_{\rm scalar}^3(q_3 ^ 3\to q_3 ^ 2 ) \nonumber\\ \gamma_{\rm scalar}^{\rm bt } & = & - { \mbox tr}(t^{a_{1}}[t^{a_{2}},t^{a_{3 } } ] ) \int_{0}^{\infty } \frac{dt}{t^{\frac{d}{2}}}{\rm e}^{-m^2 t}\int_{0}^{t}d\tau_{1 } \dot{g}_{b12}\dot{g}_{b21 } \bigl\lbrack\varepsilon_3\cdot f_1\cdot\varepsilon_2~ { \rm e}^{g_{b12}p_{1}\cdot ( p_{2}+p_{3 } ) } + { \rm 2\,perm } \bigr\rbrack\nonumber\\ q_{3}^3&=&\dot{g}_{b12}\dot{g}_{b23}\dot{g}_{b31}{\mbox tr}(f_1f_2f_3 ) \nonumber\\ q_{3}^2&=&\frac{1}{2}\dot{g}_{b12}\dot{g}_{b21}{\mbox tr } ( f_1f_2 ) \sum_{k=1,2}\dot{g}_{b3k}\varepsilon_{3}\cdot
p_{k}+{\rm 2\,perm}\nonumber\\ \label{q3}\end{aligned}\ ] ] the abelian field strength tensors @xmath23 appear automatically in the ibp procedure .
the @xmath24 s are boundary terms of the ibp .
we rescale to the unit circle , @xmath25 and rewrite these integrals in term of the standard _
feynman / schwinger _ parameters , related to the @xmath26 by @xmath27 for the scalar case , we find @xmath28)(\gamma_{\rm scalar}^3 + \gamma_{\rm scalar}^2 + \gamma_{\rm scalar}^{\rm bt})\nonumber\\ \gamma_{\rm scalar}^3 & = & \gamma\bigl(3-\frac{d}{2}\bigr)\mbox{tr } ( f_1f_2f_3 ) i^d_{3,b}(p_1 ^ 2,p_2 ^ 2,p_3 ^ 2 ) \nonumber\\ \gamma_{\rm scalar}^2 & = & \frac{1}{2}\gamma\bigl(3-\frac{d}{2}\bigr)\bigl\lbrack \mbox{tr } ( f_1f_2)\bigl(\varepsilon_3\cdot p_1 i^d_{2,b}(p_1 ^ 2,p_2 ^ 2,p_3 ^ 2)-\varepsilon_3\cdot p_2 i^d_{2,b}(p_2 ^ 2,p_1 ^ 2,p_3 ^ 2)\bigr)+{\rm 2\,perm}\bigr\rbrack\nonumber\\ \gamma_{\rm scalar}^{\rm bt } & = & -\gamma\bigl(2-\frac{d}{2}\bigr ) \bigl\lbrack\varepsilon_3 \cdot f_1\cdot\varepsilon_2 i^d_{{\rm bt},b}(p_1
^ 2)+{\rm 2\,perm } \bigr\rbrack\nonumber\\ \label{gammas0fin}\end{aligned}\ ] ] where @xmath29
by an off - shell generalization of the bern - koswer replacement rules @xcite , whose correctness for the case at hand we have verified , one can get the results for the spinor and gluon loop from the scalar loop one simply by replacing @xmath30 where the @xmath31 s are three integrals similar to the @xmath32 s above ( for the spinor loop one must also multiply by a global factor of @xmath33 ) . from ( [ gamma ] )
we immediately recover the binger - brodsky identity eq.([gammabb ] ) .
@xmath39)(f}+ig[a , a])\nonumber\\ \label{comparison}\end{aligned}\ ] ]
in our recalculation of the scalar , spinor and gluon contributions to the one - loop three gluon vertex we have achieved a significant improvement over previous calculations both in efficiency and compactness of the result .
this improvement is in large part due to the replacement rules ( [ gamma ] ) whose validity off - shell we have verified .
details and a comparison with the ball - chiu decomposition will be presented elsewhere .
we believe that along the lines presented here even a first calculation of the four - gluon vertex would be feasible .
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. rept . * 355 * , 73 ( 2001 ) . | the three - gluon vertex is a basic object of interest in nonabelian gauge theory .
it contains important structural information , in particular on infrared divergences , and also figures prominently in the schwinger - dyson equations . at the one - loop level , it has been calculated and analyzed by a number of authors .
here we use the worldline formalism to unify the calculations of the scalar , spinor and gluon loop contributions to the one - loop vertex , leading to an extremely compact representation . the susy - related sum rule found by binger and brodsky follows from an off - shell extension of the bern - kosower replacement rules .
we explain the relation of the structure of our representation to the low - energy effective action .
= 11.6pt |
in future experiments , the determination of the leptonic cp phase @xmath4 is one of the most important aim in elementary particle physics .
a lot of effort have been dedicated both from theoretical and experimental point of view in order to attain this aim , see @xcite and the references therein .
the cp asymmetry , @xmath9 , is widely used as the index of the cp phase dependence . here ,
@xmath10 and @xmath11 are the oscillation probabilities for the transition @xmath12 and @xmath13 respectively . however , this index has to be improved on the following three points .
the first one is that the fake cp violation due to matter effect @xcite can not be separated clearly in @xmath14 .
the second one is that only the effect originated from @xmath15 is included in @xmath14 .
the third one is that we need to observe the channels both in neutrino and anti - neutrino for calculating @xmath14 . in this letter
, we introduce a new index of the cp phase dependence improved on the above three points . in arbitrary matter profile
, we derive the maximal condition of this index exactly for @xmath12 transition .
this index can be extended to the case for other channels and other parameters @xcite .
we can simply find the situation that the cp phase effect becomes large by using this index . as an example , we demonstrate the following interesting phenomena .
it is commonly expected that a large @xmath3 appearance signal is observed in the jparc experiment @xcite if the 1 - 3 mixing angle @xmath16 is relatively large @xmath2 and is determined by the next generation reactor experiments like the double chooz experiment @xcite and the kaska experiment @xcite . however , there is the possibility that @xmath3 appearance signal can not be observed in certain mass squared differences and mixing angles even the case for large @xmath16 .
we call this `` @xmath16 screening '' .
this occurs due to the almost complete cancellation of the large @xmath16 effect by the cp phase effect .
if the background can be estimated precisely , we can obtain the information on the cp phase through the @xmath16 screening .
this means that we can not neglect the cp phase effect , which is actually neglected in many investigations as the first approximation .
at first , we write the hamiltonian in matter @xcite as @xmath17 by factoring out the 2 - 3 mixing angle and the cp phase , where @xmath18 is the rotation matrix in the 2 - 3 generations and @xmath19 is the phase matrix defined by @xmath20 .
the reduced hamiltonian @xmath21 is given by @xmath22 where @xmath23 , @xmath24 , @xmath25 is the fermi constant , @xmath26 is the electron number density , @xmath27 is neutrino energy and @xmath28 is the mass of @xmath29 .
the oscillation probability for @xmath12 is proportional to the @xmath30 and @xmath15 in arbitrary matter profile @xcite and can be expressed as @xmath31 here @xmath32 , @xmath33 and @xmath34 are determined by parameters other than @xmath4 and are calculated by @xmath35c_{23}s_{23 } \label{eq a } , \\
b&=&2{\rm im}[s_{\mu e}^{\prime * } s_{\tau e}^{\prime}]c_{23}s_{23 } , \\ c&=&|s_{\mu e}^{\prime}|^2c_{23}^2+|s_{\tau e}^{\prime}|^2s_{23}^2 \label{eq c},\end{aligned}\ ] ] where @xmath36_{\alpha\beta}$ ] , @xmath37 and @xmath38 is the cp dependent term and @xmath34 is the cp independent term .
next , let us introduce a new index of the cp phase dependence @xmath0 .
suppose that @xmath39 and @xmath40 as the maximal and minimal values when @xmath4 changes from @xmath41 to @xmath42 .
then , we define @xmath0 as @xmath43 namely , the new index is expressed by the ratio of the coefficient of the cp dependent term to the cp independent term .
@xmath0 is a useful tool to explore where is the most effective region in parameter spaces to extract the cp effect from long baseline experiments although @xmath0 is not an observable .
@xmath14 is also similar one and this is an observable .
however @xmath14 have to be expressed by @xmath4 though @xmath4 is still unknown parameter so that @xmath14 seems not to be so good index to make the exploration . on the other hand , @xmath0 is calculated without using @xmath4 .
this is the main difference between these two indices and it is more effective to use @xmath0 . [ cols="^,^ " , ] fig.3 .
cp dependence of @xmath3 appearance signal in the jparc - sk experiment .
we use the parameters as in fig.1 ( right ) except for @xmath44 and @xmath45 .
the condition ( [ screening - condition ] ) is satisfied in the top - left figure , and is not satisfied in other figures .
the statistical error is also shown within the 1-@xmath46 level .
we also show the value of @xmath0 calculated at @xmath47gev in figures . as expected from the oscillation probability in fig.2 , @xmath3 appearance signal will become almost zero around @xmath48 even during the five years data acquisition in the sk experiment in the top - left of fig .
3 . note that this occurs only when the maximal condition ( [ screening - condition ] ) is satisfied , namely @xmath1 .
other panels in fig.3 show that the minimal value of @xmath3 appearance signal rise and is a little different from zero because ( [ screening - condition ] ) is not satisfied so precisely .
we obtain the similar results in the case that @xmath49 or @xmath50 changes within the allowed region obtained from solar and the kamland experiments .
let us here illustrate how the value of @xmath4 is constrained by the experiment .
below , suppose that the atmospheric parameters have some uncertainties as @xmath51- @xmath52 and @xmath53-@xmath54 , while the solar parameters @xmath49 and @xmath50 and @xmath55 are fixed for simplicity .
for example , if 15 appearance signals are observed in the experiment , we obtain the allowed region of @xmath4 as @xmath41-@xmath56 or @xmath57-@xmath58 or @xmath59-@xmath42 from four figures in fig.3 .
namely , combined range of all allowed region is totally @xmath60 .
next , we consider the case that no appearance signal is obtained .
this gives the allowed region of @xmath4 as @xmath61-@xmath62 .
namely , combined range of all allowed region is totally @xmath56 .
thus , we found from above rough estimation that the stronger constraint is obtained in the case of @xmath16 screening even if the uncertainties of parameters except for @xmath4 are considered .
in other words , we can also obtain the information on the atmospheric and solar parameters .
although the precise estimation of the background is a difficult problem , it is interesting to have strong constraint for not only the value of the cp phase but also other parameters like @xmath44 and @xmath45 when the @xmath3 appearance signal is not observed and the 1 - 3 mixing angle has a comparatively large value @xmath2 .
in summary , we introduced a new index of the cp phase dependence @xmath0 and derived their maximal condition in a simple and general form . in particular
, we showed that @xmath1 is realized in a rather wide region in the @xmath27-@xmath63 plane at certain values of parameters . in the case
that @xmath16 has a comparatively large value @xmath64 , ( namely @xmath16 will be observed in next generation reactor experiments ) nevertheless we can not observe @xmath3 appearance signal in the jparc experiment , we obtain the information on the cp phase as @xmath65 for @xmath66 without depending on the uncertainties of other parameters .
also for @xmath67 , there is a possibility that the @xmath16 screening will occur . in this case , we need to consider the reason for the absence of @xmath3 appearance signal in the jparc experiment more carefully , in order to understand whether @xmath16 is small or the @xmath16 effect is canceled out by the cp phase effect .
we also note that the @xmath16 screening may be realized for not only @xmath12 oscillation in super - beam experiments but also @xmath68 oscillation in neutrino factory experiments .
we can also use the zero probability in the @xmath16 screening to explore new physics like non - standard interaction .
we would like to thank prof . wilfried wunderlich ( tokai university ) for helpful comments and advice on english expressions . | we introduce a new index of the leptonic cp phase dependence @xmath0 and derive the maximal condition for this index in a simple and general form .
@xmath1 may be realized even in the jparc experiment . in the case that the 1 - 3 mixing angle can be observed in the next generation reactor experiments , namely @xmath2 , and nevertheless @xmath3 appearance signal can not be observed in the jparc experiment , we conclude that the cp phase @xmath4 becomes a value around @xmath5 @xmath6 for @xmath7 @xmath8 without depending the uncertainties of solar and atmospheric parameters . |
although conspicous inss such as the crab and vela pulsars have been observed from the very beginning of the mission , hst started to play a key role on the study of the optical behaviour of these faint targets after the first refurbishing mission in 1993 .
the study did not proceed systematically , e.g. from the brighter to the dimmer , but rather following a random walk dictated by the allocation of observing time .
table 1 lists all the inss ( be they bona fide pulsars or radio - silent neutron stars ) observed so far by the hst .
ccccc + i d & log(yr ) & log(de / dt ) & d(kpc ) & mag + + crab & 3.1 & 38.6 & 2.0 & 16.6 + b0540 - 69 & 3.2 & 38.2 & 55 & 22.5 + vela & 4.1 & 36.8 & 0.5 & 23.6 + b0656 + 14 & 5.0 & 34.6 & 0.76 & 25.0 + geminga & 5.5 & 34.5 & 0.16 ( ) & 25.5 + b1055 - 52 & 5.7 & 34.5 & 1.5 & 24.9(u ) + b1929 + 10 & 6.5 & 33.6 & 0.17 ( ) & 25.7(u ) + b0950 + 08 & 7.2 & 32.7 & 0.28 ( ) & 27.1(u ) + + rxj 1856 - 3754 & & & @xmath4 & 25.6 + although their number is limited , the objects in table 1 sample 10 magnitude in brightness and 4 decades in age , going from the youngest pulsars , such as the crab and psr b0540 - 69 , to rather old ones , such as psr b0950 + 08 .
all inss , but the crab , are faint .
all challenging , sometimes plainly impossible to observe from the ground .
this was the case of psr b1055 - 52 ( mignani et al .
1997@xcite ) which , together with psr b1929 + 10 and psr b0950 + 08 ( pavlov et al .
1996@xcite ) have been seen only with the hst using the foc and the u filter . to the score of hst identifications we can add the ins candidate rxj 1856 - 3754 ( walter & matthews 1997@xcite ) .
over the years , hst has collected light curves , for the crab ( percival et al .
1993@xcite ) and psr b0540 - 69 ( boyd et al .
1995@xcite ) , spectra , for the same two objects ( gull et al . 1998@xcite
; hill et al .
1997@xcite ) , and images in different filters for all of them .
the major results obtained by hst in pulsar astronomy have been reviewed by mignani et al .
( 2000)@xcite .
the observational efforts pursued by different groups with the imaging instruments on board hst are summarized in table 2 , where , for sake of clarity , the spectral coverage provided by hst has been roughly divided in two infrared channels ( ir and i ) , four optical ones ( r , v , b , u)- plus narrow bands ( nb)- and one ultraviolet . in table 2 ,
nicmos , wfpc2 , and foc observations are indicated .
if an observation has been done more than once , the number in parenthesis gives the number of repetitions .
lcccccccc + i d & ir & i & r & v & b & u & uv & nb + crab & & & & & & & & 547 m ( several ) + b0540 - 69 & & & & wfpc2 & & & & 656n , 658n + vela & & wfpc2 & wfpc2 & wfpc2(5 ) & & & & + b0656 + 14 & nicmos & & & wfpc2(2 ) & foc & foc & foc & + geminga & nicmos & & wfpc2 & wfpc2(4 ) & foc & foc & foc & + _ b1055 - 52 _ & & & & & & _ foc _ & & + & & & & & & _ foc _ & _ foc _ & + _ b0950 + 08 _ & & & & & & & _ foc _ & + & & & & _
wfpc2(2 ) _ & _ wfpc2 _ & _ wfpc2(2 ) _ & _ wfpc2 _ + table 2 shows quite eloquently that not all the entries in table 1 received the same amount of observing time : it is worth noticing that , apart from the `` dancing crab '' , the objects with the highest number of observations is the rather dim geminga , followed by psrb0656 + 14 , to show that objects fainter than v=25 were not discriminated in this study .
the amount of information contained in this comprehensive list has been used : * to measure pulsars proper motions and parallactic displacements , * to study plerion phenomenology * to assess the spectral distribution of objects too faint for spectroscopy the major achievements are summarized in the next sections .
for all the pulsars observed more than once , namely the crab , vela , psr b0656 + 14 and geminga , a proper motion has been measured , yielding also new and independent measurements of the objects transverse velocities .
this topic is reviewed in these proceedings by mignani et al .
sometimes , the accurate determination of the proper motion has been a by - product of a sequence of observations aimed at the measurement of the object s parallactic displacement and hence its distance ( see also de luca et al .
, these proceedings ) .
this has been done for geminga ( caraveo et al .
1996@xcite ) and is currently underway for the vela pulsar .
determining the distance to a pulsar allows the assessment of the absolute optical luminosity which , compared with the overall energy loss de / dt , yields the efficiency to convert rotational energy loss into optical emission , an important parameter in pulsar modelling .
hst imaging of crab , vela and psr b0540 - 69 allows one to trace the relativistic pulsar wind and to better study the plerion phenomenology .
moreover , with the proper motion vectors clearly aligned with the axes of symmetry of the crab and vela plerions , proper motions , or rather the mechanisms responsible for them , seem to play a role in shaping the inner remnants ( see mignani et al . , these proceedings , and pavlov et al .
2000@xcite ) .
comparisons between hst frames and recently obtained chandra high resolution images open new avenues to study the multiwavelength behaviour of young energetic plerions .
the case of psr b0540 - 69 is discussed in an accompanying paper by caraveo et al . .
hst multicolor imaging appears to be the next best thing to a spectrum for studying the spectral shape of faint objects and discriminating between thermal emission from the ins surface and non thermal magnetospheric one .
two classical examples are * psr b0656 + 14 , where pavlov et al .
( 1997)@xcite have shown a composite spectral shape featuring both a thermal and non - thermal components ( see fig.1 , left panel ) * geminga , for which bignami et al .
( 1996)@xcite and mignani et al .
( 1998)@xcite have provided the evidence of a cyclotron spectral feature on top of a thermal continuum ( see fig.1 , right panel ) .
if correct , the cyclotron identification ( discussed also by jacchia et al .
1999@xcite ) of the feature would provide the first in situ measurement of the magnetic field of an isolated neutron star .
all in all , the study of inss , in spite of their faintness , has yielded a wealth of interesting results definitely worth the time and efforts devoted to them .
new identifications have been secured while new insights have been achieved for pulsars already identified .
of course , a lot remains to be done .
young pulsars are definitely promising targets , thus we should concentrate on newly discovered young objects , such as the 16 msec one in the lmc . here
the timing capability of the stis , so far poorly exploited , should be fully used .
bignami , g.f .
1996 , apj 456 , l111 boyd , p.t .
1995 , apj 448 , 365 caraveo , p.a . ,
bignami , g.f , mignani , r. & taff , l.g .
1996 , apj 461 , l91 gull , t.r .
et al . 1998 , apj 495 , l51 hill , r.j .
et al . 1997 , apj 486 , l99 jacchia , a. et al . 1999 ,
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, & kurt , v.g . 2000 , a&a , submitted , astro - ph/0009064 mignani , r. , caraveo , p.a . & bignami , g.f .
1997 , apj 474,l51 mignani , r. , caraveo , p.a . & bignami , g.f .
1998 , a&a 332 , l37 mignani , r.p . ,
caraveo , p.a . & bignami , g.f .
2000 , stsci newsletter 17 , no 1 , 3 pavlov , g.g . ,
stringfellow , g.s . & cordova , f.a .
1996 , apj 467,370 pavlov , g.g . ,
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1997 apj 489 , l75 pavlov , g.g . ,
sanwal , d. , garmire , g.p . ,
zavlin , v.e . ,
burwitz , v. & dodson , r.g .
2000 , aas meeting 196 , @xmath5 percival , j.w .
1993 , apj 407 , 276 walter , f.m . & matthews l.d .
1997 , nature 389 , 358 | hst observations have contributed significantly to our knowledge on the behaviour of isolated neutron stars ( inss ) as optical emitters .
first , hst has been instrumental both to discover new optical counterparts ( psr b1055 - 52 , psr b1929 + 10 , psr b0950 + 08 ) and to confirm proposed identifications ( psr b0656 + 14 ) .
second , hst multicolor photometry provided useful information to characterize the optical emission mechanism(s ) at work in middle - aged inss like psr b0656 + 14 and geminga .
last , but not least , the superior angular resolution of the hst allowed both to perform a very accurate morphological study of the plerionic environments of young pulsars ( e.g. the crab and psr b0540 - 69 ) and to perform very accurate astrometric measurements yielding proper motions ( crab , vela , geminga , psr b0656 + 14 ) and parallaxes ( geminga ) .
psfig.sty @xmath0 ifc - cnr , via bassini 15 , i-20133 milan , italy @xmath1 st - ecf , karl schwarzschild str.2 , d8574o garching b. munchen , germany @xmath2 pennsylvania state univ . , 525 davey lab , university park , pa 16802 , usa @xmath3 asi , via liegi 26 , i-00198 rome , italy |
hidden in batse s superb gamma - ray burst lightcurves in different energy bands are temporal and spectral signatures of the fundamental physical processes which produced the observed emission .
various techniques have been applied to the batse data to extract these signatures , such as : auto- and crosscorrelations of lightcurves in different energies@xcite ; fourier transforms@xcite ; lightcurve averaging@xcite ; cross - fourier transforms@xcite and pulse fitting@xcite . here
we propose to use linear state space models ( lssm ) to study the gamma - ray burst lightcurves .
lssm estimates a time series underlying autoregressive ( ar ) process in the presence of observational noise .
an ar process assumes that the real time series is a linear function of its past values ( `` autoregression '' ) in addition to `` noise , '' a stochastic component of the process .
since the noise adds information to the system , it is sometimes called the `` innovation''@xcite .
a moving average of the previous noise terms is equivalent to autoregression , and therefore these models are often called arma ( autoregressive , moving average ) processes@xcite .
while arma processes are simply mathematical models of a time series , the resulting model can be interpreted physically , which is the purpose of their application to astrophysical systems .
for example , the noise may be the injection of energy into an emission region , while the autoregression may be the response of the emission region to this energy injection , such as exponential cooling .
the application of lssm to burst lightcurves can be viewed as an exploration of burst phenomenology devoid of physical content : how complicated an ar process is necessary to model burst lightcurves ? can all bursts be modeled with the same ar process ? however , because different types of ar processes can be interpreted as the response of a system to a stochastic excitation , characterizing bursts in terms of ar processes has physical implications .
since we have lightcurves in different energy bands , we can compare the response at different energies .
for example , the single coefficient in the ar[1 ] process ( the nomenclature is described below ) is a function of an exponential decay constant .
if the lightcurves in all energy bands can be modeled by ar[1 ] then we have decay constants for every energy band .
since most bursts undergo hard - to - soft spectral evolution@xcite and temporal structure is narrower at high energy than at low energy@xcite , we expect the decay constants to be shorter for the high energy bands .
the purpose of the lssm methodology is to recover the hidden ar process . if the time series @xmath0 is an ar[p ] process then @xmath1 where time is assumed to advance in integral units .
the `` noise '' ( or `` innovation '' ) @xmath2 is uncorrelated and possesses a well - defined variance @xmath3 ; the noise is usually assumed to be gaussian . since the burst count rate can not be negative , we expect the noise also can not be negative .
a kolmogorov - smirnov test is used to determine when p is large enough to model the system adequately@xcite .
if p=1 , the system responds exponentially to the noise with a decay constant @xmath4 , and @xmath5 the p=2 system is a damped oscillator with period @xmath6 and relaxation time @xmath4 , @xmath7 thus , the lowest order ar processes lend themselves to obvious physical interpretations .
unfortunately , we do not detect @xmath0 directly , but a quantity @xmath8 which is a linear function of @xmath0 and observational noise : @xmath9 where in our case @xmath10 is an irrelevant multiplicative factor and @xmath11 is a zero - mean noise term with variance @xmath12 ; @xmath11 is also often assumed to be gaussian .
the lssm code uses the expectation - maximization algorithm@xcite .
we have thus far applied our lssm code@xcite to 17 gamma - ray bursts .
we used the 4-channel batse lad discriminator lightcurves extracted from the discsc , preb , and discla datatypes , which have 64 ms resolution ; the energy ranges are 2550 , 50100 , 100300 and 3002000 kev .
each channel was treated separately , resulting in 68 lightcurves . of these lightcurves ,
52 could be modeled by ar[1 ] , 13 by ar[2 ] and 3 by ar[4 ] .
thus there is a preference for the simplest model , ar[1 ] .
note that chernenko @xcite found an exponential response to a source function in their soft component .
figure 1 presents the normalized relaxation time constants for the bursts in our sample , as well as their average . even for models more complicated that ar[1 ] a relaxation time constant can be identified .
as expected , the averages of these time constants become shorter as the energy increases from channel 1 to channel 4 , consistent with the trend found in quantitative studies of spectral evolution@xcite and the qualitative inspection of burst lightcurves . in figure 2
we present the analysis of grb 940217 , the burst with an 18 gev photon 90 minutes after the lower energy gamma - ray emission ended@xcite . as can be seen ,
the residuals are much smaller than the model and are consistent with fluctuations around 0 ; plots for the data and the model are indistinguishable , and only one is presented .
the amplitude of the residuals increases as the count rate increases ( attributable in part to counting statistics ) , but there is no net deviation from 0 .
we plan to apply the lssm code to a large number of bursts .
we will compare the order of the underlying ar process and the resulting coefficients obtained for the different energy lightcurves of the same burst and for different bursts . in this way we can search for hidden classes of bursts and explore the universality of the physical processes .
the `` noise '' @xmath13 might be a measure of the energy supplied to the emission region ( although which physical processes are the noise and which the response is model dependent ) . therefore characterizing @xmath13 may probe a deeper level of the burst phenomenon .
the @xmath13 lightcurves for the different energy bands should be related ; we expect major events to occur at the same time in all the energy bands , although the relative intensities may differ . many of the bursts consist of well - separated spikes or complexes of spikes .
we will apply the lssm code to each part of the burst to determine whether the same order ar process characterizes the entire burst , and if so , whether the ar process has the same coefficients .
this will test whether the physical processes remain the same during the burst .
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we present preliminary results from modeling a sample of 4 channel batse lad lightcurves .
we determine the order of the ar process necessary to model the bursts .
the comparison of decay constants for different energy bands shows that structure decays more rapidly at high energy .
the resulting models can be interpreted physically ; for example , they may reveal the response of the burst emission region to the injection of energy . |
consider that alice holds the qubit system and bob holds the qutrit system .
like in the @xmath26-qubit scenario here also the following two cases are possible : ( a - i ) all the povm elements are rank one operators ; ( a - ii ) some of the povm elements may have more than one rank . * case(a - i ) * : alice and bob perform three - outcome rank one povms on their respective parts of the shared qubit - qutrit state . like the @xmath105 scenario ,
consider @xmath70 as basis for the alice s qubit system .
for bob s qutrit system consider @xmath106 as basis .
then the other vectors on bob s side can be expressed as : @xmath107 forms a basis for the @xmath54 tensor product hilbert space . according to the conditions ( [ h31])-([h33 ] ) the qubit - qutrit state exhibiting hardy s test ( [ h3 ] ) must be orthogonal to the following nine vectors : among the above nine vectors the set @xmath109 are linearly independent.and the rest four vectors ( i.e. @xmath110 )
can be expressed in terms of these vectors provided the following conditions are satisfied : @xmath111 the unique qubit - qutrit state orthogonal to the subspace spanned by the set @xmath112 reads as : @xmath113 being a product state the above qubit - qutrit state can not manifest the hardy s argument ( [ hardy3 ] ) . * case(a - ii ) * : in this case some povm elements are greater than rank one operators .
the analysis goes similar as case(ii ) .
the @xmath54 state exhibiting hardy s argument ( [ hardy3 ] ) need to be orthogonal to the support of the each product operator in table-([table1 ] ) .
for some cases the ranges of theses operators together span the six dimension of the @xmath54 hilbert space and hence in such cases , there is no possibility for hardy s state . for rest of the cases
the ranges together span five dimension and hence the cases boil down to the case(a - i ) . a , k. ekert , https://journals.aps.org/prl/abstract/10.1103/physrevlett.67.661[phys .
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it is important to note that , in the case of bb84 cryptography protocol if the required correlation results from measurements in the @xmath114 and @xmath115 bases on qubit pairs then security follows only if it is obtained from @xmath26-qubit maximally entangled state .
however , the same correlation can also be obtained from higher dimensional separable state and the security analysis breaks down ( see @xcite ) .
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m. banik , http://arxiv.org/abs/1401.1338[arxiv:1401.1338 ] . | schmidt rank of bipartite pure state serves as a testimony of entanglement .
it is a monotone under local operation @xmath0 classical communications ( locc ) and puts restrictions in locc convertibility of quantum states . identifying the schmidt rank of an unknown quantum state therefore
seek importance from information theoretic perspective . in this work
it is shown that a modified version of hardy s argument , which reveals the contradiction of quantum theory with _ local realism _ , turns out to be useful for inspecting the minimal schmidt rank of the unknown state and hence also the minimal dimension of the system .
use of hardy s test in such task provides a practical advantage : the schmidt rank can be determined without knowing the detailed functioning of the experimental devices i.e. , hardy s test suffices to be a device independent schmidt rank witness . among various counterintuitive features of quantum mechanics , certainly , one of the most bizarre property is quantum entanglement @xcite .
this holistic property of compound quantum systems , which involves non - classical correlations among subsystems , has potential for many quantum processes , including canonical ones : quantum cryptography @xcite , quantum teleportation @xcite , and dense coding @xcite . according to the quantum formalism ,
the total hilbert space @xmath1 of the @xmath2 separate systems is a tensor product of the subsystem spaces , i.e. , @xmath3 . when the number of the involved subsystems are two , the pure state @xmath4 of the bipartite system can always be described by its schmidt decomposition , i.e. , the representation of @xmath4 in an orthogonal product basis with minimal number of terms @xcite .
a bipartite pure state @xmath5 , with @xmath6 and @xmath7 , has schmidt rank @xmath8 if its schmidt decomposition reads : @xmath9 , where @xmath10 , @xmath11 , @xmath12 and @xmath13 is an orthonormal set of vectors in the hilbert space @xmath14 and @xmath15 is an orthonormal set of vectors in the hilbert space @xmath16 .
the schmidt number for a bipartite mixed state @xmath17 is the number @xmath18 such that : ( a ) for any decomposition @xmath19 of @xmath20 with @xmath21 at least one of the vectors @xmath22 has at least schmidt rank @xmath18 , and ( b ) and there exists a decomposition of @xmath20 with all vectors @xmath22 of schmidt rank at most @xmath18 @xcite . here
, @xmath23 denotes the collection of positive , trace-@xmath24 operators acting on @xmath25 .
the schmidt rank is the number of non vanishing terms in schmidt decomposition .
this decomposition gives a clear insight into the number of degrees of freedom that are entangled between both parties if the schmidt rank is greater than unity then the pure bipartite state must be entangled .
furthermore it has been proved that the schmidt number is non - increasing under local operations and classical communication ( locc ) , i.e. , it is a monotone under locc .
hence , it puts restriction in locc convertibility of states @xcite . a necessary condition for a pure state to be convertible by locc to another pure state
is that the schmidt rank of the later can not be larger than that of the previous one @xcite . from an information theoretic point of view
, the schmidt rank of a state , therefore , can be considered as a resource .
identifying the schmidt rank of a state is also important for quantifying the power of quantum correlations , a central issue in quantum information theory . in this work
the problem of determining the schmidt rank of an unknown bipartite state has been addressed .
interestingly , it has been shown that considering a modified version of the hardy s paradox , recently introduced by chen _
et.al _
@xcite , one can know the minimal schmidt rank of the given unknown state .
it also provides information about the minimal hilbert space dimension of the concerned system .
the use of nonlocality argument in this task comes up with a novel advantage .
the schmidt rank can be determined from measurement data alone , in a scenario in which all devices used in the experiment , including the measurement device , are uncharacterized or in other words no assumption about the internal working of the devices is needed .
the original hardy s argument was defined for _ dichotomic _ observables , i.e. , observables with two outcomes @xcite .
the authors in ref.@xcite have generalized it for observables with arbitrary many outcomes .
moreover , they have shown that , unlike the original hardy s argument , the success probability of the many - outcome argument increases with the increase of the system s dimension . in this work
the three - outcome hardy s argument has been considered .
firstly , it has been shown that neither a @xmath26-qubit state nor a qubit - qutrit state exhibits this argument for three - outcome generalized measurement , i.e. , positive - operator - valued - measurement ( povm ) @xcite . using this result
it has been further shown that this argument can be designed as a device independent schmidt rank as well as hilbert space dimension witness . before going to the main result
a quick overview on the hardy s argument has been presented .
l. hardy provided an elegant argument which , like bell s inequality @xcite , reveals nonlocality within quantum mechanics @xcite and it is commonly called ` hardy paradox ' .
hardy s proof is usually considered `` the simplest form of bell s theorem '' @xcite . the argument requires two spatially separated observers , say alice and bob , each with two measurements ( the measurements for alice and bob are denoted by @xmath27 and @xmath28 respectively , with @xmath29 ) , each with two possible outcomes denoted by ` @xmath30 ' and ` @xmath24 ' .
it puts restrictions on a certain choice of @xmath31 out of @xmath32 joint probabilities in the correlation matrix .
one such choice is : @xmath33 [ hardy ] here @xmath34 denotes the conditional joint probability of obtaining outcome ` @xmath35 ' by alice and outcome ` @xmath2 ' by bob when they perform measurement @xmath27 and @xmath28 , respectively ; @xmath36 . the non zero probability in eq.([hardy ] )
( i.e. left hand side of eq.([h4 ] ) ) is called hardy s success probability , @xmath37 . for @xmath26-qubit system
the maximum achievable value of hardy s success is @xmath38 @xcite .
it is important to note that for @xmath26-qudit system this maximum success probability remains same @xcite , i.e. , for showing the contradiction of quantum mechanics with _ local realism _ , higher dimensional systems give no advantage in experimental implementation of such a test .
recently , the authors in @xcite have introduced a hardy like argument for @xmath39-outcome measurements , i.e. , @xmath40 . denoting the joint conditional probability as @xmath41
the argument reads as @xmath42 , @xmath43 , @xmath44 , @xmath45 . for two outcomes the argument boils down to the original hardy s argument , i.e. eq.([hardy ] ) . for three outcomes
their argument explicitly looks : @xmath46 [ hardy3 ] likewise ( [ h4 ] ) , the left hand side in ( [ h34 ] ) measures the success probability of three - outcome hardy s test and similarly for the @xmath39-outcome cases . higher value of this quantity implies that experimentally it is easier to demonstrate the contradiction of quantum mechanics with _
local realism_. in quantum theory the joint conditional probabilities are calculated as : @xmath47 where , @xmath48 and @xmath49 are povms acting on alice s and bob s side respectively and @xmath50 is the shared state between alice and bob .
considering @xmath26-qudit pure states and projective measurements the authors in @xcite find the optimal success probability for @xmath39-outcome hardy s test .
as for example , for @xmath51-outcome case the optimal achievable success probability is @xmath52 , which is strictly greater than the optimal two - outcome hardy s success probability .
this value can be achieved by performing three - outcome projective measurements on @xmath26-qutrit system .
it seems to imply that the success probability increases with increasing system s dimension .
however this implication is not conclusive .
cause it has not yet been proved that by sharing a @xmath53 state ( or @xmath54 state ) and performing three - outcome generalized measurement one can not exhibit the hardy s paradox ( [ hardy3 ] ) with success probability greater than @xmath55 . in the following a more powerful result
has been proved that neither a @xmath26-qubit state nor a qubit - qutrit state exhibits the three - outcome hardy s paradox ( [ hardy3 ] ) .
first the 2-qubit case has been considered .
let alice and bob share a 2-qubit state . both of them perform two three - outcome povms , with outcomes denoted by @xmath56 respectively .
let @xmath57 denote the povm element corresponding to alice s outcome @xmath35 and similarly @xmath58 for bob s outcome @xmath2 .
thus we have : @xmath59 there are following possible cases : ( i ) all the povm elements are rank one operators ; ( ii ) some of the povm elements may have more than one rank . in the course of analysis , intuitively , it will become clear that if the measurements with rank one povm elements do not pass the three - outcome hardy s test then it is even more difficult for the measurements with higher rank povm elements to pass it .
* case ( i ) * : in this case all the povm elements can be considered as proportional to projection operators on some ray vectors , i.e. , @xmath60,~~\mbox{and}~~\mathcal{f}^n_j\propto\pi[\phi_j^n],\ ] ] where @xmath61\equiv|\psi_i^m\rangle\langle\psi_i^m|$ ] and @xmath62\equiv|\phi_j^n\rangle\langle\phi_j^n|$ ] .
the 2-qubit state that exhibits the hardy s argument ( [ hardy3 ] ) must satisfy the conditions ( [ h31])-([h33 ] ) , which imply that each term on the left hand side of these equations must be zero .
the condition @xmath63 implies that the concerned 2-qubit state is orthogonal to the product vector @xmath64 and similar is true for other cases .
thus the conditions ( [ h31])-([h33 ] ) altogether imply that the concerned state must be orthogonal to the following nine vectors : @xmath65 @xmath66 @xmath67 @xmath68 @xmath69 without loss of generality , consider @xmath70 as the basis for alice s qubit system .
other states on alice s side when written in linear combination of this basis , read as : @xmath71 similarly choosing @xmath72 as the basis for bob s qubit : @xmath73 consider the set latexmath:[$\{|\psi_1 ^ 0\rangle\otimes|\phi_1 ^ 0\rangle,|\psi_1 ^ 0\rangle\otimes|\phi_1 ^ 1\rangle,|\psi_1 ^ 1\rangle\otimes|\phi_1 ^ 0\rangle , product space @xmath53 .
the nine vectors in the set @xmath75 written in the above basis read as : @xmath76 among the above nine vectors if it turns out that four are linearly independent then those four vectors span the whole 2-qubit tensor product hilbert space and hence there will be no vector to exhibit the hardy s argument ( [ hardy3 ] ) . however , from the above expressions it is clear that the set of vectors @xmath77 is linearly independent .
if we consider the set @xmath78 then it will be linearly dependent provided @xmath79=-\alpha_1 ^ 2\beta_1 ^ 2\gamma_2 ^ 1=0 $ ] .
eq.([a1 ] ) tells that neither @xmath80 nor @xmath81 can be zero .
but , no such restriction applies for @xmath82 to be nonzero . in the similar way ,
analyzing the criteria for linear dependence of the different sets @xmath83 with @xmath84 , we obtain the following conditions : @xmath85 for exhibiting the hardy s argument ( [ hardy3 ] ) the concerned 2-qubit state must be orthogonal to the subspace spanned by the set @xmath77 and this unique state reads as : @xmath86 as the state turns out to be a product state it can not manifest the hardy s argument ( [ hardy3 ] ) .
* case(ii ) * : here all the povm elements are in general not rank one operator . to satisfy the conditions ( [ h31])-([h33 ] ) the concerned 2-qubit state must be orthogonal to the subspace spanned by the following nine product operators : .any @xmath26-qubit state that manifest the hardy s argument ( [ hardy3 ] ) must be orthogonal to the support of each of these nine product operators . [
cols="^,^,^,^,^",options="header " , ] if @xmath87 is rank two and all others are rank one then it is straightforward to argue that ranges of these operators together span four dimension of the tensor product hilbert space @xmath53 and thus there is no space left for exhibiting hardy s argument ( [ hardy3 ] ) .
similar is true for other cases .
in some cases ( e.g. @xmath88 is rank two and rest are rank one ) ranges of these operators together span three dimension and in such cases the analysis boils down to the case(i ) .
form the analysis so far presented , it is clear that no 2-qubit state exhibits the three - outcome hardy s argument .
this fact provides information about the hilbert space dimension of the composite system s , i.e. , any system that manifests the hardy s argument ( [ hardy3 ] ) can not be a @xmath53 system . at this point
one can not make any comment about the schmidt rank of the system , since a @xmath54 state may also have schmidt rank @xmath26 and can exhibit the hardy paradox ( [ hardy3 ] ) .
similar analysis shows that no @xmath53 exhibits the hardy paradox ( [ hardy3 ] ) ( see the appendix ) .
moving further it will be now shown that the hardy s argument ( [ hardy3 ] ) is useful for witnessing the minimal schmidt rank in device independent manner . in device
independent scenario one does not have detailed knowledge about the experimental apparatus .
so a black - box description of the experiment has been shown in fig([fig1 ] ) .
on each side , the experimental device is depicted like a box with some knobs .
a knob with different positions on each device , denoted respectively by @xmath27 and @xmath28 , allows alice and bob to change the parameters of each measuring apparatus .
each measurement performed by alice and bob has @xmath39 possible outcomes .
finally , the frequencies @xmath34 of occurrence of a given pair of outcomes for each pair of measurements have been collected .
after some calculations with the observed frequency the aim is to make some conclusion about the schmidt rank of the state shared between the two devices . for a given unknown bipartite state alice and bob
are asked to perform two different measurements with three outcomes .
the resulting statistics @xmath89 have been collected .
it will be checked whether the collected statistics satisfy the conditions described in eq.([hardy3 ] ) . according to these conditions the left hand side of ( [ h34 ] )
must be strictly greater than zero . among the three terms of ( [ h34 ] ) if one is nonzero ( say , @xmath90 ) and the rest two are zero then also the required condition is satisfied .
it is important to note that sharing a @xmath26-qubit pure entangled state @xcite ( i.e. a state with schmidt rank two ) and performing suitable two - outcome measurements on each side the required conditions can be satisfied . here
each of alice and bob will assign zero probability for the third outcome . in this way
the maximum value of left hand side of ( [ h34 ] ) can reach up to @xmath55 @xcite .
one can impose a more stringent restriction that all the three terms in the left hand side of ( [ h34 ] ) should be nonzero .
the previous analysis tells that in quantum theory this stringent conditions can not be satisfied by performing three - outcome generalized measurements on @xmath26-qubit ( qubit - qutrit ) state .
however , alice and bob can have the following strategy .
suppose they share the following higher dimensional state : @xmath91 where the particles @xmath92 and @xmath93 are in alice s lab and the particles @xmath94 and @xmath95 are in bob s lab .
each @xmath96 is a @xmath26-qubit pure entangled states and hence each of them are of schmidt rank two . here
the primed particles behave as _ flag _ variable . whenever the primed particles are in the state @xmath97 ( which alice and bob can know by performing a von neumann measurement in @xmath98 basis ) then alice and bob certainly know that the unprimed particles are in the state @xmath99 .
note that in the bipartition @xmath100 vs @xmath101 the schmidt number is two .
if the state is @xmath102 , then on their respective particle ( unprimed ) they perform suitable two - outcome measurements , which exhibits the two - outcome hardy s argument ( [ hardy ] ) and rename the outcomes accordingly .
thus they are able to make the first term in the left hand side of ( [ h34 ] ) nonzero .
similarly , when the unprimed particles are in the state @xmath103 ( @xmath104 ) , alice and bob can make the second ( third ) term in ( [ h34 ] ) nonzero by performing suitable measurements and renaming the outcomes accordingly @xcite . sharing this type of states
the stringent conditions , that all the terms in ( [ h34 ] ) are nonzero , can be satisfied .
but , due to convexity the success probability can not be greater than @xmath55 .
thus , whenever the success probability is strictly greater than @xmath55 , the shared state must have schmidt rank greater than @xmath26 .
this provides the information about the minimal schmidt rank of the shared bipartite system and importantly it has been done in device independent manner .
it also gives information about the minimal dimension of the shared quantum system , that the resulting statistics can not be obtained from a @xmath26-qubit or a qubit - qutrit state .
besides revealing the the contradiction of quantum mechanics with local - realism hardy s argument also finds applications in various information theoretic tasks .
it has been proved to be useful in witnessing post quantum correlations @xcite . in the recent times
various device - independent @xcite information theoretic protocols like cryptography @xcite , randomness certification @xcite , hilbert spaces dimension witness @xcite make use of nonlocality arguments @xcite . in this work
it has been shown that such an argument turns out to be useful for inspecting the minimal schmidt rank as well as the minimal hilbert space dimension in device independent manner . *
acknowledgments * : it is a pleasure to thank guruprasad kar for various simulating discussions and useful suggestions .
we also thank sibasish ghosh , samir kunkri , and ramij rahaman for useful discussions .
am acknowledge support from the csir project 09/093(0148)/2012-emr - i . |
the knowledge of the dynamics of disk galaxies is essential in order to understand their structure and history .
unfortunately , disk galaxies are difficult systems to model dynamically , for several reasons .
one of them is the presence of a large amount of interstellar dust , which obscures the light along the lines - of - sight . using extended radiative transfer models
it is nowadays possible to recover quite accurately the three - dimensional light and dust distribution in disk galaxies ( kylafis & bahcall 1987 , xilouris et al .
1999 ) . but also the observed kinematics are affected by dust obscuration
. indeed , each element along a line - of - sight carries its own kinematic information , and the projected kinematics are a weighted mean of all these contributions .
we adopt the technique outlined in baes et al .
( 2000a , b ) in order to investigate in detail the effects of dust extinction on the mean projected velocity @xmath0 and the projected velocity dispersion @xmath1 .
we adopt a galaxy model which consists of a double exponential disk and a de vaucouleurs bulge . we construct a dynamical model ( i.e. a potential and a phase - space distribution function ) for this galaxy .
we choose a potential that gives rise to a flat rotation curve and represents a halo - disk structure ( batsleer & dejonghe 1994 ) . using the quadratic programming modelling procedure ( dejonghe 1989 ) we then construct a two - integral distribution function that is consistent with the light density . we add a double exponential dust disk to this model .
finally , the dust - affected @xmath0 and @xmath1 can be calculated for various values of the inclination and optical depth . for galaxies which are face - on or moderately inclined ,
the effects of dust extinction on @xmath0 and @xmath1 are negligibly small . in the edge - on case
, the dust - affected @xmath0-profile tends to apparent solid body rotation , as we only see the stars moving on the outer near edge of the disk .
in meanwhile , the projected dispersion decreases drastically as a function of optical depth for the inner lines - of - light , as dust obscuration strongly reduces the contribution of the high random motions of the bulge stars . both effects are critically dependent on inclination , and they are already much weaker for galaxies which are only a few degrees from exactly edge - on ( see also bosma et al .
from our results it is clear that the effects of dust obscuration on @xmath0 and @xmath1 are negligible for moderately inclined galaxies .
hence it is quite safe to neglect dust extinction in the interpretation of projected kinematics .
this leads us to propose the following strategy to construct dynamical models for disk galaxies .
intermediately inclined disks are the best choice , as spectra at different position angles will then show different projections of the velocity ellipsoid .
first , one should determine the three - dimensional light distribution of the galaxy , using deprojection techniques which take the dust into account .
the accuracy of the results can be tested by comparing models in different wavebands with the galactic extinction curve ( xilouris et al .
1999 ) or by comparing the derived extinction profile with fir / submm emission ( alton et al .
then , a set of potentials which are consistent with the rotation curve and the light distribution need to be determined . for each potential a three - integral model can be constructed .
input for the fit should be the light density and the projected kinematics along ( at least ) both major and minor axes .
the goodness of fit of the different models can then be used to constrain the set of possible potentials , which will reveal the mass distribution in the galaxy .
the velocity field can then be analysed , in particular the behaviour of the velocity ellipsoid .
this can shed a light on the mechanism responsible for the dynamical history of the disk ( jenkins & binney 1990 , gerssen et al .
1997 , 2000 ) .
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, papamastorakis j. , 1999 , a&a , 344 , 868 | disk galaxies contain a large amount of interstellar dust , which affects the projection of kinematic quantities .
we investigate in detail the effects of dust extinction on the mean projected velocity and the projected velocity dispersion .
we use our results to construct a general strategy to determine the dynamical structure of disk galaxies , with the aim to constrain their mass distribution and dynamical history . |
working out a quantitative description of the properties of dense strongly interacting matter produced in ultrarelativistic heavy ion collisions presents one of the most fascinating problems in high energy physics .
the simplest ( albeit not unique ) way of putting the experimental data from rhic @xcite and lhc @xcite into a coherent framework is to describe the essential physics of these collisions as a hydrodynamical expansion of primordial quark - gluon matter that , after a short transient period , reaches sufficient level of local equilibration allowing the usage of hydrodynamics .
the features of the experimentally observed energy flow , in particular the presence of a strong elliptic flow , suggest early equilibration of the initially produced matter and small shear viscosity of the expanding fluid , see e.g. the discussion in @xcite and @xcite devoted to rhic and lhc results respectively . can stylized features of primordial quark - gluon matter , in particular its anomalously low viscosity , be described within a weakly coupled theory , i.e. as a plasma composed of quasiparticles with the quantum numbers of quarks and gluons ? to address this question let us recall that extensive experimental studies of `` ordinary '' electromagnetic plasma has demonstrated , see e.g. @xcite , that it is practically never observed in the state of textbook thermal equilibrium .
realistic description of the properties of experimentally observed qed plasma is possible only through taking into account the presence , in addition to thermal excitations , of randomly excited fields .
the resulting state was termed _
turbulent plasma_. collective properties of turbulent plasmas are markedly different from those of the ordinary equilibrium plasmas .
in particular , they are characterized by anomalously low shear viscosity and conductivity , dominant effects of coherent nonlinear structures on transport properties .
thus it is natural to consider turbulent qcd plasma as a natural candidate for describing the primordial quark - gluon matter in the weak coupling regime .
calculation of shear viscosity of turbulent qgp performed in @xcite has indeed demonstrated that its shear viscosity is anomalously small . in the present paper
we focus on studying the leading turbulent contributions to polarization properties of turbulent relativistic plasma . for simplicity
we restrict our consideration to the abelian case . the non - abelian generalization is briefly described in section [ conc ] .
a weakly turbulent plasma is described as perturbation of an equilibrated system of ( quasi-)particles by weak turbulent fields @xmath0 . in the collisionless vlasov approximation ,
the plasma properties are defined by the following system of equations ( @xmath1 is a regular non - turbulent field ) : @xmath2f(p , x , q)=0 \nonumber\\ & & \partial^{\mu}\left ( f^r_{\mu \nu } + f^t_{\mu \nu } \right)= j_{\nu}(x ) = e \sum_{q , s}\int dp\ , p_{\nu}\ , q\ , f(p , x , q ) .
\label{kinetic+maxw}\end{aligned}\ ] ] the stochastic ensemble of turbulent fields is assumed to be gaussian and characterized by the following correlators : @xmath3 in the present study we use the following parametrization of the two - point correlator @xmath4 @xcite : @xmath5\ ] ] turbulent polarization arises as a ( linear ) response to a regular perturbation that depends on turbulent fields .
it is fully characterized by the polarization tensor @xmath6 defined as a variational derivative of the averaged induced current @xmath7 over the regular gauge potential @xmath8 : @xmath9 let us rewrite the kinetic equation in ( [ kinetic+maxw ] ) in the following condensed form @xmath10 where @xmath11 is a distribution function characterizing the original non - turbulent plasma and introduce the following systematic expansion in the turbulent and regular fields : @xmath12 where powers of @xmath13 count those of @xmath14 and powers of @xmath15 count those of @xmath16 .
turbulent polarization is described by contributions of the first order in the regular and the second in the turbulent fields .
the lowest nontrivial contribution to the induced current ( [ incur ] ) is thus given by @xmath17 .
we have @xmath18 where @xmath19 generic expression for the polarization tensor taking into account turbulent effects can be written as @xmath20 where @xmath21 .
both longitudinal and transverse components can be presented as a sum of hard thermal loops ( htl ) contributions and the gradient expansion in the turbulent scale @xmath22 : @xmath23 \label{gradexp } \nonumber\end{aligned}\ ] ] @xmath24 and the standard htl contribution @xmath25 , \nonumber \\ & & \pi_{t}^{\mathrm htl } ( \omega,{\left| \mathbf { k } \right|})= m^2_d \dfrac{x^2}{2 } \left[1+\dfrac{1}{2 x } \ ; ( 1-x^2 ) \ ; l(x ) \right ] \nonumber \\ & & l(x ) \equiv \ln\left|\dfrac{1+x}{1-x}\right|-\imath\pi\theta(1-x ) ; \;\;\ ; m^2_d = e^2 t^2/3 . \label{htl}\end{aligned}\ ] ] the computation of turbulent polarization was carried out to second order in the gradient expansion @xcite . in what follows
we restrict ourselves to discussing the leading contribution to the imaginary part of the polarization function corresponding to the turbulent modification of landau damping in ( [ htl ] ) : @xmath26 the functions @xmath27 and @xmath28 are shown in fig .
[ pct1 ] .
$ ] ( solid lines ) and @xmath29 $ ] ( dashed lines ) . left : transverse response ; right : longitudinal response.,title="fig:",scaledwidth=45.0% ] $ ] ( solid lines ) and @xmath29 $ ] ( dashed lines ) . left : transverse response ; right : longitudinal response.,title="fig:",scaledwidth=45.0% ] the conclusions following from fig .
[ pct1 ] can be formulated as follows : 1 .
* timelike domain . * from fig .
[ pct1 ] we see that the sign of the imaginary part of the turbulent contribution to the polarization operator in the timelike domain @xmath30 is negative and corresponds to turbulent damping of timelike collective excitations .
this refers to both transverse and longitudinal modes .
as the htl contribution in this domain is absent , this turbulent damping is a universal phenomenon present for all @xmath31 such that @xmath32 and all values of the parameters involved ( @xmath22 , @xmath33 , @xmath34 ) .
the turbulent damping leads to an attenuation of the propagation of collective excitations at some characteristic distance .
* spacelike domain .
* the situation in the spacelike domain @xmath35 is more diverse .
in contrast with the timelike domain the gradient expansion for the imaginary part of the polarization tensor starts from the negative htl contribution corresponding to landau damping . as seen from fig .
[ pct1 ] the imaginary parts of turbulent contributions to the longitudinal polarization tensor are negative and are thus amplifying the landau damping .
the most interesting contributions come from the turbulent contributions to the transverse polarization tensor .
we see that the electric contribution @xmath36 $ ] in the spacelike domain is positive at all @xmath37 while the magnetic contribution @xmath38 $ ] is negative for @xmath39 and positive for @xmath40 .
this means that the turbulent plasma becomes unstable for sufficiently strong turbulent fields .
let us briefly discuss some relevant points : * 1 . * the above presented results
are obtained in the framework of a perturbative expansion based on two crucial assumptions .
first , one assumes slow temporal evolution of the distribution function due to particle interaction with turbulent fields thus neglecting the corresponding @xmath41 contributions .
second , changes in the distribution function are treated as small .
this , in turn , means that turbulent fields should be small enough . in this sense
the reliable results refer to small modifications of landau damping but , as the onset of turbulent instability takes place for parametrically large fields , this result should be considered as a qualitative indication .
the observed instability can be termed `` secondary '' because the turbulent fields themselves result from some `` first level '' instabilities .
the origin of the effect is in turbulent stochastic inhomogeneity and thus similar to stochastic transition radiation , which vanishes in the limit @xmath42 ) @xcite .
the non - abelian generalization of the above - described results for the imaginary part of the polarization tensor leads to identical expressions , the only difference being in trivial color factors , just as in the htl case .
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quarks 2008 , zagorsk , russia , arxiv:0809.2179 [ hep - ph ] | polarization properties of turbulent stochastically inhomogeneous ultrarelativistic qed plasma are studied .
it is shown that the sign of nonlinear turbulent landau damping corresponds to an instability of the spacelike modes and , for sufficiently large turbulent fields , to an actual instability of a system . |
the total energy formula obtained by sun is @xmath1 \label{uv}\ ] ] where @xmath2 is the total energy per atom , @xmath3 and @xmath4 are the equilibrium bulk modulus and equilibrium volume respectively . @xmath5 and @xmath6 are parameters and are related by the following relations : @xmath7 , @xmath8 , which are obtained by imposing the volume analyticity condition . since in this case
the energy of the free atoms is zero , cohesive energy of the solid at @xmath9 is the energy at which the @xmath2 is minimum which happens to be at @xmath4 .
thus the formula for cohesive energy @xmath10 turns out to be @xmath11 also , it turns out that @xmath12 .
the values of @xmath3 , @xmath4 and @xmath13 are listed for various materials in the paper@xcite .
cohesive energies calculated from the above formula are quite erroneous
. calculated values for some materials using eq.([ecoh ] ) are compared with experimental values@xcite in table._1_. also we compare the energy per particle vs volume curve of aluminum with the data obtained from ab - initio calculations@xcite in fig.([1 ] ) .
it can be seen that there is a serious mismatch between the two . however from fig.([1 ] ) , we can notice that the slopes of the mglj eos and that of the ab - initio curve are similar which is the reason for pressure calculated from mglj eos being accurate .
.[11 ] cohesive energy [ cols="^,^,^ " , ] energy vs volume curve for aluminum at temperature @xmath9 .
crosses are ab - initio data@xcite . solid line is obtained using eq.([uv ] ) , title="fig : " ]
the mglj potential is given by @xmath14 \label{glj}\ ] ] the parameters @xmath15 , @xmath16 and @xmath17 are related to @xmath3 , @xmath4 and @xmath18 denoted as @xmath19 through the following relations .
@xmath20 where @xmath21 is the structural constant which is @xmath22 for @xmath23 solids ans
@xmath24 for @xmath25 solids and @xmath15 is the depth of the potential and @xmath26 is the number of first nearest neighbors .
it can be seen that thermodynamic properties calculated using mglj potential with parameters of sun diverge for materials with @xmath19 is less than @xmath0 .
for example , consider the excess internal energy per particle ( @xmath27 ) obtained through the energy equation@xcite .
@xmath28 where @xmath29 is the density of the system and @xmath30 is the radial distribution function .
since @xmath30 becomes @xmath31 asymptotically , the integral requires that each term of @xmath32 decays faster than @xmath33 .
however , if @xmath19 is less than @xmath0 , the attractive component of @xmath32 decays slower than @xmath33 allowing @xmath27 in eq.([ee ] ) to diverge and for most of the materials @xmath19 is less than @xmath0 .
this renders the potential , as parameterized by sun , to be inapplicable to calculate thermodynamic properties as they involve evaluation of integrals similar to eq.([ee ] ) .
also the potential can not be used in molecular simulations as the tail correction for internal energy is similar to eq.([ee ] ) with lower limit being replaced by the cutoff radius of the potential .
we noted that the mglj eos predicts cohesive energies erroneously .
also we showed that the mglj potential can not be used in liquid state theories and molecular simulations for materials with @xmath34 less than @xmath0 as the thermodynamic quantities calculated using it diverge .
this may be remedied by adjusting parameter @xmath16 so that @xmath10 is properly reproduced . also , including sufficient number of neighbors so that the total energy per particle converges would improve the results .
lincoln et .
al.@xcite obtained parameters of morse potentials for various fcc and bcc materials by including up to @xmath35 neighbor shell . in a separate work ,
we have done the improvements mentioned above and obtained the parameters by fitting the mglj eos to ab - initio data .
same method is followed for eos obtained from other pair potentials and the results are analyzed@xcite .
i am thankful to dr .
chandrani bhattacharya , discussions with whom led to this paper .
i thank dr .
n.k . gupta for his encouragement .
18 g. kresse ; j. hafner , phys . rev .
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joubert , phys rev b 59 , 1758(1999 ) | the cohesive energies of solids calculated using mglj eos proposed by sun jiuxun ( sun jiuxun , j. phys . : condens .
matter 17 , l103 ( 2005 ) ) are seen to be erroneous .
also we observed that the thermodynamic properties calculated using the mglj potential diverge for materials whose pressure derivative of bulk modulus at equilibrium is less than @xmath0 .
thus the mglj potential can not be used in liquid state theories and molecular simulations to obtain thermodynamic properties .
sun jiuxun @xcite recently suggested an equation of state(eos ) based on modified generalized lennard - jones ( mglj ) potential .
the mglj eos is obtained by modifying the generalized lennard - jones potential in such a way that the eos obtained is volume analytic and satisfies spinodal condition .
the mglj eos has three parameters and are related to lattice parameter , bulk modulus and derivative of the bulk modulus at equilibrium . in the paper@xcite
it was shown that the pressure ( p ) vs compression ratio curve obtained using the mglj eos is quite accurate .
the idea of generating an eos starting from a potential is interesting and has the advantage that the potential of the material also can be known in addition to the eos .
however , we found some problems with the mglj eos and the potential so obtained from it .
they are , ( a ) the cohesive energy calculated from the mglj eos is quite erroneous and ( b ) the thermodynamic properties calculated using the mglj potential with parameters of sun diverge for most of the materials .
details about each problem are as follows : |
the authors thank s. dittmaier for useful discussions .
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lett * 75 * ( 1995 ) 1023 and 1034 | in view of the forthcoming results on @xmath0 pair production at lep 2 , we emphasize that _ direct empirical evidence _ on non - trivial properties of the weak vector bosons can be obtained with relatively limited integrated luminosity .
an integrated luminosity of @xmath1 at @xmath2 gev will be sufficient to provide direct experimental evidence for non - vanishing self - couplings of non - abelian type among the weak vector bosons .
an integrated luminosity of @xmath3 at @xmath2 gev will provide direct evidence for the existence of an anomalous magnetic dipole moment of the charged vector bosons @xmath0 .
bi - tp 96/11 + hep - ph/9603283 * i. kuss , d. schildknecht * + universitt bielefeld + fakultt fr physik + postfach 10 01 31 + d33501 bielefeld , germany + revised version , may 1996 [ [ section ] ] with respect to properties of the electroweak vector bosons , there are two salient predictions of the standard electroweak theory @xcite which lack direct experimental confirmation so far : the non - abelian coupling between the members of the @xmath4 triplet of vector bosons , and , closely connected to it , the anomalous magnetic dipole moment coupling of the charged vector bosons , @xmath0 . from the detailed analysis of the lep 1
precision data there is strong _ indirect _ evidence @xcite that indeed the standard couplings are realized in nature .
the production of @xmath5 at lep 2 will nevertheless open up a new domain of investigations by providing _
direct _ tests of the non - abelian structure and the anomalous magnetic dipole moment prediction .
limited luminosity will restrict the possibility of precision measurements of the trilinear @xmath6 and the @xmath7 couplings at lep 2 .
it is the purpose of the present note to point out that a rather small integrated luminosity at lep 2 , however , will nevertheless be sufficient to provide empirical evidence for the existence of a non - abelian trilinear coupling among the massive vector bosons and for the existence of an anomalous magnetic dipole moment of the @xmath0 .
we start from the phenomenological lagrangian for trilinear vector boson couplings widely used in the simulation of future data @xcite , @xmath8\nonumber\\ & & -iex_\gamma f_{\mu\nu}w^{+\mu}w^{-\nu}\nonumber\\ & & -ie(\frac{c_w}{s_w}+\delta_z)[z_\mu(w^{-\mu\nu}w^+_\nu - w^{+\mu\nu}w^-_\nu ) + z_{\mu\nu}w^{+\mu}w^{-\nu}]\nonumber\\ & & -iex_z z_{\mu\nu}w^{+\mu}w^{-\nu}. \label{xdellag}\end{aligned}\ ] ] it contains the three arbitrary parameters @xmath9 , @xmath10 and @xmath11 and reduces to the standard form for @xmath12 .
the parameter @xmath9 is directly related to the anomalous magnetic dipole moment @xmath13 of the @xmath0 via @xmath14 where @xmath15 is the value in the standard model .
this value follows from the linear realization of the @xmath16 symmetry in conjunction with the restriction to dimension-4 terms as embodied in the standard electroweak theory @xcite . realizing @xmath17 symmetry non - linearly , or else removing the restriction to dimension-4 terms in the linearized form , removes the restriction @xmath18 , e.g. @xcite .
we also note that @xmath18 corresponds to a gyromagnetic ratio , @xmath19 , of the @xmath0 of magnitude @xmath20 , in units of the particle s bohr - magneton @xmath21 , while @xmath22 corresponds to @xmath23 as obtained for a classical rotating charge distribution . in general @xmath24 .
the value of @xmath20 puts the electromagnetic properties of the @xmath0 in close analogy to the @xmath20 value of the spin-@xmath25 dirac theory . in order to relate @xmath10 and @xmath11 to the parameters in the lagrangian before diagonalization of the neutral sector , it is advantageous to rewrite ( [ xdellag ] ) in terms of unmixed neutral vector boson fields . for the present purpose
it is useful to describe mixing in terms of current - mixing @xcite , i.e a mixing term between the third component of the weak isotriplet , @xmath26 , and the photon field tensor , which is denoted by @xmath27 in order to discriminate @xmath28 from the physical photon field tensor @xmath29 emerging upon diagonalization .
for details we refer to @xcite .
carrying out the transformtion to the unmixed fields , @xmath30 the lagrangian ( [ xdellag ] ) becomes @xmath31,\label{lint}\end{aligned}\ ] ] where the third component of @xmath32 is understood to be @xmath33 .
the relations between @xmath34 , @xmath35 , @xmath13 and @xmath9 , @xmath11 and @xmath10 are given by ( [ kappagam ] ) and @xmath36 the standard model thus corresponds to @xmath37 , @xmath38 and @xmath15 .
let us consider the lagrangian ( [ lint ] ) in some detail .
it contains @xcite : * an @xmath4 symmetric interaction term of non - abelian form with arbitrary strength @xmath34 which coincides with the standard term for the special choice @xmath37 .
note that this term is contained in the kinetic term for the @xmath32 fields , @xmath39 provided we use the non - abelian field tensor , @xmath40 for @xmath41 , the kinetic term reduces to a triplet of abelian vector boson fields , is obviously broken by the mass terms for the vector bosons . ] .
accordingly , the case of @xmath41 may be referred to as the abelian triplet model . *
a term of strength @xmath35 which violates @xmath4 symmetry independently of the presence of the photon field
. imposing the constraint of no intrinsic @xmath4 violation@xcite , i.e. @xmath4 symmetry , when electromagnetism in ( [ lint ] ) is absent , we have to require @xmath38 , i.e. @xmath42 this requirement is abstracted from its empirical validity in the vector boson mass term and is sometimes called custodial @xmath43 symmetry . * the two terms describing the electromagnetic interactions .
the term containing @xmath44 in ( [ lint ] ) is simply obtained by applying the minimal substitution principle , @xmath45 , @xmath46 being the charge operator , @xmath47 and @xmath48 , to the derivatives in the kinetic term ( [ wkin ] ) of the @xmath32 triplet .
the anomalous magnetic moment term @xmath13 , @xmath49 in ( [ lint ] ) , on the other hand , need not necessarily be present , even though it is not excluded by the principle of minimal substitution @xcite .
in fact , adding the @xmath4-invariant total derivative term @xmath50 to the kinetic term ( [ wkin ] ) and carrying out the minimal substitution prescription implies the electromagnetic interaction ( [ lint ] ) with an arbitrary value of @xmath51 .
+ we note that both the charge coupling , @xmath52 , as well as the magnetic moment coupling , @xmath13 , appearing in connection with the unmixed field @xmath44 , @xmath28 in ( [ lint ] ) , are identical to the couplings in the lagrangian ( [ xdellag ] ) for the physical fields , @xmath53 , @xmath29 .
this is in contrast to the case of the massive neutral vector boson , where the third component of the triplet in ( [ lint ] ) couples with a strength @xmath34 different from the strength of the @xmath54 coupling , @xmath55 , in ( [ xdellag ] ) .
we note in passing that the mentioned @xmath4-symmetry properties of the terms multiplied by @xmath34 and @xmath35 in ( [ lint ] ) are not a unique feature of the @xmath56 basis .
the physical interpretation of the parameters @xmath34 and @xmath35 is thus not only valid in this basis . indeed , expressing ( [ xdellag ] ) in terms of the more conventional @xmath57 basis via @xmath58 one obtains the lagrangian in the form @xmath59.\label{lbw3}\end{aligned}\ ] ] this form of the lagrangian coincides with ( [ lint ] ) in the first two terms apart from @xmath60 being replaced by @xmath61 .
this is a consequence of the fact that the second columns of the matrices in ( [ trafo1 ] ) and ( [ trafo2 ] ) are identical . obviously , however , the @xmath62-dependent terms in ( [ lbw3 ] ) differ from the @xmath63 terms in ( [ lint ] ) . in summary
, it is a characteristic feature of a non - abelian theory to contain a coupling @xmath64 .
experimental evidence for @xmath64 thus provides evidence for a non - abelian structure of the interactions among the members of the @xmath32 triplet and rules out a theory based on three abelian vector boson fields . it is a second characteristic feature of the non - abelian nature of the standard model interactions to contain an anomalous magnetic dipole moment term of definite strength , @xmath15 .
while a precision measurement of @xmath13 will be difficult , empirical evidence for @xmath65 will nevertheless provide first direct experimental evidence for the existence of an anomalous magnetic dipole moment of the @xmath0 vector bosons .
we turn to the experimental search for a non - abelian coupling , @xmath64 , and the search for an anomalous magnetic dipole moment , @xmath49 .
we note that the present most stringent direct bound to the @xmath66-coupling @xmath9 @xcite is @xmath67 at 95% cl coupling .
the bounds to the @xmath68 couplings reported in @xcite are based on specific model assumptions which are inconsistent with the present work .
] , corresponding to @xmath69 .
we consider a measurement of the total cross section of @xmath70 at lep 2 with a cut @xmath71 on the scattering angle .
formulae for the cross section in terms of the parameters @xmath72 and @xmath10 have been given in @xcite .
we assume that the decay mode @xmath73 will be detected at lep 2 , where the lepton @xmath74 can be either an electron ( positron ) or a muon ( anti - muon ) .
the branching ratio for this decay mode is 29.6% .
we assume that future data are identical to the standard model predictions and calculate the lines of constant @xmath75 ( 86.5% cl ) and @xmath76 ( 39.4% cl ) in the @xmath9-@xmath10-plane according to such that the statistical error is given by @xmath77 .
if one uses the error estimated from the experiment , @xmath78 , instead of the statistical error in the denominator of ( [ chi2 ] ) , the values of the parameter pair ( @xmath79 ) which have @xmath75 or @xmath76 change only little provided the number of measured events , @xmath80 , is much greater than one , @xmath81 .
] @xmath82 in ( [ chi2 ] ) , @xmath80 and @xmath83 denote the number of events in the sm and in the alternative model with the @xmath4 constraint ( [ su2c_rel ] ) and @xmath84 , respectively . in figure [ fig1 ]
we show the @xmath85 and @xmath86 contours in the @xmath87 plane for an integrated luminosity of @xmath88 , at @xmath89 175 gev .
we see that this very small value of @xmath90 , corresponding to a few weeks of running at lep 2 , is sufficient to detect a genuine non - zero non - abelian coupling , @xmath64 , at the @xmath86 level .
likewise , a vanishing anomalous magnetic moment , @xmath22 , in conjunction with an abelian @xmath32 triplet , @xmath41 , is excluded .
we note that similar results can be obtained with @xmath91 at @xmath92 gev and with @xmath93 at @xmath94 gev .
to detect a non - vanishing magnetic dipole moment , @xmath49 , in the presence of a non - vanishing non - abelian coupling , @xmath64 , needs a somewhat higher integrated luminosity .
the result in figure [ fig2 ] corresponds to a luminosity of @xmath95 at @xmath2 gev , thus providing direct evidence for a non - vanishing anomalous magnetic dipole moment of the @xmath96 , @xmath65 . since a sufficient number of standard events , @xmath97 , is expected in this case ,
the events can be arranged in 6 bins equidistant over the scattering angle @xmath98 , leading to the result also presented in figure [ fig2 ] . in the same figure
we also show the theoretical prediction corresponding to a vanishing @xmath99 coupling , @xmath100 , corresponding to @xmath101 in ( [ xdellag ] ) , and @xmath102 , which is similarly ruled out . in conclusion ,
after a few weeks of running at @xmath2 gev at lep 2 , definite direct evidence for the existence of a genuine , non - vanishing coupling among the members of the @xmath103 triplet , characteristic of a non - abelian structure , can be obtained . likewise , after 7 months of running at lep 2 , definite evidence for a non - vanishing anomalous magnetic dipole moment of the charged vector bosons may be expected . |
here we give the details of the calculation of the proximity induced amplitudes @xmath146 .
because the superconductor is only weakly coupled through the tunnel barrier @xmath52 , we can derive an effective 1d model via low - order quasi - degenerate perturbation theory .
we split @xmath147 into two parts , where @xmath59 is diagonal in the eigenbasis @xmath37 , and @xmath148 $ ] .
since @xmath62 is diagonal in spin and valley , we suppress the indices @xmath149 in the following . to first order in @xmath62 , @xmath150 and to second order , @xmath151 \notag\\&\hspace{.5cm}\times \int dx{\tilde\phi}^{0\dagger}_{p_x , p_y}(x)h_1(x ) \phi^{0,n'}_{p_y}(x ) , \end{aligned}\ ] ] where @xmath152 are the unperturbed free states above the gap @xmath153 with real @xmath154 and @xmath32 at energy @xmath155 .
we impose the quantization condition @xmath156 and normalize the extended wavefunctions according to @xmath157 .
the quantization length @xmath101 and the highest momentum @xmath154 are increased until the second order matrix elements converge . to study cooper pair transport only the parts of @xmath158 , @xmath159 are relevant which are proportional to @xmath160 , i.e. , they mix electron and hole states and therefore change the particle number .
the relevant momenta @xmath32 are close to the crossing of the respective electron and hole band ( see the discussion on approximate momentum conservation in the main text ) .
this can involve one band , @xmath161 and @xmath162 , or both , @xmath163 , where @xmath164 are the fermi points of the unperturbed dispersion , eq . . the linearized subgap dispersion , eq .
, reads @xmath165 around the fermi points and @xmath166 around zero momentum . the coefficients @xmath167 and @xmath168 used in the transport calculation , e.g. , eq .
, can be read off immediately . in the most general case
the incoming holes in a nsn junction can be transmitted @xmath169 , reflected @xmath170 , or undergo local ( @xmath171 or crossed ( @xmath172 ) andreev reflection .
the outgoing state is @xmath173 rewriting the hole operators @xmath174 in terms of electron operators @xmath175 , and the fermi sea @xmath131 in terms of the lowered fermi sea @xmath128 as explained in eq . in the main text
, we arrive at the first line contains the product state contributions , the second line local pairs , and the third line nonlocal pairs . in the conventional reflection - dominated case , @xmath177 , realized in y - junction cooper pair splitters , the leading order contributions are @xmath178\ket{}_{\delta\mu } , \end{aligned}\ ] ]
i.e. , lar produces local pairs and car produces nonlocal pairs . in the transmission - dominated situation , @xmath179 , the situation is reversed : the leading order is @xmath180\ket{}_{\delta\mu } , \end{aligned}\ ] ] so lar produces nonlocal pairs and car produces local pairs . in the situation discussed in the main text , both car and reflection are forbidden , ruling out local pairs to all orders , as long as the valley symmetry is obeyed . generally speaking it is undesirable to have simultaneously strong ordinary reflection and strong lar or to have simultaneously strong transmission and strong car to build a cooper pair splitter useful to create spin entanglement .
the notation becomes more cumbersome , when both subgap bands are considered but the considerations are completely analogous . without superconductivity
the outgoing scattering state is @xmath181 where @xmath182 is the band index . in the presence of the superconductor
, the transmitted holes can change the subgap band from @xmath183 to @xmath184 with an amplitude @xmath185 . like in the one - band case ,
whenever the energy of an incoming electron is such that the spectrum of the s region has a gap , the transmission amplitude @xmath186 is exponentially suppressed with the length of the proximity region , and due to unitarity there is a finite amplitude @xmath187 for the spin-@xmath0 hole to be andreev reflected locally as a spin-@xmath0 electron at energy @xmath134 : the higher order terms in @xmath138 contain multiple cooper pairs and are not necessarily entangled , e.g. , the @xmath190 contribution is a pure product state in which all states in the left / right lead at energy @xmath191 are occupied .
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/physrevb.63.165314 [ * * , ( ) ] link:\doibase 10.1007/s10051 - 001 - 8675 - 4 [ * * , ( ) ] link:\doibase 10.1103/physrevb.65.165327 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.89.037901 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.91.267003 [ * * , ( ) ] link:\doibase 10.1038/nphys621 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.100.147001 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.105.226401 [ * * , ( ) ] link:\doibase 10.1038/nature08432 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.104.026801 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.109.157002 [ * * , ( ) ] link:\doibase 10.1038/ncomms2169 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.114.096602 [ * * , ( ) ] http://dx.doi.org/10.1038/ncomms8446 [ * * , ( ) ] link:\doibase 10.1103/physreva.57.120 [ * * , ( ) ] link:\doibase 10.1007/s100510051010 [ * * , ( ) ] link:\doibase 10.1209/epl / i2001 - 00303 - 0 [ * * , ( ) ] @noop link:\doibase 10.1103/physrevb.84.115420 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.110.226802 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.101.120403 [ * * , ( ) ] link:\doibase 10.1103/physrevb.91.085415 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.109.036802 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.100.036804 [ * * , ( ) ] link:\doibase 10.1073/pnas.1308853110 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.80.1337 [ * * , ( ) ] http://dx.doi.org/10.1038/nphys547 [ * * , ( ) ] http://dx.doi.org/10.1038/nature14364 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.96.086805 [ * * , ( ) ] @noop _ _ ( , ) @noop link:\doibase 10.1103/physrevb.90.184517 [ * * , ( ) ] link:\doibase 10.1140/epjb / e2004 - 00284 - 8 [ * * , ( ) ] http://stacks.iop.org/1367-2630/7/i=1/a=176 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.91.157002 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.83.407 [ * * , ( ) ] link:\doibase 10.1103/physrevb.61.r16303 [ * * , ( ) ] link:\doibase 10.1103/physrevb.81.125435 [ * * , ( ) ] http://stacks.iop.org/1367-2630/12/i=8/a=083063 [ * * , ( ) ] link:\doibase 10.1103/physrevb.85.115423 [ * * , ( ) ] | bilayer graphene hosts valley - chiral one dimensional modes at domain walls between regions of different interlayer potential or stacking order .
when such a channel is brought into proximity to a superconductor , the two electrons of a cooper pair which tunnel into it move in opposite directions because they belong to different valleys related by the time - reversal symmetry .
this is a kinetic variant of cooper pair splitting , which requires neither coulomb repulsion nor energy filtering but is enforced by the robustness of the valley isospin in the absence of atomic - scale defects .
we derive an effective model for the guided modes in proximity to an @xmath0-wave superconductor , calculate the conductance carried by split and spin - entangled electron pairs , and interpret it as a result of _ local _ andreev reflection processes , whereas crossed andreev reflection is absent . creating mobile nonlocal spin - entangled electrons in a transport experiment with the help of superconductor normal junctions
has attracted a lot of attention in theory @xcite and experiment @xcite because the spin degree of freedom of the electron could serve as a solid - state qubit @xcite . in the existing experiments , the envisaged process where a cooper pair is split over two normal leads
is crossed andreev reflection ( car ) @xcite , which is enhanced by the repulsive electron - electron interaction on two quantum dots weakly coupled to the superconductor @xcite or by energy filtering @xcite .
the basic mechanism of these entanglers is not very sensitive to the specific material used , i.e. , the underlying band structure .
it has been shown that characteristic features of new materials exhibiting dirac - cones like graphene or topological insulators can be useful for splitting cooper pairs @xcite . in these proposals ,
the efficiency of the splitting process , in the absence of interactions , relies on non - protected resonance conditions or the split cooper pair is not spin - entangled due to spin - helicity or spin - polarization of the leads .
helical edge states of the quantum spin hall regime have , however , been proposed to detect spin entanglement @xcite . or different stacking order a topological valley - chiral channel forms .
cooper pairs tunneling into it from a nearby @xmath0-wave superconductor ( s ) are split because the two electrons belong to opposite valleys @xmath1 and thus have opposite velocities .
they remain spin entangled and propagate to separate normal leads ( n ) .
( b ) in each valley two subgap modes along the domain wall emerge .
energy and momentum conservation along the ns interface single out four points in the subgap spectrum at which cooper pairs are injected . ] here , we propose to exploit the valley degree of freedom in bilayer graphene ( bg ) , where valley - chiral , spin - degenerate one - dimensional ( 1d ) channels are formed at domain walls .
such domain walls can be engineered by switching the sign of an interlayer voltage or by reversing the stacking order @xcite .
if brought into proximity to a superconductor , the pairs emitted into the channel are split , i.e. , two electrons propagate in different directions but remain spin - entangled since , as required by time - reversal symmetry , the two electrons forming the cooper pair in the superconductor are from different valleys @xcite .
as long as the valley degree of freedom is robust , the splitting efficiency is unity , independent of resonance conditions .
the device extends the upcoming `` valleytronics '' in graphene @xcite to nonlocal einstein - podolsky - rosen pairs .
a 1d channel defined by opposite stacking order has recently been created experimentally in bg @xcite with mean free paths over several 100 nm , demonstrating weak intervalley scattering . in this scenario , the normal reflection of an incoming hole ( or electron ) and car are absent . in the limit of a weak proximity effect , where the normal transmission through the proximity region of the channel is almost perfect , the spin - entangled pair emission with electrons moving to opposite normal terminals ( fig .
[ fig - setup ] ) is equivalent to local andreev reflection ( lar ) processes , opposite to the normal reflection - dominated case , where car produces entangled pairs .
we analyze the setup of fig .
[ fig - setup ] in two steps : first , we investigate the influence of the superconductor on the 1d channel by solving a bogoliubov - de gennes ( bdg ) equation , and derive an effective 1d model to describe the proximity effect in the channel .
second , we calculate the subgap conductance when applying a bias voltage between the superconductor and the channel using a rate equation approach .
we interpret the subgap transport in a scattering matrix picture and show that the outgoing scattered state is a two - particle spin - entangled state on top of a filled normal - state fermi sea with a chemical potential lowered by the bias voltage . to leading order its weight
is given by the lar amplitude . _
model._ we consider a bg sheet with bernal @xmath2 stacking in the presence of an interlayer voltage @xmath3 @xcite .
we model the superconductor region as bg in which the bands are shifted by a scalar potential @xmath4 due to doping and which has an induced @xmath0-wave pairing amplitude @xmath5 .
we employ the low - energy approximation for bg , valid at energies and ( inter)layer voltages smaller than the interlayer hopping @xmath6 ev . without the superconductor , the valley index @xmath7 distinguishing the two @xmath8-points @xmath9 and the electron spin @xmath10 are good quantum numbers and we write the bogoliubov - de gennes equation as @xmath11 @xmath12\tau_z + \delta({\bm r})\tau_x , \label{eq - hbdg } \end{aligned}\ ] ] where @xmath13 .
the pauli matrices @xmath14 act in the pseudospin @xmath15 space and @xmath16 in electron - hole space and we set the fermi energy @xmath17 .
the 4-component spinor is @xmath18 where we have introduced the electron @xmath19 and hole components ( @xmath20 ) on the two sublattices .
excitations with energy @xmath21 are then expanded as @xmath22 with the vector of field - operators @xmath23 . in the absence of the superconductor ( @xmath24 ) and assuming the modes to propagate along the @xmath25-direction along a domain wall at @xmath26 , i.e. , @xmath27 with @xmath28 , the topologically confined modes can be found analytically @xcite .
the electron and hole sectors in eq . decouple . in the electron sector , the solutions in each half space have the form @xmath29 where @xmath30 with @xmath31 for any fixed energy @xmath21 and momentum @xmath32 there are four allowed values @xmath33 which become complex when @xmath34 , i.e. there are no propagating modes in the bulk at energies below @xmath35 . matching the wavefunctions decaying away from the domain wall and their derivatives , one obtains the two electronic subgap solutions @xmath36 in each valley , @xmath37 , with the dispersion relation @xmath38 with velocities opposite in the two valleys @xcite . the solutions for the hole sector @xmath39 where @xmath40 at energy @xmath41 are obtained from eqs . and by setting @xmath42 .
the relevant momenta @xmath32 are close to the @xmath8 points : taking @xmath43 , we obtain from eq .
the momentum scale @xmath44 , on which the k - points are located at @xmath45 for @xmath46 . the guided modes decay into the bulk on a length scale of @xmath47 , which then is on the order of several @xmath48 nm .
this sets the scale of the separation between the guided mode and a superconductor required to obtain a proximity effect .
_ perturbation theory for superconducting pairing._ assuming a superconductor / normal interface with translational invariance along the @xmath25-direction , there are three distinct areas : in the superconductor area , @xmath49 , the pairing amplitude @xmath50 is finite and @xmath51 is negative .
the area @xmath52 is in the normal state as before , @xmath53 , but the interlayer voltage is finite , @xmath54 .
this region is a tunnel barrier between the superconductor and the domain wall at the interface to the third region @xmath55 , where @xmath53 and @xmath56 . in this situation
guided modes exist at @xmath57 because states above @xmath35 can propagate in the normal regions and states above @xmath58 can propagate in the superconductor . because of the tunnel barrier the guided modes are only weakly affected by the superconductor and we can apply standard quasidegenerate perturbation theory @xcite , for which the unperturbed hamiltonian @xmath59 is obtained from @xmath60 by setting @xmath61 everywhere and so the perturbation @xmath62 , which adds the missing parts , is finite only at @xmath49 . as a result of the perturbation the electron and hole states of the channel acquire a finite overlap @xmath63 , where @xmath64 label the subgap bands .
this allows for particle number non - conserving processes , i.e. , cooper pair transport . to first order only the electron and hole states belonging to the same subgap band mix , @xmath65 , @xmath66
this agrees with the result one expects when introducing superconductivity phenomenologically by constructing the bdg equation directly from the guided modes with a uniform pairing @xmath67 .
the second order corrections , which take into account the modification of the wavefunctions due to the superconductor , however , reveal that the situation is different in the geometry we consider . the electron hole overlap differs in both bands , @xmath68 , and band mixing is finite , @xmath69 ( fig .
[ fig - pert ] ) .
this is confirmed by the full dispersion relation of @xmath60 we obtain by matching the 4-component spinor and its derivatives at both interfaces numerically ( fig .
[ fig - pert ] , inset ) : two gaps of different size open at zero energy ( @xmath70 and @xmath71 ) and two gaps open at zero momentum where electron and hole states from different subgap bands cross ( @xmath72 ) .
this means that there is cooper pair transport at zero energy as well as at the finite energies @xmath73 .
( @xmath71 ) in the 1d channel at the respective fermi point @xmath74 and induced interband superconductivity @xmath75 at the band crossing @xmath76 . for illustrative purposes we choose the bulk superconducting gap @xmath77 and the doping @xmath78 ( @xmath79 is equally feasible ) .
the amplitudes decay exponentially with the separation @xmath80 between the superconductor and the channel because the @xmath81 region acts as a tunnel barrier .
inset : in the normal state dispersion ( dashed ) two different - sized gaps open at the fermi energy because @xmath68 , shown for @xmath82 . additionally , @xmath75 opens a gap at the electron - hole crossing at @xmath76 .
this point contributes significantly to cooper pair transport because compared to the fermi points the normal density of states is higher and because the energy is larger such that the bound states extend further into the bulk , increasing the coupling to the superconductor . ]
_ cooper pair transport._ we use fermi s golden rule to calculate the cooper pair current @xmath83 , where @xmath84 is the transition rate from an initial state @xmath85 with probability @xmath86 at energy @xmath87 to the final state @xmath88 with 2 more ( less ) electrons at energy @xmath89 . the tunnel hamiltonian @xmath90 comprises the particle number non - conserving terms of the second - quantized perturbative model with electron operators @xmath91 and hole operators @xmath92 , where @xmath93 , @xmath94 because the superconductor interface has a finite width @xmath95 , we restrict the pairing amplitude in real space @xmath96 to @xmath97 $ ] . in momentum space
( suppressing all indices ) this amounts to @xmath98 with @xmath99 from the microscopic calculation and @xmath100}{(l - k)\frac{l}{2 } } \frac{\sin\big[(l+k')\frac{w}{2}\big]}{(l+k')\frac{l}{2 } } , \end{aligned}\ ] ] where @xmath101 is the total length of the system , which does not enter the final results , and we have exploited that the integrand is peaked around @xmath102 . with this , the rates for removing ( adding ) a cooper pair , @xmath103 , become @xmath104 , where at low temperatures the occupation probability @xmath105 with @xmath106 the voltage applied between the superconductor and the channel . rewriting the sum over momenta as energy integrals ,
the current becomes @xmath107 the combination of energy conservation and approximate momentum conservation implies that the pair tunneling probability @xmath108 has a single peak as a function of @xmath21 for each pair @xmath64 .
injection into the same subgap band , @xmath109 , happens near @xmath110 , and into different subbands , @xmath111 , near @xmath112 ( fig .
[ fig - setup]b ) . linearizing the dispersion around these points @xcite , @xmath113
, the tunnel amplitude becomes @xmath114 /l(\varepsilon-\varepsilon_0^{nn'})$ ] and we obtain the conductance @xmath115 , \label{eq - cond } \end{aligned}\ ] ] where @xmath116 is the conductance quantum , @xmath117/(\pi w\varepsilon^2)$ ] becomes the delta function for @xmath118 , and @xmath119 is the effective tunneling strength . note that the conductance grows with the length of the interface .
this is in contrast to conventional cooper pair splitters , which suffer from an exponential suppression in the spatial size .
the reason is that here cooper pairs are split kinematically only after having tunneled locally into the channel , a process which can happen simultaneously along the whole interface .
the conductance contains a central zero - bias peak and two characteristic side peaks [ fig .
[ fig - conductance](a ) ] , which arise because of the special subgap band structure and which correspond to the injection points marked in fig . [ fig - setup](b ) .
the peak height is proportional to the induced superconducting pairings .
a factor of 4 arises due to the spin and valley degeneracy and a factor of 2 due to pair transport . and cooper pair current @xmath120 of a @xmath121 long interface between the superconductor and the 1d channel at a distance @xmath122 with @xmath123 .
the peak structure reflects simultaneous energy and approximate momentum conservation .
the oscillations are caused by the sharp boundary of the superconductor region and vanish if an exponential cutoff is used instead ( dashed ) .
( b ) interpretation of cooper pair splitting in terms of andreev processes .
incoming holes ( open circles ) filled up to the bias @xmath106 are either transmitted ( t ) or locally andreev - reflected ( lar ) .
ordinary reflection and crossed andreev reflection ( car ) are zero by the valley chirality .
a lar process creates an outgoing electron ( filled circle ) on the same side and no outgoing hole on the opposite side , which corresponds to an electron of opposite spin , momentum and energy ( dashed arrow ) .
these two electrons are spin entangled ( text ) . ] _ local andreev reflection and cooper pair splitting._ in eq .
the singlet nature of the injected cooper pairs is manifest .
it is well established that cooper pair splitting is closely related to car @xcite .
this applies if the dominant process is ordinary reflection . in our device , the 1d channel with a proximity - induced superconducting region is a nsn junction , in which only transmission through the s - region with amplitude @xmath124 and _ local _ andreev reflection ( an incoming quasiparticle in valley @xmath1 is reflected as an outgoing antiparticle with opposite velocity in valley @xmath125 ) with amplitude @xmath126 are possible .
we consider the general scattering problem with finite car and normal reflection in the supplemental material @xcite .
when a voltage bias @xmath106 is applied between the superconductor and the channel to extract cooper pairs , the incoming modes are filled with holes up to @xmath127 . without the superconductor , all
are transmitted and fill the outgoing modes up to @xmath127 , which is equivalent to a fermi sea for electrons @xmath128 with the fermi energy @xmath129
@xcite @xmath130 here , @xmath131 is the quasiparticle vacuum with respect to the fermi level @xmath132 of the superconductor and @xmath133 creates outgoing holes with spin @xmath0 at energy @xmath134 in the left / right lead , which is the same as annihilating an electron with opposite spin @xmath135 at energy @xmath136 .
we drop the valley index which is fixed by the requirement that outgoing modes move away from the superconducting region and the band index for simplicity @xcite . due to
the proximity effect lar becomes finite .
the key observation is that when lar occurs , no hole with spin @xmath0 at energy @xmath134 is transmitted to the other side .
the outgoing mode is therefore occupied by a spin @xmath135 electron at energy @xmath136 [ fig . [ fig - conductance](b ) ] . to see this
, we use eq . to write the outgoing state in terms of @xmath128 @xcite , @xmath137\ket{}_{\delta\mu}. \end{aligned}\ ] ]
if @xmath138 is small , it becomes @xmath139 \ket{}_{\delta\mu}$ ] , where the desired nonlocal singlet state is explicit .
this corresponds to a situation , where individual splitting events are well separated and it is meaningful to talk about pairs . in this regime of interest
the perturbative result from the previous section holds .
only the emitted pairs contribute to the shot noise of the scattering state . in the opposite limit of perfect lar with @xmath140 , @xmath141 ,
the outgoing state is a nonentangled product state .
lar is most pronounced at energies @xmath142 and @xmath143 [ fig .
[ fig - conductance](a ) ] where the superconductor opens gaps @xmath144 in the spectrum for the case of an infinitely long ( @xmath118 ) tunnel - junction ( fig .
[ fig - pert ] ) .
the lar process becomes weak for all energies , when @xmath95 falls below the coherence lengths @xmath145 . _
conclusion._ our setup allows for highly efficient creation of nonlocal spin - entangled electrons without the need for repulsive interaction or energy filters .
we note that the topological channel can be created electrically in the bulk of the bg sample , completely avoiding sharp sample edges , the main source of intervalley scattering @xcite , which could reduce the splitting efficiency .
moreover , using an electrically tunable channel geometry ballistic beamsplitters could be created to prove the spin entanglement via noise @xcite , so far an elusive goal .
the spin relaxation and decoherence in bg are expected to be weak due to the small spin - orbit coupling @xcite and the sparsity of nuclear spins .
we thank a. baumgartner , p. samuelsson , c. schnenberger , and a. levy yeyati for helpful discussions and acknowledge support from the eu - fp7 project se2nd , no .
271554 , the dfg , grant no .
re 2978/1 - 1 and research training group grk1952/1 `` metrology for complex nanosystems '' , and the braunschweig international graduate school of metrology b - igsm . |
electron spins confined in carbon nanotube@xcite ( cnt ) quantum dots@xcite ( qd ) are considered attractive for quantum information storage and processing due to the absence of the hyperfine interaction@xcite which is the main source of decoherence in iii - v nanostructures .
the spin - orbit ( so ) coupling that is intrinsically present in cnts due to s - p hybridization accompanying the curvature of the graphene plane @xcite paves the way for electrical control of the confined carrier spins . in particular
the so interaction allows for spin flips induced by ac electric fields @xcite according to the mechanism of the electric - dipole spin resonance as studied earlier for iii - v quantum dots.@xcite in nanotube quantum dots the so coupling splits the four - fold degeneracy of energy levels with respect to the spin and valley into kramers doublets with spin - orbit coupling energy varying from a fraction of mev @xcite to several mev .
@xcite in this work we study the states confined in a qd defined electrostatically within the cnt and simulate spin and valley transitions driven by ac electric field between the quadruple of nearly degenerate energy levels in external magnetic field . for clean cnts the coupling between the @xmath0 and @xmath1 valleys is absent which motivates ideas to use the valley degree of freedom as a carrier of the quantum information alternative for the electron spin .
in the transport experiments the valley filters and valves were proposed @xcite for clean samples in which the inter - valley scattering can be neglected . for clean cnt double quantum dots
the phenomenon of valley blockade has been demonstrated in experiment @xcite and studied theoretically @xcite as the equivalent of the pauli spin blockade .
@xcite a theory for rabi inter - valley resonance for cnt has also been presented @xcite within a continuum approximation of the tight - binding hamiltonian . in this work
we report on time - dependent tight - binding simulations for the spin - valley transitions driven by ac field . in the present model the electron confinement within the dot , the lattice disorder , and
the spin - valley dynamics are monitored at the atomic scale .
we work with a direct solution of the time dependent schrdinger equation which allows us to resolve not only the rabi oscillations corresponding to the first order transition but also the fractional resonances in higher - order transitions observed in edsr experiments on iii - v @xcite as well as cnt @xcite qds .
we discuss the effects driving the spin - flips with a particular focus on the electric field component that is perpendicular to the axis of the cnt , and which is bound to appear in experimental setups with cnts deposited or suspended above the gates.@xcite we show that a very similar dynamics of transitions is obtained for a bent cnt .
the bend of the nanotube for electric dipole spin resonance in nanotubes was previously proposed@xcite but in the context of the electron motion along the bend in the external magnetic field and the resulting variation of the effective zeeman splitting . in the present system
the motion of the electron is limited to the qd area and has a secondary effect on the transitions , still the bend of the nanotube in external _ electric _ field lowers the symmetry of the eigenstates which allows for the spin flips .
we discuss the consequences of the perpendicular electric field , disorder and the bend of the cnt for selection rules and transition times .
[ cols= " < , < " , ]
in summary , we presented simulations of the spin flip and inter - valley transitions in a quantum dot defined within a semiconducting carbon nanotube .
we considered a single excess electron in the quantum dot and evaluated the dynamics of the spin and valley transitions driven by external ac electric field .
time - dependent calculations used the basis of localized eigenstates as determined by the tight - binding approach . for a straight and clean cnt
the spin - flips are forbidden even for strong so coupling .
the spin transitions are triggered by electric field perpendicular to the axis of the cnt .
we demonstrated that the spin - flip transition times are inversely proportional to the value of the perpendicular electric field component .
we demonstrated that the bend of the cnt in external electric field allows for the spin - flips due to lifting of the selection rules by lowering the angular symmetry of the eigenstates with the spin - flip transition times scaling linearly with @xmath2 .
we demonstrated that when so coupling is present the atomic disorder alone allows for all types of transitions including spin flips .
we discussed the disorder introduced by a vacancy which even when far from the qd perturbs the angular symmetry of the eigenstates lifting the selection rules prohibiting the inter - valley transitions .
the inter - valley transitions when allowed by the lattice disorder appear roughly 100 to 1000 times faster than the spin flips and are insensitive to the electric fields perpendicular to the axis of the cnt .
this work was supported by national science centre according to decision dec-2013/11/b / st3/03837 , by pl - grid infrastructure and by ministry of science and higher education within statutory tasks of the faculty .
calculations were performed in ack cyfronet
agh on the rackserver zeus .
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94 * , 186806 ( 2005 ) . | we describe dynamics of spin and valley transitions driven by alternating electric fields in quantum dots defined electrostatically within semiconducting carbon nanotubes ( cnt ) .
we use the tight - binding approach to describe the states localized within a quantum dot taking into account the circumferential spin - orbit interaction due to the s - p hybridization and external fields .
the basis of eigenstates localized in the quantum dot is used in the solution of the time - dependent schrdinger equation for description of spin flips and inter - valley transitions that are driven by periodic perturbation in the presence of coupling between the spin , valley and orbital degrees of freedom .
besides the first order transitions we find also fractional resonances .
we discuss the transition rates with selection rules that are lifted by atomic disorder and the bend of the tube .
we demonstrate that the electric field component perpendicular to the axis of the cnt activates spin transitions which are otherwise absent and that the resonant spin - flip time scales with the inverse of the electric field . |
in this study we suggest a new family of spherical mass distribution models that generalizes models by an & evans ( 2006 , hereafter ae ) and models by kuzmin et al . @xcite .
the family depends on two structural parameters .
it includes plummer s spheres @xcite , hnon s isochrones @xcite and the model by hernquist @xcite as special cases .
let us consider the dimensionless potential @xmath0 here @xmath1 and @xmath2 are structural parameters . if @xmath3 , @xmath4 we obtain a model by ae , for @xmath5 , @xmath6 we have a model by kuzmin et al .
( 1969 , 1972 ) .
poisson s equation yields the following expression for density @xmath7.\ ] ] it follows from ( [ rho ] ) that our models with @xmath8 are cusped ( as models by ae are ) .
the density profiles for different values of parameters are shown in figures [ raspopova - fig1 ] , [ raspopova - fig2 ] .
the circular speed is found to be @xmath9
a run of velocity dispersion @xmath10 can be found from an equation of hydrostatic equilibrium @xmath11 the results of calculations for an isotropic velocity distribution ( @xmath12 ) are shown in figure [ raspopova - fig3 ] .
central minima will appear in all models with density cusp .
it can be obtained from ( [ phi ] ) that @xmath13^{1/p}}{\alpha\phi}.\ ] ] then it is possible to find an augmented density @xmath14 and calculate an isotropic distribution function .
stability of such models can be studied using the third antonov law @xcite , namely , if @xmath15 the model is stable against spherical perturbation .
the validity of this inequality can be established after some laborious calculations .
using the equipotential method by @xcite one can construct axisymmetric generalizations of the suggested model .
we considered a potential of such models @xmath16 where @xmath17 is the same function as and @xmath18 is an equation of equipotential surfaces , @xmath19 , @xmath20 being cylindrical coordinates .
we considered the equipotentials by @xcite : @xmath21 and by @xcite : @xmath22 here @xmath23 $ ] is a new structure parameter . for spherical systems @xmath24 .
we found that for @xmath25 close to @xmath26 the density is positive for @xmath19 , @xmath20 everywhere .
so we concluded that such non - spherical model can be used for approximating mass distribution in non - spherical star clusters and non - highly flattened galaxies . an , j. h. , evans , n. w. 2006 , , 131 , 782 binney , j. , tremaine , s. 1987 , galactic dynamics , princeton univ . press , princeton hnon , m. 1959 , ann . dastrophys . , 22 , 126 hernquist , l. 1990 , , 356 , 359 kutuzov , s. a. , ossipkov , l.p .
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japan . , 32 , 41 | a new two - parametric family of mass distribution for spherical stellar systems is considered .
it generalizes families by @xcite and by @xcite .
steady velocity dispersions are found for these models by solving an equation of hydrostatic equilibrium .
axisymmetric generalizations of the model are discussed . |
the most common method for determining the distances to radio pulsars is based on their dispersion measure and models of the galactic distribution of free electrons ( @xcite ) .
these distance estimates typically have an uncertainty of 30% .
distances may also be determined by measuring annual parallax , based on either timing ( @xcite ) or interferometric measurements ( @xcite ) .
hi absorption by interstellar hydrogen is also a common distance indicator ( @xcite ) .
however , no pulsar has a distance estimate more accurate than @xmath2% , and for all but two , the errors are greater than 20% .
any acceleration of a pulsar along the line of sight will change the observed pulse period derivative @xmath3 . as shklovskii ( 1970 ) pointed out , an apparent acceleration occurs when the proper motion is significant .
the magnitude of this contribution is @xmath4 , where @xmath5 is the pulse period , @xmath6 is the transverse velocity , @xmath7 is the pulsar distance , and @xmath8 is the speed of light . for many millisecond pulsars ,
this effect is of similar magnitude to the intrinsic pulse period derivative , making it hard to determine accurately from timing data either the intrinsic pulse period derivative ( @xcite ) , or the distance and transverse velocity .
this apparent acceleration also applies to orbital period derivatives , and the contribution is @xmath9 , where @xmath10 is the orbital period ( @xcite ) . in fact , for many nearby millisecond pulsars , it is expected to completely dominate future observed orbital period derivatives .
this means that @xmath11 can be obtained and , when combined with the measured proper motion @xmath12 , the distance and transverse velocity can be easily separated .
hence , the proper - motion contribution to the pulse period derivative can also be determined , giving accurate estimates of the intrinsic pulse period derivative and hence the magnetic field strengths , ages and spin - down luminosities of binary millisecond pulsars .
the amplitude and functional form of the residuals from a least - squares fit to the observed pulse arrival times , if one parameter is set to zero , is often called the `` timing signal '' for that parameter . for proper motion ,
the timing signal is often relatively large , with its amplitude increasing linearly with time . with continued measurement therefore , its relative error decreases as @xmath13 .
the peak - to - peak amplitude @xmath14 of the timing signal owing to the contribution of the proper motion to the observed orbital period derivative , is @xmath15 where @xmath16 is the semi - major axis of the pulsar s orbit and @xmath17 is the orbital inclination .
the accuracy of distances obtained in this way are limited by the accuracy of the orbital period derivative measurements .
their accuracy , and therefore the accuracy of distances improve as @xmath18 .
the fact that the relative error in both of these critical parameters decreases in such a spectacular fashion with time demonstrates the power of this method for determining distance and transverse velocity .
table [ t : pbdot ] shows the predicted size of the timing signal @xmath19 after 10 years of regular timing observations for a selection of binary millisecond pulsars .
where the proper motion was not available , we used the median transverse velocity for millisecond pulsars of 69 km s@xmath20 was used .
also shown is the timing signal due to parallax ( @xcite ) , @xmath21 , where @xmath22 is the radius of the earth s orbit and @xmath23 is the angle between the line of sight to the pulsar and the earth s orbital plane . after 10 years , the new method will provide better distance estimates than parallax measurements .
this is possible because @xmath24 , while @xmath25 is constant .
if an rms timing residual of 1.0 @xmath26s could be obtained it would be possible to determine distances this way for several of the currently known binary millisecond pulsars . on average , for the pulsars listed in table [ t
: pbdot ] , 23 years of precise timing data have been recorded by various observers .
so , to reap the rewards of this method a further 78 years of precise timing will be required .
many other effects could contribute to an observed orbital period derivative ; for example , changes in the gravitational constant ( @xcite ) , tidal effects ( @xcite ) , companion mass loss ( @xcite ) and accelerations in globular cluster potentials ( @xcite ) .
these contributions are indistinguishable from the proper - motion contribution , and so it is important to determine which of them are significant .
known pulsars possess one of 5 types of companion : a neutron star , a main sequence star , a white dwarf , a very low mass helium star , or a planetary system ( @xcite ) . fortunately , binary pulsars with either white dwarf or neutron star companions are very `` clean '' , and their orbital periods not affected by tidal or mass - loss effects ( @xcite ) .
systems with low - mass companions such as psr b1957 + 20 possess large orbital period derivatives , possibly caused by tidal effects ( @xcite ) .
the small @xmath27 induced by planetary companions in the pulsar orbit makes it extremely difficult to measure their orbital period derivatives .
the only significant contributions to the orbital period derivatives in neutron star and white dwarf systems are those due to acceleration in the galactic potential @xmath28 , galactic differential rotation @xmath29 , proper motion @xmath30 , and general relativity @xmath31 . table [ t : pbdot ] lists those contributions showing , that the proper - motion term will dominate for many of the binary millisecond pulsars .
for the nearby millisecond pulsar j0437@xmath324715 , the uncertainty in @xmath28 is approximately 1% of @xmath30 .
hence , measurement of the orbital period derivative will ultimately provide a distance estimate which is limited in accuracy to about 1% . if the distance could be independently estimated with superior accuracy , it would be possible to determine the acceleration of the binary in the galactic gravitational potential and thereby constrain the distribution and composition of dark matter ( @xcite ) .
however , pulsars such as psr j2317 + 1439 with large z - heights are probably better suited to such an exercise , because contribution from the galactic acceleration in such pulsars is comparable to the contribution from the proper motion .
this emphasises the importance of monitoring known binary millisecond pulsars and searching for new ones .
the double neutron - star system psr b1534 + 12 has been predicted to provide an even better relativistic laboratory than the binary pulsar b1913 + 16 ( @xcite ) .
unfortunately , the distance to this pulsar is known only to an accuracy of some 30% ( @xcite ) , and therefore the proper motion contribution to the orbital period derivative is uncertain by a similar amount .
recent measurements ( @xcite ) indicate that the predicted orbital period derivative due to gravitational wave emission @xmath31 is @xmath33 , whereas the observed value @xmath34 is only @xmath35 . using the dispersion - measure distance of @xmath36 pc and the measured proper motion ,
the contribution to the observed value from the proper motion is @xmath37 . since @xmath38 , the observed value is in excellent agreement with the general relativistic prediction .
unless the distance estimate can be improved , the orbital period decay due to the emission of gravitational waves can not be verified to better than @xmath39 5% in the psr 1534 + 12 system .
this is a surprising result , which underlines the importance of obtaining independent distance estimates to this system .
.predicted orbital period derivatives and timing signals .
@xmath40@xcite , @xmath41@xcite , @xmath42@xcite , @xmath43@xcite , @xmath44@xcite , @xmath45@xcite , @xmath46@xcite , @xmath47@xcite , @xmath48@xcite , @xmath49@xcite , @xmath50@xcite , @xmath51@xcite . [ cols="<,>,>,^,^,^,^ " , ] | we demonstrate how measuring orbital period derivatives can lead to more accurate distance estimates and transverse velocities for some nearby binary pulsars . in many cases
this method will estimate distances more accurately than is possible by annual parallax , as the relative error decreases as @xmath0 .
unfortunately , distance uncertainties limit the degree to which nearby relativistic binary pulsars can be used for testing the general relativistic prediction of orbital period decay to a few percent
. nevertheless , the measured orbital period derivative of psr b1534 + 12 agrees within the observational uncertainties with that predicted by general relativity if the proper - motion contribution is accounted for . |
sgr a * is believed to be the radio source associated with the @xmath1 ( haller et al .
1996 ; ghez et al . 1998 & 1999 ; eckart & genzel 1996 ; genzel & eckart 1999 ; zhao & goss 1999 ) dark mass concentration in the center of the galaxy .
since we know very little about this source from other wavelengths , where it is extremely faint ( see falcke 1996 for a review ) , a detailed study of its radio properties is an important prerequisite for its interpretation .
the overall shape of the sgr a * radio spectrum has been discussed in many papers ( e.g. , serabyn et al .
1997 ; falcke et al .
1998 ) and the variability has been investigated by zhao et al .
( 1989 & 1992 ) .
the spectral index ( @xmath2 ) of the source tends to be in the range @xmath3 with an increasing value of @xmath4 at mm - wavelength and a possible cut - off at lower frequencies . at high frequencies the spectrum cuts off in the infrared .
a major problem with the investigation of its radio variability is that sgr a * is at relatively low elevation for most interferometers , that it is embedded in a large confusing structure , and that it becomes scatter - broadened at low frequencies .
the confusion especially is a major problem for single - baseline interferometers with short baselines like the green bank interferometer ( gbi ) that is often used for variability studies .
for this reason the exact nature of the variability of sgr a * has remained inconclusive .
flux density variations are clearly seen between different epochs , but the timescale of the variability at various frequencies is not well determined and it is not clear whether some of the more extreme claims of variability are real or instrumental artifacts .
so far , zhao et al .
( 1989,1992 ) probably have presented the largest database of sgr a * flux - density measurements .
they found a number of outbursts at higher frequencies and tentatively concluded that the small - amplitude variability at longer wavelengths is caused by scattering effects in the ism while the variability at higher frequencies is intrinsic . in this
paper new results of a continuous monitoring program of sgr a * at cm - wavelengths performed with the gbi are presented and evaluated .
sgr a * has been part of the nasa / nrao green bank interferometer ( gbi ) monitoring program for the past two years .
the gbi is a two - element interferometer ( 26 m dishes ) with a separation of 2400 meters , operating simultaneously at x- and s - band ( 8.3 & 2.3 ghz ) with 35 mhz bandwidth .
the resolution of the pencil beam is 3 and 11 arcseconds and 1 @xmath5 noise levels are typically 30 and 6 mjy at x and s - band respectively .
the data are publically available but need further processing , since the baseline gains depend on hourangle .
in addition observations of sgr a * will also suffer from severe confusion due to the small baseline and the extended structure of sgr a west as mentioned in the introduction .
the data were post - processed in the following way : an hourangle dependent gain correction was fitted to 1622 - 297 which serves as a calibrator to sgr a*. absolute gains were obtained using 3c286 as the primary flux density calibrator .
this gain corrections were then applied to all sources and outliers were clipped when flux density measurements deviated by more than 3 @xmath5 from the median flux density within a 20 day interval . for some calculations
the data were further averaged and gridded in three - day intervals . only data after july 1997 were considered due to initial calibration problems with the gbi .
all subsequent observations were made at almost the same hour angle .
sgr a * was also corrected for confusion .
comparison of the gbi data with contemporaneous observations of sgr a * at 5 and 8 ghz with the vla and vlba ( bower et al .
1999a ; lo et al .
1998 ; goss 1998 , p.c . )
were used to calculate the difference between the gbi - single baseline flux density and the total flux density of sgr a * , where the 2.3 ghz total flux density was obtained by extrapolation .
thus for an hourangle of @xmath6 0.88 hrs a flux of 70 and 177 mjy was added to the x and s - band data respectively .
the final light curves are shown in figure 1 .
one can see a peak - to - peak variability of 250 mjy and 60 mjy with an rms of 6% and 2.5% at 8.3 & 2.3 ghz , respectively ( i.e. , modulation index ) .
the median spectral index between the two frequencies for the whole period is @xmath7 ( @xmath2 ) , varying between 0.2 and 0.4 .
there is a trend for the spectral index to become larger when the flux density in both bands increases .
to characterize the variability pattern better , fig . 2 shows the structure function @xmath8 of the two lightcurves , where @xmath9 a maximum in the structure function indicates a characteristic timescale , a minimum indicates a characteristic period .
a characteristic period in radio - lightcurves usually does not persist for a long time , and hence , similar to x - ray astronomy , is commonly called a quasi - periodicity , even though the underlying physical processes are probably very different from those seen in x - ray binaries . interestingly ,
the structure functions at both frequencies look very differently . while at both frequencies the characteristic time scale is somewhere between 50 and 200 days
, we find a clear signature of quasi - periodic variability at 2.3 ghz , which is not obvious at 8.3 ghz .
all the three maxima and the two minima in the structure function are consistent with a period of 57 days .
a cross correlation of the two light curves gives a strong peak near zero time - lag which indicates a certain degree of correlation between the emission at 8.5 ghz and 2.3 ghz ( fig .
a slight offset of the peak by 2 - 3 days is visible ( fig . 3 , right panel ) .
usually such an offset would indicate that the 8.5 ghz light curve precedes the one at 2.3 ghz .
this would be qualitatively expected by a model where outbursts travel outwards , from high to low frequencies as for example in a jet model ( falcke et al .
1993 ) , however , the time lag one obtains is also close to the sampling rate and it is not clear how significant this offset really is .
another noteworthy feature of the cross correlation is that the 2.3 ghz quasi - periodicity can still be seen .
this could indicate that the quasi - periodicity is also present at 8.3 ghz , but is swamped by another , more erratic type of variability .
to summarize the results one can say that there is clear evidence for variability of a few percent at cm wavelengths in sgr a*. the variability does not seem to be consistent with a simple model of refractive interstellar scintillation ( riss ) as suggested by zhao et al .
( 1989&1992 ) .
the timescales at 2.3 ghz and 8.3 ghz both seem to be comparable to the one found at 5 ghz by zhao et al .
( 1989&1992 ) and does not follow a @xmath10 law .
moreover , the modulation index apparently decreases towards lower frequencies .
the quasi - periodicity is reminiscent to those in some quasar cores .
for example the qso 0917 + 624 is know to show episodes of quasi - periodicity ( kraus et al .
unfortunately the frequency of these quasi - periodicities in quasar cores and perhaps also sgr a * , may not be related to a well defined and constant ( e.g. , precession ) frequency like the qpos in x - ray binaries , but could simply be due to intermittent periodic phenomena in the accretion disk ( e.g. , waves ) or the jet ( e.g. , helical motion ) . in the case of sgr
a * all characteristic timescales associated with a black hole or a relativistic outflow at these frequencies are less than a day and hence one might consider global accretion flow instabilities for such a behaviour . on the other hand
the possibility whether the quasi - periodicity could be produced by interstellar scattering needs to be explored as well .
helpful discussions with a. kraus are gratefully acknowledged .
goss provided vla data for calibration purposes .
this work was supported by the deutsche forschungsgemeinschaft , grants fa 358/1 - 1&2 .
the green bank interferometer is a facility of the national science foundation operated by nrao with support from the nasa high energy astrophysics program .
bower , g.c , falcke , h. , backer , d. , wright , m. 1999 , this volume , p. serabyn , e. , carlstrom , j. , lay , o. , lis , d.c . , hunter , t.r . ,
lacy , j.h .
1997 , apj 490 , l77 eckart a. , genzel r. 1996 , nature 383 , 415 falcke , h. 1996 , in `` unsolved problems of the milky way '' , iau symp .
169 , l. blitz & p.j .
teuben ( eds . ) , kluwer , dordrecht , p. 169
- 180 falcke h. , goss w.m . , matsuo h. , teuben p. , zhao j .- h . , zylka r. 1998 , apj 499 , 731 genzel , r. , eckart , a. 1999 , this volume , p. ghez , a. et al . 1999 , this volume , p. ghez , a. m. , klein , b. l. , morris , m. , and becklin , e. e. 1998 , apj 509 , 678 haller j. , rieke , m. , rieke , g. , tamblyn , p. close , l. , melia , f. 1996 , ap.j .
468 , 955 kraus , a. et al .
, 1999 , new astronomy reviews , submitted lo , k.y . , et al . 1998 , apj 508 , l61 zhao , j .- h . , goss w.m . 1999 , this volume , p. | results of two years of continuous monitoring of flux density variations at 8.3 and 2.3 ghz of the galactic center super - massive black hole candidate sgr a * are reported .
the average rms modulation indices are 6% and 2.5% at 8.3 & 2.3 ghz respectively .
there is a certain degree of correlation between both frequencies .
the timescale of variability at 8.3 & 2.3 ghz is between 50 and 200 days .
we can not confirm a @xmath0 dependence of the timescale . at 2.3 ghz
a quasi - periodic behaviour with a period of 57 days was discovered which is reminiscent to , though longer than , those found in some compact extragalactic radio sources . |
studies of angular and energy dependence of muon flux at the earth s surface give important information as about processes of muon generation and propagation in the atmosphere so about primary cosmic rays .
measurements of muon flux at large zenith angles up to 90@xmath0 are especially actual since primary particles for such muons have higher energies than in the vertical direction .
experimental studies of muon intensity at large zenith angles at the ground level can be conditionally separated in two groups : measurements of muon integral intensity with threshold energies less than 1 gev [ 1][8 ] and investigations of integral and differential muon spectra for muon energies higher than 10 gev ( see review [ 9 ] ) .
regions of measurements of muon spectrum at large zenith angles are presented in fig .
it is remarkable that for threshold energies from 1 gev to 10 gev and zenith angles 60@xmath1 muon intensity data are absent . to explore this region
, a setup capable to measure near - horizontal muon flux at different threshold energies with a good angular accuracy of track reconstruction is needed .
coordinate detector decor , which is a part of experimental complex nevod situated in mephi ( moscow ) , is such a detector .
regions of threshold energies and zenith angles accessible for decor and analyzed in this work are shown by the dashed areas in fig . 1 .
experimental complex nevod includes a water cherenkov calorimeter nevod [ 10 ] with sensitive volume 2000 m@xmath2 equipped with quasispherical modules of pmts , and large - area ( @xmath3 110 m@xmath4 ) coordinate detector decor [ 11 ] ( fig . 2 ) .
eight supermodules ( sm ) of decor are situated in the gallery around the water tank , and four sm on its cover .
sm of side part of decor represents eight parallel planes with sensitive area @xmath5
m@xmath6 m , suspended vertically with 6 cm distance from each other .
these planes consist of 16 chambers which contain 16 tubes with inner cross - section @xmath7 @xmath8 cm .
chambers are operated in a limited streamer mode and are equipped with two - coordinate external strip read - out system .
thus , coordinates of passing particle can be obtained for each plane with spatial accuracy of muon track location @xmath3 1 cm .
first level trigger is formed when there are at least two even and two odd triggered planes in a given sm . for the analysis ,
particles passing through two sm situated at different sides of the water pool were selected .
different pairs of sm correspond to different values of threshold energy .
accuracy of zenith angle reconstruction for tracks passing through selected sm pairs is @xmath9 .
selection procedure includes the following conditions . *
`` onetrack '' criterion : two tracks reconstructed from data of different supermodules must coincide within 5@xmath0 cone . in this case the tracks in separate sms are considered as tracks of the same particle .
straight line connecting the middles of two reconstructed track segments is taken as the trajectory of the particle .
* the events in which muon passed closer than 3 cm from the boundary of sm are rejected in order to decrease the edge effects .
* there must be two and only two track projections ( x , y ) in each sm for unambiguous reconstruction of geometrical characteristics of muon track ( the absence of accompanying particles ) .
data collected over a period from december 2002 to june 2003 are analyzed .
total time of registration is equal to 3390 hours .
the total number of selected events is more than 20 millions . [
cols="^,^,^,^,^,^ " , ]
threshold energy @xmath10 of muons passing through selected pair of sm is calculated by means of range - energy tables [ 12 ] .
it is calculated for each selected event , and then the event is placed in data array @xmath11 .
the bin of zenith angle @xmath12 , the bin of azimuth angle @xmath13 , the bin of threshold energy @xmath14 mev .
integral muon intensity is calculated in the following way : @xmath15 where @xmath11 is the number of registered muons in a given angular and threshold energy bin .
@xmath16 is `` live time '' of registration .
the parameter @xmath17 is efficiency of single sm triggering , and @xmath18 takes into account event rejection because of accompanying particles .
results of simulations and additional experimental data analysis give the following values : @xmath19 , @xmath20 varies from 0.83 to 0.91 for different @xmath21 and @xmath10 ( uncertainty of @xmath20 is less then 0.35% ) .
the function @xmath22 is the setup acceptance calculated by means of mc method taking into account the structure of sm and selection requirements .
absolute muon intensity averaged in azimuth angle for zenith angles 61@xmath23 and for five threshold energies is represented in table i and is shown in fig .
[ fig03 ] ( points ) .
errors in the table include statistical and systematical uncertainties ( uncertainty of threshold energy estimation , uncertainty of @xmath24 , muon energy loss in the walls of surrounding buildings ) .
for approximation of measured experimental data , the following simple formula is used : @xmath25 the factor in front of the exponent reflects the form of muon spectrum in the upper atmosphere , and the exponential function takes into account muon decay . here
@xmath26 is the normalization ; @xmath27 is the threshold muon energy ( gev ) at production level . in this formula @xmath28
gev@xmath29cm@xmath4/g is effective specific energy loss ; @xmath31 is the path of muon in the atmosphere ; @xmath32 g / cm@xmath4 is the total thickness of atmosphere ( altitude of setup under see level is taken into account ) ; @xmath33 g / cm@xmath4 is the effective depth of muon generation .
@xmath34 is the effective critical energy for muon ; @xmath35 is the effective length at which the density of atmosphere is changed by a factor of @xmath36 [ 13 ] ; @xmath37 is the velocity of light ; @xmath38 is muon life time and @xmath39 is it s mass ( gev ) ; @xmath40 is the approximation of effect of atmosphere sphericity . as a result of fitting ,
the following values of free parameters were obtained : @xmath41 , @xmath42 , @xmath43 km , @xmath44 and @xmath45 . in fig . 3 , integral muon intensity calculated by formula ( 2 ) for five threshold energies ( the curves )
is compared with the present experimental data .
dependence of integral muon intensity on zenith angle calculated for lower thresholds ( 1 and 0.3 gev ) and experimental data of earlier measurements [ 1][8 ] are presented in fig .
comparison of calculated values with data [ 1,4,5,7,8 ] shows a reasonable agreement . in works [ 2 ] and [ 6 ] ,
the intensity is somewhat higher than measured in [ 1 ] or calculated by ( 2 ) .
the integral intensity data at @xmath46 gev obtained in [ 3 ] decrease with the increase of zenith angle more slowly than it follows from [ 1 ] and calculation by ( 2 ) , but at angles less than 72@xmath0 the agreement is quite well .
experimental data of coordinate detector decor cover unexplored earlier region for integral muon intensity at threshold energies @xmath47 gev and zenith angles 61@xmath23 .
it is important to mark that the measurements for all thresholds were performed simultaneously with a single setup , that minimizes systematic uncertainties .
extrapolation of the present data to lower thresholds is in a reasonable agreement with the results of other measurements .
the research is performed at the experimental complex nevod with the support of the federal agency of education and federal agency for science and innovations ( contracts 02.452.11.7064 , 02.434.11.7039 ; program of support of leading scientific schools 10113.2006.2 ) .
karmakar , a. paul and n. chaudhuri , `` measurements of absolute intensities of cosmic - ray muons in the vertical and greatly inclined directions at geomagnetic latitudes 16 degrees n. '' , _ nuovo cimento b _ , vol . 17 , pp . 173 - 186 , 1973 . m.b .
amelchakov et al . , `` high - resolution large area coordinate detector for investigations of high energy cosmic ray phenomena at the ground level '' , _ proc .
27th intern .
cosmic ray conf .
_ , hamburg , vol . 3 , pp .
1267 - 1270 , 2001 . | high - statistics data on near - horizontal muons collected with russian - italian coordinate detector decor are analyzed .
precise measurements of muon angular distributions in zenith angle interval from 60@xmath0 to 90@xmath0 have been performed . in total , more than 20 million muons are selected .
dependences of the absolute integral muon intensity on zenith angle for several threshold energies ranging from 1.7 gev to 7.2 gev are derived .
results for this region of zenith angles and threshold energies have been obtained for the first time .
the dependence of integral intensity on zenith angle and threshold energy is well fitted by a simple analytical formula . |
the extended hubbard model with anisotropic spin exchange interactions @xcite is a conceptually simple phenomenological model for studying correlations and for a description of magnetism and other types of electron orderings in narrow band systems with easy - plane or easy - axis magnetic anisotropy . in this report
we will focus on the zero - bandwidth limit of the extended hubbard model with magnetic interactions for the case of arbitrary electron density .
we consider the @xmath0-@xmath1 hamiltonian of the following form : @xmath4 where @xmath0 is the on - site density interaction , @xmath5 is @xmath6-component of the intersite magnetic exchange interaction , restricts the summation to nearest neighbours .
@xmath7 denotes the creation operator of an electron with spin @xmath8 at the site @xmath9 , , and .
the chemical potential @xmath10 depending on the concentration of electrons is calculated from @xmath11 with and @xmath12 is the total number of lattice sites . the model ( [ row:1 ] ) can be treated as an effective model of magnetically ordered insulators . the interactions @xmath0 and @xmath1 will be assumed to include all the possible contributions and renormalizations like those coming from the strong electron - phonon coupling or from the coupling between electrons and other electronic subsystems in solid or chemical complexes . in such a general case
arbitrary values and signs of @xmath0 are important to consider . we restrict ourselves to the case of positive , because of the symmetry between ferromagnetic ( ) and antiferromagnetic ( ) case for lattice consisting of two interpenetrating sublattices such as for example sc or bcc lattices .
we have performed extensive study of the phase diagram of the model ( [ row:1 ] ) for arbitrary @xmath13 and @xmath10 @xcite . in the analysis
we have adopted a variational approach ( va ) which treats the on - site interaction @xmath0 exactly and the intersite interaction @xmath1 within the mean - field approximation ( mfa ) .
we restrict ourselves to the case of the positive @xmath1 , as it was mentioned above .
let us point out that in the mfa , which does not take into account collective excitations , one obtains the same results for the model and the model , where the term is replaced with , describing interactions between @xmath14-components of spins at neighbouring sites , . in both cases
the self - consistent equations have the same form , only the replacement is needed and a magnetization along the @xmath6-axis becomes a magnetization in the @xmath14-plane @xcite . for the model ( [ row:1 ] )
only the ground state phase diagram as a function of @xmath10 @xcite and special cases of half - filling ( ) @xcite and @xcite have been investigated till now . within the va the intersite interactions are decoupled within the mfa , what let us find a free energy per site @xmath15 . the condition ( [ row:2 ] ) for the electron concentration and a minimization of @xmath15 with respect to the magnetic - order parameter lead to a set of two self - consistent equations ( for homogeneous phases ) , which are solved numerically .
the order parameter is defined as , where is the average magnetization in a sublattice in the direction ( @xmath16 corresponds @xmath17 here ) .
if @xmath18 is non - zero the ferromagnetic phase ( f@xmath3 ) is a solution , otherwise the non - ordered phase ( no ) occurs .
phase separation ( ps ) is a state in which two domains with different electron concentration exist in the system ( coexistence of two homogeneous phases ) .
the free energies of the ps states are calculated from the expression : @xmath19 where @xmath20 are values of a free energy at @xmath21 corresponding to the lowest energy homogeneous solutions and is a fraction of the system with a charge density @xmath22 . we find numerically the minimum of @xmath23 with respect to @xmath22 and @xmath24
. in the model considered only ps@xmath3 state ( i. e. a coexistence of f@xmath3 and no phases ) can occur . in the paper
we have used the following convention .
a second ( first ) order transition is a transition between homogeneous phases with a ( dis-)continuous change of the order parameter at the transition temperature .
a transition between homogeneous phase and ps state is symbolically named as a `` third order '' transition . during this transition a size of one domain in the ps state decreases continuously to zero at the transition temperature .
second order transitions are denoted by solid lines on phase diagrams , dotted curves denote first order transitions and dashed lines correspond to the `` third order '' transitions .
we also introduce the following denotation : for , where @xmath25 is the number of nearest neighbours .
obtained phase diagrams are symmetric with respect to half - filling because of the particle - hole symmetry of the hamiltonian ( [ row:1 ] ) , so the diagrams will be presented only in the range .
in the ground state the energies of homogeneous phases have the form : for no : and for f@xmath26 : if and if . comparing the energies we obtain diagram shown in fig .
[ rys : gdpd ] . at the first order transition f@xmath3no takes place in the system .
this transition is associated with a discontinuous disappearance of the magnetization . without consideration of ps states .
the dotted line denotes discontinuous transition.,scaledwidth=45.0% ] the first derivative of the chemical potential for in the lowest energy phases is negative what implies that homogeneous phases are not stable ( except ) .
finite temperature phase diagrams taking into account only homogeneous phases and plotted as a function of @xmath27 for chosen @xmath13 are shown in fig .
[ rys : pdjed]a .
the tricritical point @xmath28 , which is connected with a change of transition order , for is located at and @xcite .
the range of the occurrence of f@xmath3 phase is reduced with decreasing @xmath13 . for and any
we observe only one transition f@xmath3no with increasing temperature . in the range
the @xmath27 coordinate of the remains constant , so for the transition is discontinuous .
however , for in some range of there can appear a sequence of two transitions : . in fig .
[ rys : pdjed]b there are shown dependencies of the transition temperature as a function of @xmath13 for chosen values of .
the range of f@xmath3 stability is reduced with decreasing of . for and
any @xmath13 we observe only one second order transition f@xmath3no with increasing temperature .
there exist ranges of @xmath13 and , where the sequence of transitions : is present . at sufficiently low temperatures homogeneous phases
are not states with the lowest free energy and there ps state can occur . on the phase diagrams , where we considered the possibility of appearance of the ps states ,
there is a second order line at high temperatures , separating f@xmath3 and no phases .
a `` third order '' transition takes place at lower temperatures , leading to a ps into f@xmath3 and no phases . the critical point for
the phase separation ( denoted as @xmath29 , a tricritical point ) lies on the second order line .
phase diagrams for and are shown in fig .
[ rys : pdsep ] . in the ranges of ps stability
the homogeneous phases can be metastable ( if ) or unstable ( if ) .
we leave a deeper analyses of meta- and unstable states to future publications .
we considered a simple model for magnetically ordered insulators .
it was shown that at the sufficiently low temperatures homogeneous phases do not exist and the states with phase separation are states with the lowest free energy . on phase diagrams
we also observe the tricritical points , which are associated with a change of transition order ( , fig .
[ rys : pdjed ] ) or are located in the place where the second order line connects with `` third order '' lines ( , fig .
[ rys : pdsep ] ) .
let us stress that the knowledge of the zero - bandwidth limit can be used as starting point for a perturbation expansion in powers of the hopping and as an important test for various approximate approaches ( like dynamical mfa ) analyzing the corresponding finite bandwidth models . | a simple effective model for a description of magnetically ordered insulators is analysed .
the tight binding hamiltonian consists of the effective on - site interaction ( @xmath0 ) and intersite magnetic exchange interactions ( @xmath1 , @xmath2 ) between nearest - neighbours .
the phase diagrams of this model have been determined within the variational approach , which treats the on - site interaction term exactly and the intersite interactions within the mean - field approximation .
we show that , depending on the values of interaction parameters and the electron concentration , the system can exhibit not only homogeneous phases : ( anti-)ferromagnetic ( f@xmath3 ) and nonordered ( no ) , but also phase separated states ( ps@xmath3 : ) . |
hard x - ray surveys are the most direct probe of supermassive black hole ( smbh ) accretion activity , which is recorded in the cosmic x - ray background ( cxb ) , in wide ranges of smbh masses , down to @xmath3 , and bolometric luminosities , down to @xmath4 erg / s .
x - ray surveys can therefore be used to : study the evolution of the accreting sources ; measure the smbh mass density ; constrain models for the cxb @xcite , and models for the formation and evolution of the structure in the universe @xcite .
these studies have so far confirmed , at least qualitatively , the predictions of standard agn synthesis models for the cxb : the 2 - 10 kev cxb is mostly made by the superposition of obscured and unobscured agns ( @xcite and references therein ) .
quantitatively , though , rather surprising results are emerging : a rather narrow peak in the range z=0.7 - 1 is present in the redshift distributions from ultra - deep chandra and xmm - newton pencil - beam surveys , in contrast to the broader maximum observed in previous shallower soft x - ray surveys made by rosat , and predicted by the above mentioned synthesis models .
however , the optical identification of the faint sources in these ultra - deep surveys is rather incomplete , especially for the sources with very faint optical counterparts , i.e. sources with high x - ray to optical flux ratio ( x / o ) .
indeed , the optical magnitude of @xmath5 of the sources , those having the higher x / o , is r@xmath6 , not amenable at present to optical spectroscopy .
this limitation leads to a strong bias in ultra - deep chandra and xmm - newton surveys against agn highly obscured in the optical , i.e. against type 2 qsos , and in fact , only 10 type 2 qsos have been identified in the cdfn and cdfs samples @xcite . to help overcoming this problem
, we are pursuing a large area , medium - deep surveys , the hellas2xmm serendipitous survey , which , using xmm - newton archival observations @xcite has the goal to cover @xmath7 deg@xmath8 at a 2 - 10 kev flux limit of a few@xmath9 . at this flux
limit several sources with x / o@xmath1 have optical magnitudes r=24 - 25 , bright enough for reliable spectroscopic redshifts to be obtained with 10 m class telescopes .
we have obtained , so far , optical photometric and spectroscopic follow - up of 122 sources in five xmm - newton fields , covering a total of @xmath10 deg@xmath8 ( the hellas2xmm ` 1df ' sample ) , down to a flux limit of f@xmath11 erg @xmath12 s@xmath13 .
we found optical counterparts brighter than r@xmath14 within @xmath15 from the x - ray position in 116 cases and obtained optical spectroscopic redshifts and classification for 94 of these sources @xcite .
the source breakdown includes : 61 broad line qso and seyfert 1 galaxies , and 33 _ optically obscured agn _
, i.e. agn whose nuclear optical emission , is totally or strongly reduced by dust and gas in the nuclear region and/or in the host galaxy ( thus including objects with optical spectra typical of type 2 agns , emission line galaxies and early type galaxies , but with x - ray luminosity @xmath16 erg s@xmath13 ) .
we have combined the hellas2xmm 1df sample with other deeper hard x - ray samples including the cdfn @xcite , lockman hole @xcite , and ssa13 @xcite samples , to collect a `` combined '' sample of 317 hard x - ray selected sources , 221 ( 70% ) of them identified with an optical counterpart whose redshift is available .
the flux of the sources in the combined sample spans in the range @xmath17 and the source breakdown includes 113 broad line agn and 108 optically obscured agn .
-5.7truecm [ xos ] -0.5truecm fig .
[ xos ] shows the x - ray ( 2 - 10 kev ) to optical ( r band ) flux ratio ( x / o ) as a function of the hard x - ray flux for the combined sample . about 20% of the sources have x / o@xmath1 , i.e ten times or more higher than the x / o typical of optically selected agn . at the flux limit of the hellas2xmm 1df sample several sources with x
/ o@xmath1 have optical magnitudes r=24 - 25 , bright enough to obtain reliable spectroscopic redshifts .
indeed , we were able to obtain spectroscopic redshifts and classification of 13 out of the 28 hellas2xmm 1df sources with x / o@xmath18 ; _ 8 of them are type 2 qso at z=0.7 - 1.8 _ , to be compared with the total of 10 type 2 qsos identified in the cdfn @xcite and cdfs @xcite .
[ xolx ] show the x - ray to optical flux ratio as a function of the x - ray luminosity for broad line agn ( left panel ) and non broad line agn and galaxies ( central panel ) .
while the x / o of the broad line agns is not correlated with the luminosity , a striking correlation between log(x / o ) and log(l@xmath19 ) is present for the obscured agn : higher x - ray luminosity , optically obscured agn tend to have higher x / o .
a similar correlation is obtained computing the ratio between the x - ray and optical luminosities , instead of fluxes ( because the differences in the k corrections for the x - ray and optical fluxes are small in comparison to the large spread in x / o ) .
all objects plotted in the right panel of fig .
[ xolx ] do not show broad emission lines , i.e. the nuclear optical - uv light is completely blocked , or strongly reduced in these objects , unlike the x - ray light .
indeed , the optical r band light of these objects is dominated by the host galaxy and , therefore , _ x
/ o is roughly a ratio between the nuclear x - ray flux and the host galaxy starlight flux_. the right panel of figure [ xolx ] helps to understand the origin of the correlation between x / o and l@xmath19 . while the x - ray luminosity of the optically obscured agns spans about 4 decades , the host galaxy r band luminosity is distributed over less than one decade .
the ratio between the two luminosities ( and hence the ratio between the two fluxes , see above ) results , therefore , strongly correlated with the x - ray luminosity . -0.5truecm
we have obtained spectroscopic redshifts and classification of 13 out of the 28 hellas2xmm 1df sources with x / o@xmath1 : the majority of these sources ( 8) are type 2 qsos at z=0.7 - 1.8 , a fraction of type 2 qsos much higher than at lower x / o values .
we find a strong correlation between x / o and the x - ray luminosity of optically obscured agn , x / o=10 corresponding to an ( average ) 2 - 10 kev luminosity of @xmath20 erg s@xmath13 .
sources of this luminosity and flux @xmath21 , reachable in chandra and xmm - newton ultra - deep surveys , would be at z@xmath22 .
although only 20% of the x - ray sources have such high x / o , they may carry the largest fraction of accretion power from that shell of universe .
intriguingly , mignoli et al .
( 2003 in preparation ) find a strong correlation between the r - k color and the x / o ratio for a selected sample of 10 high x / o hellas2xmm 1df sources , all of them having r - k@xmath23 , i.e. they are all extremely red objects .
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2002 , , 393 , 425 | we present results from the photometric and spectroscopic identification of 122 x - ray sources recently discovered by xmm - newton in the 2 - 10 kev band ( the hellas2xmm 1df sample ) .
one of the most interesting results ( which is found also in deeper sourveys ) is that @xmath0 of the sources have an x - ray to optical flux ratio ( x / o ) ten times or more higher than that of optically selected agn . unlike the faint sources found in the ultra - deep chandra and xmm - newton surveys , which reach x - ray ( and optical )
fluxes @xmath1 times lower than in the hellas2xmm sample , many of the extreme x / o sources in our sample have r@xmath2 and are therefore accessible to optical spectroscopy .
we report the identification of 13 sources with extreme x / o values .
while four of these sources are broad line qso , eight of them are narrow line qso , seemingly the extension to very high luminosity of the type 2 seyfert galaxies .
x - ray : background , x - ray : surveys , qso : evolution |
the solutions of the helmholtz equation for the right isosceles triangle with sidelength , @xmath3 ( chosen for convenience ) are given by @xmath4 @xmath5 .
this consists of two terms , each being a product of @xmath6 functions . of course
, it can be re - written in a variety of equivalent ways by employing trigonometric identities . with just one term of a product of sine functions ,
the nodal lines are straight lines and they form a checkerboard pattern
. this would be the case also for a product of any other special function .
+ , ( b ) @xmath7 and ( c ) @xmath8 .
all three eigenfunctions belong to the same equivalence class @xmath9 $ ] and the similarity of the nodal pattern is evident as the wavefunction evolves from one state to another within members of the same class.,title="fig:",height=124 ] ( a ) , ( b ) @xmath7 and ( c ) @xmath8 .
all three eigenfunctions belong to the same equivalence class @xmath9 $ ] and the similarity of the nodal pattern is evident as the wavefunction evolves from one state to another within members of the same class.,title="fig:",height=124 ] ( b ) , ( b ) @xmath7 and ( c ) @xmath8 .
all three eigenfunctions belong to the same equivalence class @xmath9 $ ] and the similarity of the nodal pattern is evident as the wavefunction evolves from one state to another within members of the same class.,title="fig:",height=124 ] ( c ) for instance , the solutions of the helmholtz equation for a circular , elliptical , circular annulus , elliptical annulus , confocal parabolic enclosures are each a product of functions like bessel for circular , mathieu for elliptic and so on @xcite . + eq .
( [ eq : iso ] ) can be rewritten in a way that will be more useful : @xmath10 \nonumber \\ & = & \frac{1}{2 } \re { \rm tr~ } \left[\begin{array}{cc } \{e^{i(mx - ny)}-e^{i(mx+ny)}\ } & 0\\ 0 & \{-e^{i(my - nx)}+e^{i(my+nx)}\ } \end{array}\right ] \nonumber \\ & : = & \frac{1}{2 } \re { \rm tr~ } { \mathcal i}. \end{aligned}\ ] ] all the eigenfunctions can be classified into equivalence classes labelled by @xmath11 @xcite . within each class
, it was shown that the number of domains , @xmath12 for one eigenfunction is related to @xmath13 by a difference equation @xcite .
we can , in fact , write down the operator ( in the matrix form ) which actually takes us along the ladder of states beginning with @xmath14 , up and down .
the matrix is @xmath15.\ ] ] to confirm , we get the eigenfunction @xmath16 as @xmath17 thus , we have generated all the states beginning anywhere ; note that @xmath18 could be any integer as long as we keep the inequality between the two quantum numbers .
the eigenfunctions of an equilateral triangle of side length @xmath3 , satisfying the dirichlet boundary conditions , can be written as three terms , each a product of trigonometric functions @xcite .
there are two possible solutions - one with cosine and th other with sine functions .
first we discuss the function with cosines : @xmath19 this can be re - written as @xmath20 \nonumber \\ & = & \im \frac{1}{2}{\rm tr~}{\mathcal a}\end{aligned}\ ] ] where @xmath21 is @xmath22\end{aligned}\ ] ] the matrix operator for this state is @xmath23\ ] ] similarly for the eigenfunctions written in terms of sine functions , @xmath24 in complex form , it can be re - written as @xmath25\end{aligned}\ ] ] and in matrix form as @xmath26.\ ] ] where @xmath27 is @xmath28\ ] ] the corresponding matrix operator is @xmath23\ ] ] this operator is the same as for the cosine form of the eigenfunctions for equilateral triangle billiard .
the eigenfunctions of separable billiards are a single product of special functions - trigonometric for rectangular billiard , bessel and trigonometric functions for circular billiards ( and related annuli ) , mathieu and trigonometric functions for elliptical billiards ( and annuli ) , and parabolic cylinder functions for confocal parabolic billiards . in all these cases ,
the tower of states can be trivially constructed along the lines described here .
this is because the index that classifies states for all separable billiards is ( @xmath29 ) . for the non - separable billiards described here , we have shown in earlier papers that all the states can be classified by ( @xmath30 ) or ( @xmath31 ) .
here , we have shown that within a class , all the states can be constructed from the energetically lowest state .
we can also make a transformation from an excited state to the lowest state .
we hesitate to call this a ` ground state ' as there will be one lowest state for an index , @xmath32 , @xmath33 .
the results given here are for billiards with dirichlet boundary conditions .
of course , these results are trivially extended to the case of periodic boundary conditions .
the raising and lowering operators will remain the same .
for twisted boundary conditions , these may be generalized by introducing phases in the matrix representation of raising and lowering operators . | for planar integrable billiards , the eigenstates can be classified with respect to a quantity determined by the quantum numbers .
given the quantum numbers as @xmath0 , the index which represents a class is @xmath1 for a natural number , @xmath2 .
we show here that the entire tower of states can be generated from an initially given state by application of the operators introduced here .
thus , these operators play the same role for billiards as raising and lowering operators in angular momentum algebra
. quantum billiards are systems where a single particle is confined inside a boundary on which the eigenfunctions vanish @xcite .
one seeks the solutions of the time - independent schrdinger equation , which is the same as the helmholtz equation in the context of general wave phenomena .
the solutions of this problem for an arbirarily shaped enclosure is a very challenging open problem , even when we restrict ourselves to two - dimensional cases @xcite .
there are some very interesting connections between exactly solvable models and random matrix theories , a summary may be seen in @xcite .
the helmholtz operator is separable in certain coordinate systems - for these cases , the solutions can be found @xcite . the non - separable problems for which the classical dynamics is integrable have been recently studied in detail @xcite .
although the solutions of these systems have been known , there remain many questions regarding the nature of nodal curves and domains .
the nodal domains of the eigenfunctions of the systems for which the schrdinger equation is separable , form a checkerboard pattern @xcite .
the number of crossings actually count the number of domains .
moreover , the checkerboard patterns are trivially self - similar . counting the nodal domains of non - separable plane polygonal billiards
is very difficult in general @xcite .
even if we restrict to systems that are classically integrable , the problem poses considerable challenge .
progress on this otherwise intractable problem could be made recently due to the observation that the eigenfunctions could be classified in terms of equivalence classes @xcite .
fig .
[ fig : iso ] shows examples of eigenfunctions belonging to an equivalence class in the right isosceles triangle billiard .
one can not miss the remarkable similarity in each family , they seem genetically related . here we shall present operators that make any other state appear starting from one in a family .
thus , we can construct the tower of states by repeated application of this operator .
this reminds us of the usual raising and lowering operators in quantum mechanics .
we explain in the following sections the construction of raising " and lowering " operators for the right isosceles and equilateral triangle billiard , and summarize with remarks about other systems . |
with wilson fermions , straightforward calculations of @xmath0 using the 1-loop improved @xmath2 operator fail due to the large mixing with the wrong chirality operators @xcite .
since this mixing is an artifact of lattice discretization , one hopes that it can be significantly reduced by improving the action . by comparing results obtained using the wilson and the tadpole improved clover action ( @xmath3 ) on the same quenched gauge lattices ( 170 lattices of size @xmath4 at @xmath5 )
we show that this is indeed the case .
[ f : bkw ] shows the wilson and clover data as a function of @xmath6 . for each data
set , @xmath0 is written as the sum of two parts @xmath7 the contribution of the diagonal ( the 1-loop tadpole improved @xmath8 ) operator , and the mixing term which is proportional to @xmath9 .
the general form , ignoring chiral logarithms and terms proportional to @xmath10 , for @xmath11 is @xcite @xmath12 the coefficients @xmath13 are pure artifacts , therefore their value can be used to quantify improvement . of these @xmath14
is the most serious as it causes @xmath0 to diverge in the chiral limit .
the divergence , in the limit @xmath15 , of the diagonal term due to a non - zero @xmath14 is evident in fig .
[ f : bkw ] for wilson fermions .
this artifact is only partially cancelled by the 1-loop mixing operator .
the situation is considerably improved with clover fermions .
the corresponding values at @xmath16 mev are @xmath17 whereas @xmath18 .
this improvement arises because the two dominant artifacts @xmath19 and @xmath20 are significantly reduced ; @xmath21 versus @xmath22 , and @xmath23 versus @xmath24 . -0.8 cm
-0.6 cm [ f : bkw ] as explained in @xcite , the contributions proportional to @xmath13 can be removed completely by studying the momentum dependence of the matrix elements .
short of calculating the mixing coefficients non - perturbatively , the way to remove the artifacts in @xmath25 is to extrapolate to @xmath26 .
we have done the calculation at @xmath27 only , where our final results are @xmath28 and @xmath29 for wilson and clover formulations respectively .
the benchmark value , including @xmath30 extrapolation , is @xmath31 , as obtained by the jlqcd collaboration @xcite .
the chiral condensate @xmath32 is not simply related to the trace of the wilson quark propagator @xmath33 .
the breaking of chiral symmetry by the @xmath34 term introduces contact terms that need to be subtracted non - perturbatively from @xmath33 @xcite .
this has not proven practical . instead , the methods of choice are to either evaluate the right hand side of the continuum ward identity @xmath35 or cast the gell - mann , oakes , renner relation @xmath36 in terms of lattice correlation functions @xcite .
these estimates have errors of both @xmath37 and @xmath38 , and at fixed @xmath39 are therefore expected to agree only in the chiral limit .
a comparison of the efficacy of the two methods is shown in fig .
[ f : xbarx ] .
we find that a reliable extrapolation to the chiral limit can be made using a linear fit , and the two methods give consistent results for both wilson and clover fermions . also , the @xmath38 corrections are significantly smaller for clover fermion .
-0.8 cm -0.6 cm [ f : xbarx ]
in ref . @xcite we presented a detailed analysis of mass - splittings in the baryon octet and decuplet with wilson fermions . we had found a large non - linear dependence on quark mass for the @xmath40 , @xmath41 , and @xmath42 splittings .
extrapolation of the data to the physical masses including these non - linearities gave estimates consistent with observed values . on the other hand we had found a surprisingly good linear fit to the decuplet masses , and the splittings were underestimated by @xmath43 .
the data with clover fermions show the same qualitative features . as an illustration
, we show a comparison of the @xmath44 splitting in fig .
[ f : siglam ] .
details of the analysis will be published elsewhere @xcite .
-0.8 cm -0.6 cm [ f : siglam ]
the improvement coefficient for the axial current , @xmath1 , is calculated using the the axial wi @xcite . if the clover coefficient @xmath45 is tuned to its non - perturbative value @xmath46 at @xmath27 @xcite , the sum @xmath47 of quark masses defined by @xmath48^{(12)}(\vec{x},t ) j^{(21)}(0 ) \rangle } { \sum_{\vec{x } } \langle p^{(12)}(\vec{x},t )
j^{(21)}(0 ) \rangle } \label{ca } \end{aligned}\ ] ] should be independent of @xmath49 and the initial pseudoscalar state created by @xmath50 , up to corrections of @xmath51 .
we vary the composition of the initial state by using @xmath52 or @xmath53 and by using `` wall '' or `` wuppertal '' smearing functions in the calculation of the quark propagators . the results in fig .
[ f : ca ] show a large dependence on the initial state for wilson fermions and almost none already for @xmath3 !
we estimate @xmath54 from this clover data , whereas the alpha collaboration report @xmath55 at @xmath56 @xcite . we are repeating the calculation at @xmath56 to understand this difference .
-0.8 cm -0.6 cm [ f : ca ]
the explicit breaking of chiral symmetry in wilson - like fermions gives rise to the problem of `` exceptional configurations '' in the quenched theory .
the cause is that the wilson @xmath34 term breaks the anti - hermitian property of the massless dirac operator . as a result ,
zero modes of the dirac operator extend into the physical region @xmath57 .
thus , on a given configuration , as the quark mass is lowered and approaches the first of the unphysical modes , one encounters exceptionally large fluctuations in the correlation functions .
such configurations dominate the ensemble average and as discussed in @xcite there is no basis for excluding them .
tuning @xmath58 reduces the @xmath37 chiral symmetry breaking artifacts as shown above , however , it does not reduce this problem @xcite .
we find , by comparing fluctuations in 2-point and 3-point correlation functions between wilson and clover fermions , that the problem , in fact , gets worse . a deeper understanding of the persistence of the zero mode problem even though the chiral behavior is improved is missing .
this work was supported by the doe grand challenges award at the advanced computing lab at los alamos , and by the nato collaborative research grant , contract no .
940451 .
9 r. gupta , , ( 1997 ) 4036 .
jlqcd collaboration , ( 1998 ) 5271 .
m. bochicchio , , ( 1985 ) 331 .
d. daniel , , ( 1992 ) 3130 .
t. bhattacharya , , ( 1996 ) 6486 .
t. bhattacharya , , in preparation .
m. lscher _ etal .
_ , nuc.phy . *
b491 * ( 1997 ) 323 .
-1 w. bardeen , , ( 1998 ) 1633 . | we present evidence for improvement with tadpole improved clover fermions based on an analysis of the chiral behavior of @xmath0 and the quark condensate . also presented
are a comparison of the mass splittings in the baryon octet and decuplet , a calculation of @xmath1 using standard 2-point correlation functions , and the problem of zero modes of the dirac operator .
# 1#1 |
planetpack is a software tool that facilitates the detection and characterization of exoplanets from the radial velocity ( rv ) data , as well as basic tasks of long - term dynamical simulations in exoplanetary systems . the detailed description of the numeric algorithms implemented in planetpack is given in the paper @xcite , coming with its initial 1.0 release .
after that several updates of the package were released , offering a lot of bug fixes , minor improvements , as well as moderate expansions of the functionality .
as of this writing , the current downloadable version of planetpack is 1.8.1 . the current source code , as well as the technical manual , can be downloaded at ` http://sourceforge.net/projects/planetpack ` . here
we pre - announce the first major update of the package , planetpack 2.0 , which should be released in the near future .
in addition to numerous bug fixes , this update includes a reorganization of the large parts of its architecture , and several new major algorithms .
now we briefly describe the main changes .
the following new features of the planetpack 2.0 release deserve noticing : 1 .
multithreading and parallelized computing , increasing the performance of some computationally heavy algorithms .
this was achieved by migrating to the new ansi standard of the c++ language , c++11 .
several new models of the doppler noise can be selected by the user , including e.g. the regularized model from @xcite .
this regularized model often helps to suppress the non - linearity of the rv curve fit .
3 . the optimized computation algorithm of the so - called keplerian periodogram @xcite , equipped with an efficient analytic method of calculating its significance levels ( baluev 2014 , in prep . ) .
4 . fitting exoplanetary transit lightcurves is now implemented in planetpack .
this algorithm can fit just a single transit lightcurve , as well as a series of transits for the same star to generate the transit timing variation ( ttv ) data .
these ttv data can be further analysed as well in order to e.g. reveal possible periodic variations indicating the presence of additional ( non - transiting ) planets in the system .
the transit lightcurve model is based on the stellar limb darkening model by @xcite .
also , the transit fitting can be performed taking into account the red ( correlated ) noise in the photometry data .
some results of the planetpack ttv analysis of the photometric data from the exoplanet transit database , ` http://var2.astro.cz/etd/ ` , will be soon presented in a separate work . concerning the evolution of the planetpack code
, we plan to further develop the transit and ttv analysis module and to better integrate it with the doppler analysis block .
we expect that in a rather near future planetpack should be able to solve such complicated tasks as the simultaneous fitting of the rv , transit , and ttv data for the same star .
this integration should also take into account subtle intervenue between the doppler and photometry measurements like the rositter - mclaughlin effect . | we briefly overview the new features of planetpack2 , the forthcoming update of planetpack , which is a software tool for exoplanets detection and characterization from doppler radial velocity data . among other things
, this major update brings parallelized computing , new advanced models of the doppler noise , handling of the so - called keplerian periodogram , and routines for transits fitting and transit timing variation analysis . |
in the ctf ii drive beam gun , cs - te photocathodes are used to produce a pulse train of 48 electron bunches , each 10ps long and with a charge of up to 10nc @xcite . in ctf , the main limit to lifetime is the available laser power , which requires a minimal quantum efficiency ( qe ) of 1.5% to produce the nominal charge .
although cs - te photocathodes are widely used , a complete understanding , especially of their aging process , is still lacking .
spectra of the qe against exciting photons may help to understand the phenomenon .
according to spicer @xcite , the spectra of the quantum efficiency ( qe ) of semiconductors with respect to the energy of the exciting photons ( @xmath0 ) can be described as : @xmath1 where @xmath2 is the threshold energy for photoemission , c@xmath3 and c@xmath4 are constants . to measure the spectral response of photocathodes , wavelengths from the near uv throughout the visible are necessary . to attain these , an * o*ptical * p*arametrical * o*scillator was built @xcite .
a frequency - tripled nd : yag laser pumps a betabarium borate ( bbo ) crystal in a double - pass configuration , as shown in fig.[fig : opo ] .
the emerging signal - beam , with wavelengths between 409 nm and 710 nm , is frequency doubled in two bbo crystals .
the wavelengths obtained are between 210 nm and 340 nm .
the idler - beam delivers wavelengths between 710 nm and @xmath5 nm . the measurements of the spectral response of photocathodes were made in the dc - gun of the photoemission lab at cern @xcite , at a field strength of about 8 mv / m .
spectra were taken shortly after the evaporation of the cathode materials onto the copper cathode plug , as well as after use in the ctf ii rf - gun @xcite at fields of typically 100 mv / m . to be able to interpret the spectra in terms of spicer s theory , it was necessary to split the data into 2 groups , one at `` low photon energy '' and one at high photon energy , see fig.[fig : cath87 ] .
then , the data can be fitted well with two independent curves , following eq.([eq : spicer ] ) , which give two threshold energies . for a typical fresh cs - te cathode ,
the high energy threshold is 3.5ev , the low one is 1.7ev , as shown in fig.[fig : cath87 ] , upper curve .
this might be a hint that two photo - emissive phases of cs - te on copper exist .
several explanations are possible : the copper might migrate into the cs - te , creating energy levels in the band gap ; or possibly not only cs@xmath4te , but also other cs - te compounds might form on the surface and these might give rise to photoemission at low photon energy . a hint to this
might be that the ratio of evaporated atoms of each element is not corresponding to cs@xmath4te , see below .
after use , we found that not only the complete spectrum shifted towards lower quantum efficiency , but also that the photoemission threshold for high qe increased to 4.1ev , which is shown in fig.[fig : cath87 ] , lower curve .
one might expect that the photocathode is poisoned by the residual gas , preventing low - energy electrons from escaping .
however , because typical storage lifetimes are of the order of months , the effect must be connected to either the laser light , or the electrical field .
we also produced a cs - te cathode on a thin gold film of 100 nm thickness .
as shown in fig.[fig : cath120 ] , the shoulder in the low energy response disappeared .
it is difficult to fit a curve for the spicer model to the low energy data .
the high " photoemission threshold is at 3.5ev . at the moment , this cathode is in use in the ctf ii gun and will be remeasured in the future . in terms of lifetime , this cathode is comparable to the best cs - te cathodes , as it has already operated for 20 days in the rf - gun . as a new material presented first in @xcite , we tested rubidium - telluride .
we took spectra of qe before and after use in the ctf ii gun , as for cs - te .
remarkably , with this material , there was no shift in the photoemission threshold towards higher energies , but only a global shift in qe , see fig.[fig : rb2te ] .
this might be due to the lower affinity of rubidium to the residual gas .
detailed investigations are necessary to clarify this .
long lifetimes for cs - te cathodes are achieved only when they are held under uhv ( @xmath6 mbar ) .
other photocathode materials like k - sb - cs are immunized against gases like oxygen by evaporating thin films of csbr onto them @xcite .
therefore , we evaporated a csbr film of 2 nm thickness onto the cs - te .
fig.[fig : csbr ] shows the spectrum before the csbr film ( square points ) and after it ( round points ) .
the qe at 266 nm dropped from 4.3% to 1.2% .
in addition , the photoemission threshold was shifted from 3.9ev to 4.1ev .
a long - term storage test showed no significant difference between uncoated and coated cathodes .
more investigations will determine the usefulness of these protective layers . in order to increase the sensitivity of the on - line qe measurement during evaporation of the photocathodes
, we monitored the process with light at a wavelength of 320 nm .
we did not see any significant improvement in sensitivity , notably in the high qe region .
film thicknesses are measured during the evaporation process by a quartz oscillator @xcite .
typical thicknesses for high quantum efficiencies at @xmath7 nm are 10 nm of tellurium and around 15 nm of cesium .
this results in a ratio of the number of atoms of each species of @xmath8 , far from the stoichiometric ratio of 0.5 for cs@xmath4te .
it is known that tellurium interacts strongly with copper @xcite , so that not all of the evaporated tellurium is available for a compound with subsequently evaporated cesium
. therefore , we used also mo and au as substrate material .
however , the ratio between the constituents necessary for optimum qe , did not change significantly .
another reason might be that instead of cs@xmath4te , cs@xmath4te@xmath9 is catalytically produced on the surface .
this compound , as well as some others , was found to be stable @xcite .
lifetime in ctf depends on parameters like maximum field strength on the cathode , vacuum and especially extracted charge .
typically , a cathode is removed from the gun , if the qe falls below 1.5% .
as shown in fig.[fig : lifetime ] , lifetime does not depend on the initial qe ; a cathode having an initial qe of 15% ( round points ) lasted as long as one with 5% ( triangles ) .
as shown in table[tab1 ] , the average current produced in ctf ii is nearly a factor 10000 lower than what is required for the clic drive beam .
a test to produce 1mc is under preparation in the photoemission laboratory at cern .
the exact reproduction of the clic pulse structure would require the clic laser , which is still in the design stage .comparison of cathode relevant parameter [ cols="^,^,^,^",options="header " , ] [ tab1 ] in a collaboration between rutherford appleton laboratory and cern .
a test which is compatible with our current installation is the production of 1ma of dc current , which requires a uv laser power of 300mw at the cathode . for this test
, we will illuminate the cathode with pulses of 100ns to 150ns pulse length , at repetition rates between 1khz and 6khz .
as table[tab1 ] shows , this is a factor 1000 more average current than in ctf ii , and also demonstrates the basic ability of the cathodes to produce the ctf 3 drive beam ( i=26@xmath10a ) .
clic is still a factor 75 away .
we are currently searching for ways to produce higher charges as well .
measurements of qe against photon energy are routinely made after production and after use of photocathodes .
we have demonstrated that both low energy and high energy responses agree well with spicer s theory .
a gold buffer layer reduces the low energy response of cs - te cathodes .
more work is needed to understand the measurements of the stoichiometric ratio of cs - te .
coating with 2 nm csbr significantly decreased the quantum efficiency , without improving the storage lifetime . for the high - charge drive beam of clic , it is still necessary to demonstrate the capabilities of cs - te , for which first tests will be done soon .
e. chevallay , j. durand , s. hutchins , g. suberlucq , m. wrgel , photocathodes tested in the dc gun of the cern photoemission laboratory " , nuclear instruments methods in physics research section a , vol .
340 , ( 1994 ) 146 - 156 , cern clic note 203 e. shefer , a. breskin , r. chechik , a. buzulutskov , b.k .
singh , m. prager , coated photocathodes for visible photon imaging with gaseous photomultipliers " , nuclear instruments methods in physics research section a , vol.433 , no.1 - 2 , ( 1999 ) 502 - 506 | for short , high - intensity electron bunches , alkali - tellurides have proved to be a reliable photo - cathode material .
measurements of lifetimes in an rf gun of the clic test facility ii at field strengths greater than 100 mv / m are presented . before and after using them in this gun , the spectral response of
the cs - te and rb - te cathodes were determined with the help of an optical parametric oscillator .
the behaviour of both materials can be described by spicer s 3-step model . whereas during the use the threshold for photo - emission in cs - te
was shifted to higher photon energies , that of rb - te did not change .
our latest investigations on the stoichiometric ratio of the components are shown .
the preparation of the photo - cathodes was monitored with 320 nm wavelength light , with the aim of improving the measurement sensitivity .
the latest results on the protection of cs - te cathode surfaces with csbr against pollution are summarized .
new investigations on high mean current production are presented . |
several diagnostic protocols are usually adopted by dermatologists for analyzing and classifying skin lesions , such as the so - called _ abcd - rule _ of dermoscopy @xcite . due to the subjective nature of examination ,
the accuracy of diagnosis is highly dependent upon human vision and dermatologist s expertise .
computerized dermoscopic image analysis systems , based on a consistent extraction and analysis of image features , do not have the limitation of this subjectivity .
these systems involve the use of a computer as a second independent and objective diagnostic method , which can potentially be used for the pre - screening of patients performed by non - experienced operators .
although computerized analysis techniques can not provide a definitive diagnosis , they can improve biopsy decision - making , which some observers feel is the most important use for dermoscopy @xcite .
recently , numerous researches on this topic propose systems for the automated detection of malignant melanoma in skin lesions ( e.g. , @xcite ) . in our previous study on dermoscopic images @xcite , the segmentation of the skin area and the lesion area was achieved by a semi - automatic process based on otsu algorithm @xcite , supervised by a human operator . here , we propose a full automatic segmentation method consisting of three main steps : selection of the image roi , selection of the segmentation band , and segmentation .
the paper is organized as follows . in section [ proposedapproach ]
we describe the proposed algorithm , providing details of its main steps . in section [ expres ]
we provide a thorough analysis of experimental results on the isic 217 dataset @xcite .
conclusions are drawn in section [ conclusioni ] .
the block diagram of the segmentation algorithm proposed for dermoscopic images , named sdi algorithm , is shown in fig . [
fig : overall ] .
the three main steps are described in the following . in order to achieve an easier and more accurate segmentation of the skin lesion ,
it is advisable to select the region of interest ( roi ) , i.e. , the subset if image pixels that belong to either the lesion or the skin .
this region excludes image pixels belonging to ( usually dark ) areas of the image border and/or corners , as well as those belonging to hair , that will not be taken into account in the subsequent steps of the sdi algorithm . in the proposed approach ,
the value band of the image in the hsv color space is chosen in order to select dark image pixels ; these are excluded from the roi if they cover most of the border or the angle regions of the image . concerning hair ,
many highly accurate methods have been proposed in the literature @xcite . here , we adopted a bottom - hat filter in the red band of the rgb image .
an example of the roi selection process is reported in fig .
[ fig : roiselection ] for the isic 2017 test image no . 15544 . here , we observe that the wide dark border on the left of the image , as well as the dark hair over the lesion , have properly been excluded from the roi mask .
[ cols="^,^ " , ]
we proposed the sdi algorithm for dermoscopic image segmentation , consisting of three main steps : selection of the image roi , selection of the segmentation band , and segmentation .
the reported analysis of experimental results achieved by the sdi algorithm on the isic 2017 dataset allowed us to highlight its pro s and con s .
this leads us to conclude that , although some accurate results can be achieved , there is room for improvements in different directions , that we will go through in future investigations .
this research was supported by lab gtp project , funded by miur .
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m. e. celebi , h. a. kingravi , b. uddin , h. iyatomi , y. a. aslandogan , w. v. stoecker , and r. h. moss , `` a methodological approach to the classification of dermoscopy images . ''
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31 , no . 6 , pp .
362373 , september 2007 .
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v. cozza , m. r. guarracino , l. maddalena , and a. baroni , `` dynamic clustering detection through multi - valued descriptors of dermoscopic images , '' _ statistics in medicine _ ,
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[ online ] .
available : http://dx.doi.org/10.1002/sim.4285 m. e. celebi , q. wen , h. iyatomi , k. shimizu , h. zhou , and g. schaefer , `` a state - of - the - art survey on lesion border detection in dermoscopy images , '' in _ dermoscopy image analysis _ , m. e. celebi , t. mendonca , and j. s. marques , eds.1em plus 0.5em minus 0.4emcrc press , 2015 , pp . | we propose an automatic algorithm , named sdi , for the segmentation of skin lesions in dermoscopic images , articulated into three main steps : selection of the image roi , selection of the segmentation band , and segmentation .
we present extensive experimental results achieved by the sdi algorithm on the lesion segmentation dataset made available for the isic 2017 challenge on skin lesion analysis towards melanoma detection , highlighting its advantages and disadvantages . |
we would like to thank d. jouan and zhang xiaofai for helpful discussions .
this work is partly supported by the national natural science founction of china .
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t. sjstrand , `` a manual to the lund monte carlo for jet fragmentation and @xmath71 physics : jetset version 7.3 '' , available upon request to the author . g. a. schuler , cern - th 7170/94 . * figure captions * + figure1 : @xmath0 cross sections divided by @xmath49 as a function of @xmath54 .
our results are compared with the experimental data from na51 , na38 and na50 @xcite .
+ figure2 : @xmath0 cross sections divided by drell - yan cross sections as a function of @xmath72 .
our results are compared with the experimental data from na38 and na50 @xcite .
+ + @xmath73 gev / c & @xmath45&@xmath74 + @xmath75&@xmath76&@xmath77 + @xmath78&@xmath79&@xmath80 + @xmath81&@xmath82&@xmath83 + @xmath84&@xmath85&@xmath86 + @xmath87&@xmath88&@xmath89 + @xmath90&@xmath91&@xmath92 + | when the cross section of @xmath0 production is considered varying with the energy of the nucleon - nucleon interaction the production of @xmath0 in pa and aa collisions has been studied using fritiof model .
the calculation shows that the cross section of @xmath0 production per nucleon - nucleon collision " decreases with increasing mass number and centrality as a consequence of continuous energy loss of the projectile nucleons to the target nucleons in their successive binary nucleon - nucleon collisions .
we have compared our model predictions with the experimental data of @xmath0 production .
pacs number : 25.75.-q 3ex report - no : bthep - th-96 - 42 + dec .
1996 + tai an@xmath1 , chao wei qin@xmath2 and yao xiao xia@xmath3 ttttt = tt = a ) ccast ( world lab . ) , p. o. box 8730 beijing , p.r .
china .
+ b ) institute of high energy physics , academia sinica , + p. o. box 918(4 - 1 ) , beijing , 100039 , p.r . china .
+ suppression of @xmath0 production in high energy heavy ion collisions was proposed as an effective signature of qgp formation ten years ago @xcite .
the ensuing experimental data confirmed a significant suppression of @xmath0 production in both pa and aa collisions @xcite .
however , alternative explanations of the @xmath0 suppression exist based on the absorption of @xmath0 in nuclear matter @xcite .
the overall set of extensive data collected and analysed by na38 seems to support the absorption mechanism in p+b@xmath4 , o+b@xmath4 and s+u collisions .
nevertheless a rather large absorption cross section ( @xmath5 6.2 mb ) has to be used in order to fit the experimental data , about three times larger than the total @xmath0-n cross section from the emc collaboration @xcite .
such a difference was already noted long time ago in @xcite .
recent calculations based on the colour octet model show that this phenomenological cross section could be understood by the absorption of pre - resonance states ( @xmath6 ) in nuclear matter @xcite .
other sources of @xmath0 suppression in nuclear collisions , such as the interaction of @xmath0 particles with the produced mesons ( called @xmath7 ) @xcite , gluon shadowing in nuclei , intrinsic charm component , energy degradation of produced @xmath8 pair , etc .
@xcite , have been introduced besides the absorption due to the @xmath0-n interaction to explain the data .
we in this paper propose a simple model to investigate @xmath0 suppression in pa and aa collisions focusing on the decrease of the cross section of @xmath0 production with increasing mass number and centrality due to the continuous energy loss of the projectile nucleons to the target nucleons in their successive binary nucleon - nucleon collisions , not on its later absorption in nuclear matter . from the calculations of this model ,
we conclude that the absorption of @xmath0 particles in nuclear matter is only part of the sources of @xmath0 suppression seen in pa and aa collisions so far .
since the probability for a nucleon - nucleon collision leading to @xmath0 production is very small it is generally accepted that multiple @xmath0 production processes in pa and aa collisions can be neglected .
the studies of @xmath0 suppression based on the absorption mechanism actually assume that the probability of @xmath0 production per nucleon - nucleon collision
" is the same independent of the masses of the colliding nuclei at a given energy .
however , each binary nucleon - nucleon collision experienced by a projectile nucleon on its way out of the target in pa and aa collisions may not be the same if the projectile nucleon loses a fraction of its energy in each binary collision to the target nucleon such that the cms energy of each binary collision of this incoming nucleon with a target nucleon is different .
for the cross sections of the hard qcd parton - parton scatterings , which is responsible for @xmath0 production , increase with increasing energy it is conceivable that the probability of @xmath0 production would also depend on the energy of a nucleon - nucleon collision in a similar way .
it is confirmed both theoretically and experimentally that @xmath0 photoproduction cross section exhibits a strong threshold behaviour at the low energy region and then increases with energy at the higher energy region @xcite . in a participant - spectator model of nucleus - nucleus collisions , like fritiof
, each projectile nucleon may collide several times with the target nucleons .
if momentum transfers are assumed to take place in each binary nucleon - nucleon collision , then the cms energy of these binary collisions will decrease with time , thereby the probability to produce @xmath0 in each binary collision going down .
we in this paper have calculated how the cross section of @xmath0 production varies with increasing mass number of colliding nuclei and centrality using fritiof model .
the calculations show that @xmath0 production is suppressed in pa and aa collisions in comparison with the nucleon - nucleon collision , and the larger the mass number of colliding nuclei and the centrality , the greater the suppression , as a result that probability of finding a qcd hard process in a binary nucleon - nucleon decreases with increasing mass number of colliding nuclei and centrality . taking into account the @xmath0 absorption by @xmath0-n interaction our results are in good agreement with experimental data with the exception of the latest data of pb@xmath9pb collisions at 158 agev / c , which show a further @xmath0 suppression @xcite .
the absorption cross section @xmath10 needed to explain the data from p+b@xmath4 , o+b@xmath4 and s+u collisions is about 1.4 mb in this paper , which is consistent with the experiments ( emc collaboration @xcite gives a total @xmath0-n cross section 2.2 @xmath11 0.7 mb and the @xmath0-n quasi - elastic cross section is given in @xcite as 0.79 @xmath11 0.012 mb ) .
furthermore , our results also imply that some new mechanism of @xmath0 suppression seems to be needed particularly for understanding pb@xmath9pb data .
the authors in @xcite @xcite have attributed the further @xmath0 suppression in pb+pb data to the formation of a qgp state . as we have mentioned before the cross section of @xmath0 production will be different in each binary nucleon - nucleon collision in pa and aa collisions if the energy loss of the projectile nucleons to the target nucleons in the successive binary collisions is taken into account .
assume that @xmath12 is the mean cross section for the production of a @xmath0 particle in a binary nucleon - nucleon collision ( here the average is done over all the binary collisions at an impact parameter @xmath13 ) , then the total probability for producing a @xmath0 particle in the collisions of a + b at an impact parameter @xmath13 is the sum @xcite @xmath14^n[1-t(b)<\sigma^{nn}_{j/\psi } > ] ^{ab - n } , \label{ff1}\ ] ] where t(b ) is the thickness function . because @xmath15 is a very small quantity ( @xmath16 @xmath17 @xcite , @xmath18@xmath19 for central s+u collisions , for instance ) , the summation given by eq.([ff1 ] ) is dominated by the first term with n=1 .
the terms with n@xmath201 represent multiple @xmath0 production processes and shadowing corrections , which are very small and can be neglected .
then the probability for @xmath0 production in a+b collisions can be approximated to be @xmath21 .
\label{ff2}\ ] ] therefore , the cross section of @xmath0 production corresponding to a centrality bin , @xmath22 , is given by the following formula @xmath23 where @xmath24 is the mean cross section of @xmath0 production `` per nucleon - nucleon collision '' within the centrality bin @xmath22 .
we know that qcd hard scatterings ( the gluon fusion and quark - antiquark annihilation ) between partons are the main source of @xmath0 production .
let @xmath25 be the probability to have a hard scattering in a nucleon - nucleon collision and @xmath26 the probability to produce a @xmath0 from the hard scattering , then we can write out @xmath12 to be @xmath27 where @xmath28 is the total cross section of a nucleon - nucleon collision .
we have assumed that @xmath29 is approximately a constant in the energy span that we are concerning , so the product is the same for all the binary collisions . combining eq.([ff4 ] ) with eq.([ff3 ] ) and replacing @xmath30 by the ratio @xmath31 ( @xmath32 is the number of binary collisions in an a+b collision and @xmath33 the number of binary collisions with a hard scattering .
both of them are the function of the impact parameter @xmath13 ) we finally obtain @xmath34 and for the minimum bias events we have @xmath35 we see from eq.([ff6 ] ) that the dependence of the quantity @xmath36 on the masses of colliding nuclei or centrality is solely determined by how the mean probability of having a hard scattering in a binary nucleon - nucleon collision varies with the masses of colliding nuclei or centrality . before calculating @xmath37 in pa and aa collisions we will give a brief introduction of fritiof dynamics focusing on how a hard parton - parton scattering is distinguished from a soft one .
fritiof is a string model based on the concepts of the lund string model @xcite , which started from the modeling of inelastic hadron - hadron collisions and it has been successful in describing many experimental data from the low energies at the isr - regime all the way to the top sps energies @xcite @xcite .
this has been achieved by the introduction of a particular longitudinal momentum transfer scenario , gluon bremsstrahlung radiation ( the dipole cascade model , dcm @xcite , and the soft radiation model , srm @xcite , this is implemented by the use of ariadne @xcite ) as well as hard parton scattering ( rutherford parton scattering , rps this is implemented by the pythia routines @xcite ) . in fritiof , during the collision two hadrons are excited due to longitudinal momentum transfers and/or a rps .
it is further assumed that there is no net color exchange between the hadrons .
the highly excited states will emit bremsstrahlung gluons according to the srm .
they are afterwards treated as excitations or the lund strings and the string states are allowed to decay into final state hadrons according to the lund prescription as implemented by jetset @xcite . in the fritiof model a hadron
is assumed to behave like a massless relativistic string ( mrs ) corresponding to a confined color force field of a vortex line character embedded in a type ii color superconducting vacuum .
a hadron - hadron collision is pictured as the multi - scatterings of the partons inside the two colliding hadrons .
this includes both the hard and the soft components depending on the four - momentum transfers @xmath38 , or equivalently the transverse momentum transfers involved .
the soft part is described by a simple phenomenological model .
the hard scatterings can however be calculated from perturbative qcd , and correspond to the rutherford parton - parton scattering ( rps ) . the divergence problem in rps
is handled by introducing the sudakov factor .
there will be color separation in the model , i.e. there will for each hadron be a color @xmath39 ( a `` diquark '' ) continuing forward along the beam direction and a valence quark , a color @xmath40 , moving in the opposite direction due to the longitudinal momentum transfer .
this will lead to bremsstrahlung of a dipole character .
a procedure therefore is adopted in fritiof that compares the `` hardness '' of the rutherford partons to that of the bremsstrahlung gluons .
the rps is accepted only if it is harder than the associated radiation . if the rps is `` drowned '' , which is to say that it is softer than the radiation , then the rps is not acceptable and the collision proceeds as a purely soft collision . with this prescription
the rps spectrum is suppressed smoothly at small to medium transverse momentum region . for the hadron - nucleus and nucleus - nucleus collisions , the process has in the fritiof model been treated as a set of incoherent collisions on the nucleons .
thus a nucleon from the projectile interacts independently with the encountered target nucleons as it passes through the nucleus . the probability distribution for the number of inelastic collisions @xmath41 is taken from geometric calculations .
each of the sub - collisions is treated in the same way as an ordinary hadron - hadron collision , although the momentum transfers will again be additive and every encounter will make the projectile more excited .
if it interacts with @xmath41 nucleons in the target , @xmath42 excited string states will be formed as a result .
these string states will then independently emit associated bremsstrahlung radiation and then fragment into hadrons in the same way as individual strings .
this picture is supported by the fact that the global features of heavy ion collisions are satisfactorily explained by the collision geometry together with the independent hadron - hadron collisions . using fritiof it is straightforward to calculate the number of binary nucleon- nucleon collisions , @xmath32 , and the number of the binary collisions with a hard scattering , @xmath43 , in pa and aa collisions at a given impact parameter @xmath13 , so that the mean probability to have a hard scattering in a binary nucleon - nucleon collision , @xmath30 = @xmath44 , can be obtained .
since we are mainly interested in @xmath0 production in pa and aa collisions relative to that in the pp collision we do not need to know how a @xmath0 is actually formed from the hard scatterings in order to investigate the dependence of @xmath0 production cross sections on mass number and centrality .
we have calculated the quantity @xmath45 for various pa and aa collisions ( and @xmath46 for different centrality bins in s+u and pb+pb collisions ) at @xmath47=200 gev / c using fritiof . after determining @xmath29 by the data of the pp collision we plot our results of @xmath48 as a function of @xmath49 in figure 1 for the minimum bias events . for the cross section of @xmath0 production in different centrality bins we plot the results of @xmath50 as a function of @xmath51 in figure 2 , where @xmath52 is the number of participants from the projectile and @xmath53 the number of participants from the target , since the drell - yan cross section in a given centrality bin is found in experiments proportional to an effective @xmath54 (= @xmath55 ) .
in the same way , a constant has to be determined by the corresponding data of the pp collision .
the impact parameter bins are taken to be the same as those extracted by na38 and na50 @xcite .
we decided not to use the absorption length @xmath56 to be the longitudinal axis as used by na50 because @xmath56 calculated from the geometry model is not sensitive to the change of impact parameter for very central pb+pb collisions .
the results of our calculations show that the decrease of quantity , @xmath57 or @xmath50 ( the cross section of @xmath0 production per nucleon - nucleon collision " ) , is due to the fact that the probability of the qcd hard scattering per binary nucleon - nucleon collision decreases with the increasing mass number and centrality .
when the absorption of @xmath0 by @xmath0-n interaction is also taken into account , i.e. the previous results are multipied by @xmath58 with @xmath59=0.14 n/@xmath60 , @xmath61=1.4 mb and @xmath56 taken to be the same as those in @xcite , our model reproduces the data of @xmath0 suppression with the exception of the latest data from pb+pb collisions at 158 gev / c , which clearly show a further suppression .
one possibility which will bring about a further suppression of @xmath0 production is that @xmath62 , the probability to produce a @xmath0 from a hard process , drops down suddenly under certain conditions .
this is equivalent to say that the @xmath8 produced from the hard processes can not form a bound state .
however at the moment our simple model can not estimate when this would happen . however , there are still other possible mechanisms of @xmath0 suppression , which are not included in our simple model .
the @xmath63 dependence of @xmath0 suppression is not investigated yet .
therefore , it is hard to make any conclusion now whether this further suppression in pb+pb collision is due to qgp formation .
it is known that there is no unique criterion to distinguish a hard process from a soft one in a nucleon - nucleon collision .
usually a @xmath64 is introduced to be the minimum transverse momentum of the produced partons from a hard process .
a dynamic criterion is applied in fritiof to chose a hard process by comparing the hardness of a rps parton with the hardness of the bremsstrahlung gluons as mentioned before . however
, the cross section of @xmath0 production should not depend on which criterion is actually used in the calculation .
we have thus calculated all the results of this paper using the conventional @xmath64 criterion in pythia ( @xmath64= 1gev / c ) , just to check if our conclusion relies on the specific criterion in fritiof .
the calculations show that the results in these two cases are in agreement with each other .
we have also checked if the quantity @xmath65 is energy - independent as we have assumed .
a parametrization form of the @xmath0 cross section is given as @xcite @xmath66 where @xmath67 stands for the cms energy per nucleon .
therefore , if @xmath65 in eq.([ff6 ] ) is energy - independent then we should have a ratio @xmath68 we have calculated @xmath45 and the ratio at various energies from @xmath47=60 gev / c to @xmath47= 450 gev / c for pp collisions ( @xmath69= 1 for a pp collision ) and the results are listed in tab.1 , which show that this ratio in this energy region is not sensitive to the change of energy in comparison with @xmath70 . but a threshold behaviour may exist at lower energies , which can be seen from the value at @xmath47=60 gev / c . |
hera deeply inelastic scattering ( dis ) results on structure functions demonstrate a rapid bremsstrahlung growth of the gluon density at small x. when interpreted in the same framework as the parton model , this growth is predicted to saturate because the gluon occupation number in hadron wave functions saturate at a value maximally of order @xmath1 ; dynamically , nonlinear effects such as gluon recombination and screening by other gluons deplete the growth of the gluon distribution@xcite .
gluon modes with @xmath2 are maximally occupied , where @xmath3 is a dynamically generated semi - hard scale called the saturation scale . for small @xmath4 , @xmath5 is large enough that high occupancy states can be described by weak coupling classical effective theory@xcite .
this color glass condensate description of high energy hadrons and nuclei is universal and has been tested in both dis and hadronic collisions .
in particular , saturation based phenomenological predictions successfully describe recent lhc p+p data @xcite and predict possible geometrical scaling of transverse momentum distribution@xcite similar to the geometrical scaling observed previously in dis . the object common to dis and hadronic collisions is the dipole cross section @xmath6 . in the cgc framework
, the dipole cross section can be expressed in terms of expectation values of correlators of wilson lines representing the color fields of the target .
the energy dependence of this quantity comes from renormalization group evolution but to get the realistic impact parameter dependence one has to rely on models involving parametrizations constrained by experimental data . in the large @xmath7 limit ,
the dipole cross section is related to the un - integrated gluon distribution inside hadron / nucleus as @xmath8^{2}. \label{eq : unint - gluon}\ ] ] for hadron - hadron collisions , the inclusive gluon distribution which is @xmath9-factorizable into the products of un - integrated gluon distributions in the target and projectile is expressed as @xmath10
two models of the dipole cross - section that have been extensively compared to hera data are the ip - sat @xcite and the b - cgc @xcite models . in the former the impact parameter dependence
is introduced through a normalized gaussian profile function @xmath11 and in the latter through a scale @xmath12 . for a detailed discussion of the parameters involved in these models and their values from fits to hera data , see ref .
@xcite .
the saturation scale in the fundamental representation for both the models can be calculated self consistently solving @xmath13=2(1-e^{-1/2})$ ] .
the corresponding adjoint saturation scale @xmath14 , relevant for hadronic collisions , is obtained by multiplying @xmath15 by 9/4 . in the range @xmath16-@xmath17 ,
the behaviour of @xmath14 ( see fig.[fig : satscale ] left ) at @xmath18 can be approximated by a function of the form @xmath19 with @xmath20 for the b - cgc model and @xmath21 for the ip - sat model .
[ fig : multdist ]
multiparticle production in high energy hadronic collisions can be treated self consistently in the cgc approach .
the glasma flux tube picture @xcite predicts @xcite that the n - particle correlation is generated by the negative binomial distribution @xmath22 .
it is characterized by two parameters , the mean multiplicity @xmath23 and @xmath24 . at a given impact parameter of the collision , the mean multiplicity @xmath25
is obtained by integrating eq .
[ eq : ktfact1 ] over @xmath26 . in the glasma picture , the parameter @xmath27 with @xmath28 @xcite .
the quantity @xmath29 shown in fig.[fig : satscale ] ( right ) is the number of flux tubes in the overlap area @xmath30 of two hadrons .
convolving @xmath31 with the probability distribution @xmath32 for an inelastic collision at @xmath33-fig .
[ fig : multdist ] ( left)-one obtains @xcite the n - particle inclusive multiplicity distribution as shown in fig .
[ fig : multdist ] ( right ) . various kinematic variables exhibit scaling with the saturation scale@xcite .
the mid - rapidity multiplicity density scales with functional forms like @xmath34 and @xmath35 whereas a linear functional form seem to provide very good fit to the energy dependence of @xmath36 as shown in fig.[fig : scaling][left ] .
these results are suggestive that @xmath37 is the only scale that controls the bulk particle multiplicity . in ref . @xcite it has been shown that @xmath26 spectra in @xmath38 collisions exhibit geometric scaling assuming a simple form of @xmath37 . in our case
we use a scaling variable @xmath39 , where @xmath37 is directly calculated in the ip - sat model . as shown in fig.[fig : scaling][right ] , an approximate scaling below @xmath40 is observed for transverse momentum distribution in @xmath38 collision energy @xmath41 gev .
going to lower energies we observe systematic deviations from the universal curve .
+ in summary , our description of multiplicity distribution successfully describes bulk lhc p+p data .
in particular , we observe that the dominant contribution to multiplicity fluctuations is due to the intrinsic fluctuations of gluon produced from multiple glasma flux tubes rather than from the fluctuations in the sizes and distributions of hotspots .
the @xmath26-spectra in p+p at high energies exhibits universal scaling as a function of @xmath39 .
the observed scaling indicates that particle production in this regime is dominantly from saturated gluonic matter characterized by one universal scale @xmath37 .
ridge like two particle correlation structures in @xmath42 in high multiplicity p+p collisions may provide more detailed insight into its properties @xcite .
v. khachatryan _ et al . _
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k. aamodt _ et al . _
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a. dumitru , k. dusling , f. gelis , j. jalilian - marian , t. lappi , r. venugopalan , arxiv:1009.5295 [ hep - ph ] . | dipole models based on various saturation scenarios provide reasonable fits to small - x dis inclusive , diffractive and exclusive data from hera .
proton un - integrated gluon distributions extracted from such fits are employed in a @xmath0-factorization framework to calculate inclusive gluon distributions at various energies .
the n - particle multiplicity distribution predicted in the glasma flux tube approach shows good agreement with data over a wide range of energies .
hadron inclusive transverse momentum distributions expressed in terms of the saturation scale demonstrate universal behavior over a wider kinematic range systematically with increasing center of mass energies .
saturation ; lhc p + p collision ; cgc ; deep inelastic scattering |
b. s. , v. s. , a. b. , and a. b. acknowledge support by the ministry of education , science , and technological development of the republic of serbia under projects on171017 , iii43007 , on171009 , on174027 and ibec , and by daad - german academic and exchange service under project ibec .
m. acknowledges support by the science and engineering research board , department of science and technology , government of india under project no .
s. k. a. acknowledges support by the cnpq of brazil under project 303280/2014 - 0 , and by the fapesp of brazil under project 2012/00451 - 0 .
numerical simulations were run on the paradox supercomputing facility at the scientific computing laboratory of the institute of physics belgrade , supported in part by the ministry of education , science , and technological development of the republic of serbia under project on171017 .
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d * 91 * ( 2015 ) 044041 . | we present hybrid openmp / mpi ( open multi - processing / message passing interface ) parallelized versions of earlier published c programs ( d. vudragovi et al . ( 2012 ) @xcite ) for calculating both stationary and non - stationary solutions of the time - dependent gross - pitaevskii ( gp ) equation in three spatial dimensions .
the gp equation describes the properties of dilute bose - einstein condensates at ultra - cold temperatures .
hybrid versions of programs use the same algorithms as the c ones , involving real- and imaginary - time propagation based on a split - step crank - nicolson method , but consider only a fully - anisotropic three - dimensional gp equation , where algorithmic complexity for large grid sizes necessitates parallelization in order to reduce execution time and/or memory requirements per node . since
distributed memory approach is required to address the latter , we combine mpi programing paradigm with existing openmp codes , thus creating fully flexible parallelism within a combined distributed / shared memory model , suitable for different modern computer architectures .
the two presented c / openmp / mpi programs for real- and imaginary - time propagation are optimized and accompanied by a customizable makefile .
we present typical scalability results for the provided openmp / mpi codes and demonstrate almost linear speedup until inter - process communication time starts to dominate over calculation time per iteration .
such a scalability study is necessary for large grid sizes in order to determine optimal number of mpi nodes and openmp threads per node .
bose - einstein condensate ; gross - pitaevskii equation ; split - step crank - nicolson scheme ; real- and imaginary - time propagation ; c program ; mpi ; openmp ; partial differential equation 02.60.lj ; 02.60.jh ; 02.60.cb ; 03.75.-b * new version program summary * + _ program title : _ gp - scl - hyb package , consisting of : ( i ) imagtime3d - hyb , ( ii ) realtime3d - hyb .
+ _ catalogue identifier : _
aedu_v3_0 + _ program summary url : _
http://cpc.cs.qub.ac.uk/summaries/aedu_v3_0.html + _ program obtainable from : _ cpc program library , queen s university of belfast , n. ireland .
+ _ licensing provisions : _ apache license 2.0 + _ no . of lines in distributed program , including test data , etc . : _ 26397 .
+ _ no . of bytes in distributed program , including test data , etc . : _ 161195 .
+ _ distribution format : _
tar.gz .
+ _ programming language : _ c / openmp / mpi .
+ _ computer : _ any modern computer with c language , openmp- and mpi - capable compiler installed .
+ _ operating system : _ linux , unix , mac os x , windows .
+ _ ram : _ total memory required to run programs with the supplied input files , distributed over the used mpi nodes : ( i ) 310 mb , ( ii ) 400 mb .
larger grid sizes require more memory , which scales with nx*ny*nz .
+ _ number of processors used : _ no limit , from one to all available cpu cores can used on all mpi nodes .
+ _ number of nodes used : _ no limit on the number of mpi nodes that can be used .
depending on the grid size of the physical problem and communication overheads , optimal number of mpi nodes and threads per node can be determined by a scalability study for a given hardware platform .
+ _ classification : _ 2.9 , 4.3 , 4.12 . + _ catalogue identifier of previous version : _ aedu_v2_0 .
+ _ journal reference of previous version : _ comput .
phys .
commun . 183 ( 2012 ) 2021 .
+ _ does the new version supersede the previous version ? : _ no .
+ _ nature of problem : _ these programs are designed to solve the time - dependent gross - pitaevskii ( gp ) nonlinear partial differential equation in three spatial dimensions in a fully anisotropic trap using a hybrid openmp / mpi parallelization approach . the gp equation describes the properties of a dilute trapped bose - einstein condensate .
+ _ solution method : _ the time - dependent gp equation is solved by the split - step crank - nicolson method using discretization in space and time
. the discretized equation is then solved by propagation , in either imaginary or real time , over small time steps .
the method yields solutions of stationary and/or non - stationary problems .
+ _ reasons for the new version : _ previous c @xcite and fortran @xcite programs are widely used within the ultracold atoms and nonlinear optics communities , as well as in various other fields @xcite .
this new version represents extension of the two previously openmp - parallelized programs ( imagtime3d - th and realtime3d - th ) for propagation in imaginary and real time in three spatial dimensions to a hybrid , fully distributed openmp / mpi programs ( imagtime3d - hyb and realtime3d - hyb ) .
hybrid extensions of previous openmp codes enable interested researchers to numerically study bose - einstein condensates in much greater detail ( i.e. , with much finer resolution ) than with openmp codes . in openmp ( threaded ) versions of programs , numbers of discretization points in x , y , and z
directions are bound by the total amount of available memory on a single computing node where the code is being executed .
new , hybrid versions of programs are not limited in this way , as large numbers of grid points in each spatial direction can be evenly distributed among the nodes of a cluster , effectively distributing required memory over many mpi nodes .
this is the first reason for development of hybrid versions of 3d codes .
the second reason for new versions is speedup in the execution of numerical simulations that can be gained by using multiple computing nodes with openmp / mpi codes .
+ _ summary of revisions : _ two c / openmp programs in three spatial dimensions from previous version @xcite of the codes ( imagtime3d - th and realtime3d - th ) are transofrmed and rewritten into a hybrid openmp / mpi programs and named imagtime3d - hyb and realtime3d - hyb .
the overall structure of two programs is identical .
the directory structure of the gp - scl - hyb package is extended compared to the previous version and now contains a folder scripts , where examples of scripts that can be used to run the programs on a typical mpi cluster are given .
the corresponding readme.txt file contains more details .
we have also included a makefile with tested and verified settings for most popular mpi compliers , including openmpi ( open message passing interface ) @xcite and mpich ( message passing interface chameleon ) @xcite .
transformation from pure openmp to a hybrid openmp / mpi approach has required that the array containing condensate wavefunction is distributed among mpi nodes of a computer cluster .
several data distribution models have been considered for this purpose , including block distribution and block cyclic distribution of data in a 2d matrix .
finally , we decided to distribute the wavefunction values across different nodes so that each node contains only one slice of the x - dimension data , while containing the complete corresponding y- and z - dimension data , as illustrated in fig .
[ fig1 ] .
this allows central functions of our numerical algorithm , calcluy , calcuz , and calcnu to be executed purely in parallel on different mpi nodes of a cluster , without any overhead or communication , as nodes contain all the information for y- and z - dimension data in the given x - sub - domain .
however , the problem arises when functions calclux , calcrms , and calcmuen need to be executed , as they also operate on the whole x - dimension data .
thus , the need for additional communication arises during the execution of the function calcrms , while in the case of fuctions calclux and calcmuen also the transposition of data between x- and y - dimensions is necessary , while data in z dimension have to stay contiguous .
transposition provides nodes with all the necessary x - dimension data to execute functions calclux and calcmuen .
however , this needs to be done in each iteration of numerical algorithm , thus necessarily increasing communication overhead of the simulation .
transposition algorithms that were considered where the ones that account for greatest common divisor ( gcd ) between number of nodes in columns ( designated by n ) and rows ( designated by m ) of a cluster configured as 2d mash of nodes @xcite .
two of such algorithms have been tested and tried for implementation : the case when gcd = 1 and the case when gcd > 1 .
the trivial situation n = m = 1 is already covered by the previous , purely openmp programs , and therefore , without any loss of generality , we have considered only configurations with number of nodes in x - dimension satisfying n > 1 . only the former algorithm ( gcd = 1 ) was found to be sound in case where data matrix is not a 2d , but a 3d structure .
latter case was found to be too demanding implementation - wise , since mpi functions and data - types are bound to certain limitations .
therefore , the algorithm with m = 1 nodes in y - dimension was implemented , as depicted by the wavefunction data structure in fig .
[ fig1 ] .
implementation of the algorithm relies on a sliced distribution of data among the nodes , as explained in fig .
[ fig2 ] .
this successfully solves the problem of large ram consumption of 3d codes , which arises even for moderate grid sizes .
however , it does not solve the question of data transposition between the nodes . in order to implement the most effective ( gcd = 1 ) transposition algorithm according to ref .
@xcite , we had to carry out block distribution of data within one data slice contained on a single node .
this block distribution of data was done implicitly , i.e. , data on one node have been put in a single 1d array ( psi ) of contiguous memory , in which z - dimension has stride 1 , y - dimension has stride nz , and x - dimension has stride ny*nz .
this is different from previous implementation of the programs , where the wavefunction was represented by an explicit 3d array .
this change was also introduced in order to more easily form user mpi datatypes , which allow for implicit block distribution of data , and represent 3d blocks of data within 1d data array .
these blocks are then swapped between nodes , effectively performing the transposition in x - y and y - x directions . together with transposition of blocks between the nodes
, the block data also have to be redistributed . to illustrate how this works ,
let us consider example shown in fig .
[ fig1](a ) , where one data block has size ( nx / gisze)*(ny / gsize)*nz .
it represents one 3d data block , swapped between two nodes of a cluster ( through one non - blocking mpi_isend and one mpi_ireceive operation ) , containing ( nx / gsize)*(ny / gsize ) 1d rods of contiguous nz data .
these rods themselves need to be transposed within the transposed block as well .
this means that two levels of transpositions need to be performed . at a single block level
, rods have to be transposed ( as indicated in upper left corner of fig .
[ fig1](a ) for sending index type and in fig .
[ fig1](b ) for receiving index type ) .
second level is transposition of blocks between different nodes , which is depicted by blue arrows connecting different blocks in fig .
[ fig1 ] .
the above described transposition is applied whenever needed in the functions calclux and calcmuen , which require calculations to be done on the whole range of data in x - dimension . when performing renormalization of the wavefunction or calculation of its norm , root - mean - square radius , chemical potential , and energy , collective operations mpi_gather and mpi_bcast are also used .
figures [ fig3 ] and [ fig4 ] show the scalability results obtained for hybrid versions of programs for small and large grid sizes as a function of number of mpi nodes used .
the baseline for calculation of speedups in the execution time for small grid sizes are previous , purely openmp programs , while for large grid sizes , which can not fit onto a single node , the baseline are hybrid programs with minimal configuration runs on 8 nodes .
the figures also show efficacies , defined as percentages of measured speedups compared to the ideal ones .
we see that an excellent scalability ( larger than 80% compared to the ideal one ) can be obtained for up to 32 nodes .
the tests have been performed on a cluster with nodes containing 2 x 8-core sandy bridge xeon 2.6 ghz processors with 32 gb of ram and infiniband qdr ( quad data rate , 40 gbps ) interconnect .
we stress that the scalability depends greatly on the ratio between the calculation and communication time per iteration , and has to be studied for a particular type of processors and interconnect technology .
+ _ additional comments : _ this package consists of 2 programs , see program title above . both are hybrid , threaded and distributed ( openmp / mpi parallelized ) . for the particular purpose of each program , see descriptions below . + _ running time : _ all running times given in descriptions below refer to programs compiled with openmpi / gcc compiler and executed on 8 to 32 nodes with 2 x 8-core sandy bridge xeon 2.6 ghz processors with 32 gb of ram and infiniband qdr interconnect . with the supplied input files for small grid sizes , running wallclock times of several minutes
are required on 8 to 10 mpi nodes .
+ _ special features : _ ( 1 ) since the condensate wavefunction data are distributed among the mpi nodes , when writing wavefunction output files each mpi process saves its data into a separate file , to avoid i / o issues . concatenating
the corresponding files from all mpi processes will created the complete wavefunction file .
( 2 ) due to a known bug in openmpi up to version 1.8.4 , allocation of memory for indexed datatype on a single node for large grids ( such as 800x640x480 ) may fail .
the fix for this bug is already in 3c489ea branch and is fixed in openmpi as of version 1.8.5 .
+ program summary ( i ) + _ program title : _
imagtime3d - hyb .
+ _ title of electronic files : _ imagtime3d - hyb.c , imagtime3d - hyb.h .
+ _ computer : _ any modern computer with c language , openmp- and mpi - capable compiler installed . + _ ram memory requirements : _ 300 mbytes of ram for a small grid size 240x200x160 , and scales with nx*ny*nz .
this is total amount of memory needed , and is distributed over mpi nodes used for execution .
+ _ programming language used : _ c / openmp / mpi .
+ _ typical running time : _ few minutes with the supplied input files for a small grid size 240x200x160 on 8 nodes .
up to one hour for a large grid size 1920x1600x1280 on 32 nodes ( 1000 iterations ) .
+ _ nature of physical problem : _ this program is designed to solve the time - dependent gp nonlinear partial differential equation in three space dimensions with an anisotropic trap .
the gp equation describes the properties of a dilute trapped bose - einstein condensate .
+ _ method of solution : _ the time - dependent gp equation is solved by the split - step crank - nicolson method by discretizing in space and time . the discretized equation is then solved by propagation in imaginary time over small time steps .
the method yields solutions of stationary problems .
+ + program summary ( ii ) + _ program title : _
realtime3d - hyb .
+ _ title of electronic files : _ realtime3d - hyb.c , realtime3d - hyb.h .
+ _ computer : _ any modern computer with c language , openmp- and mpi - capable compiler installed . + _ ram memory requirements : _ 410 mbytes of ram for a small grid size 200x160x120 , and scales with nx*ny*nz .
this is total amount of memory needed , and is distributed over mpi nodes used for execution .
+ _ programming language used : _ c / openmp / mpi .
+ _ typical running time : _ 10 - 15 minutes with the supplied input files for a small grid size 200x160x120 on 10 nodes .
up to one hour for a large grid size 1600x1280x960 on 32 nodes ( 1000 iterations ) .
+ _ nature of physical problem : _ this program is designed to solve the time - dependent gp nonlinear partial differential equation in three space dimensions with an anisotropic trap .
the gp equation describes the properties of a dilute trapped bose - einstein condensate .
+ _ method of solution : _ the time - dependent gp equation is solved by the split - step crank - nicolson method by discretizing in space and time . the discretized equation is then solved by propagation in real time over small time steps .
the method yields solutions of stationary and non - stationary problems . |