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the crab nebula has been the best laboratory for investigating the mechanism linking the pulsar wind nebula ( pwn ) with the pulsar .
the energetics confirms that the pwn is powered by the spin - down energy of the pulsar , and it is generally believed that this energy is transported by a relativistic wind ( e.g. kennel & coroniti 1984 ) .
hester ( 1998 ) and tanvir , thomson , & tsikarishvili ( 1997 ) showed that the `` wisps '' , which are elliptical ripples around the pulsar ( scargle 1969 ) , are moving outwards with a speed of about 0.5_c_. such high energy phenomena must be associated with x - ray emission .
here , we present the results of a series of monitoring x - ray observations of the crab nebula with _
chandra _ , whose spatial resolution of @xmath0 is comparable to that of ground - based optical telescopes .
we adopt a distance of 2 kpc to the crab nebula throughout this paper .
the crab nebula was observed with acis - s3 ( the back - illuminated ccd chip ) eight times , once every three weeks from 2000 november 3 to 2001 april 6 .
these observations were coordinated with the _ hubble space telescope _ ( hst ) ( hester et al . 2002 ) .
each observation has approximately 2.6 ksec of effective exposure time .
we employed a 0.2 sec frame time to reduce pileup and a restricted window to reduce dead - time .
the window size is only slightly larger than the x - ray extent of the crab nebula ( see fig [ fig:2ndimage ] ) .
all of the images shown were made using the 0.210 kev band .
figure [ fig:2ndimage ] shows one of eight images of the crab nebula .
it clearly shows an axisymmetric structure about the polar jet with the torus and the inner ring resolved in an early _ chandra _ observation ( weisskopf et al .
fine fibrous structures are also resolved at periphery of such large - scale structures .
they show clear correlation with a optical polarization measurement ( hickson & van den bergh 1990 ) , indicating that they trace local magnetic field structures .
figure [ fig:2468image ] shows a series of the observations .
two wisps moving outward are detected through all of eight observations .
they can also be seen in simultaneous hst observations ( hester et al .
2002 ) . here ,
we denote them as `` wisp a '' and `` wisp b '' .
they appear to break off from the inner ring .
with respect to the inner ring s elliptical shape , the shapes of the wisps look warped due to the time delay of light travel ( hester et al . 2002 ) .
we measured the speed of the wisps , assuming that they are moving in the equatorial plane which includes the inner ring , and taking the inclination of the plane ( the inclination angle was derived assuming the inner ring is circular ) and the time delays into account . in spite of the difference in the directions and the birth times , the speeds of the two wisps are almost same ,
@xmath10.43_c_. their similarity indicates the existence of the continuous isotropic pulsar wind in the equatorial plane .
the inner ring is also variable , but unlike the wisps , it preserves its overall ring - like shape and relative position with respect to the pulsar .
the ring never forms a continuous loop , but appears intermittent and mostly consists of knot - like features . among them , three knots , which lie along the southeast portion of the ring and are symmetric about the axis of the jet , gradually brighten by factor @xmath11.5 within our observational period of 6 months .
however , we note that these knots were bright enough to be detected 1 year before our 1st observation ( weisskopf et al .
additionally , some blob - like features appear to move outward along the jet , with a speed of @xmath10.34_c_. temporal variations can also be seen in the torus .
figure [ fig : diff ] shows the difference images of the 2nd@xmath23rd and the 2nd@xmath28th observations .
although the variation is not strongly pronounced in the 3-week difference image , except for the wisps , differences within the torus and along its boundary are quite substantial over a duration of 19 weeks .
the torus seems to be expanding at 0.10.2_c_. due to the small displacement and the ambiguous boundary , relatively large uncertainties remain .
the fact that the angular extent along the major axis measured with _
chandra _ agrees well with those measured with _
( brinkmann et al . 1985 )
, _ rosat _ ( hester et al . 1995 ; greiveldinger & aschenbach 1999 ) , and even from lunar occultation 25 years ago ( aschenbach & brinkmann 1975 ) suggests that the torus is stable on tens of arcsecond scales over decades , but varies on arcsecond scales on several months .
the northwestern region and the end of the jet do not exhibit any strong variations .
these x - ray observational pictures generally match the canonical scenario that the pwn is confined by the supernova ejecta .
the relativistic winds from the pulsar are continuously transported in the equatorial plane and accumulate at the torus , outside of which the optical filaments ejecta can be seen .
aschenbach , b. , & brinkmann , w. 1975 , , 41 , 147 brinkmann , w. , aschenbach , b. , & langmeier , a. 1985 , nature , 313 , 662 greiveldinger , c. , & aschenbach , b. 1999 , , 510 , 305 hickson , p. & van den bergh , s. 1990 , , 365 , 224 hester , j. j. et al .
1995 , , 448 , 240 hester , j. j. 1998 , in neutron stars and pulsars : thirty years after the discovery , ed .
n. shibazaki et al . , 431 hester , j. j. , et al .
2002 , in neutron stars in supernova remnants , ed .
slane & b.m .
gaensler , in press .
kennel , c. f. , & coroniti , f. v. 1984 , , 283 , 694 pavlov , g. g. , kargaltsev , o. y. , sanwal , d. , & garmire , g. p. 2001 , 554 , 189 scargle , j. d. 1696 , , 156 , 401 tanvir , n. r. , thomson , r. c. , & tsikarishvili , e. g. 1997 , new astronomy , 1 , 311 weisskopf , m. , et al .
2000 , , 536 , 81 | we present a series of monitoring observations of the crab nebula with the _ chandra x - ray observatory _ , focusing on the temporal evolution of the structure .
this series of 8 observations , spanning a period of approximately six months , shows the dynamic nature of the inner x - ray structures .
we detected outward moving `` wisps '' from the recently discovered inner ring seen in optical observations .
we also find that the inner ring itself shows temporal variations in structure .
the torus also appears to be expanding .
such temporal variations generally match the canonical scenario that an expanding synchrotron nebula injected from the pulsar is confined by the supernova ejecta .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
we test below the stability of our results to change of model parameter values : results of the calculations by using the same method as in the main text but the other choice of parameters ( @xmath90 and @xmath91 ev ) , which are close to those of ref . .
the results for the temperature dependence of the inverse local magnetic susceptibility are shown in fig .
[ fig : chi_loc2 ] .
we find the crossover discussed in the main text at lower @xmath128 k. the calculation of momentum dependent irreducible susceptibility yields only the uniform ( with respect to @xmath129 ) renormalization without change of qualitative tendencies ( see fig .
[ fig : chi_irr_q2 ] , cf . fig .
[ fig : chi : lda_vs_dmft ] of the main text ) .
we have recalculated exchange interactions from these results and obtain @xmath130 ev vs 0.18 ev in the main text .
this implies lowering of curie temperature , which agrees with approximately renormalization of @xmath30 by 1.5 times ( cf .
[ fig : inverse_chi ] of the main text ) .
the qualitative conclusions of the paper remain unchanged for these parameter values . to obtain exchange interaction , we first determine the bare propagator of magnetic degrees of freedom @xmath132 by requiring that the dressed propagator of @xmath95 field is equal to the susceptibility of itinerant subsystem .
using the random - phase - type approximation , which reduces the orbital- and frequency dependence of the bubble and vertex to the respective single - frequency orbital `` averaged '' quantities , @xmath133 and @xmath86 , we obtain @xmath134where the last term is added to cancel the corresponding bosonic self - energy correction from itinerant degrees of freedom to avoid double - counting , cf .
we represent @xmath135 with momentum - independent @xmath136 ; without loss of generality , we can assume @xmath137 such that @xmath138 from the results of fig . 4 of the main text it follows that @xmath139 . expanding eq .
( [ chis ] ) to first order in @xmath140 , we obtain @xmath141\delta \chi _ { \mathbf{q}}^{\mathrm{0}},\end{aligned}\]]where @xmath142 is the inverse local susceptibility . in practice
, the frequency dependence @xmath143 can be obtained from the dynamic local spin correlation functions , which is characterized by the temperature - independent moment @xmath144 its damping @xmath145 , and the corresponding weiss temperature @xmath146 ( see refs . of the main text ) . since @xmath147ev and
@xmath148ev the momentum dependence is almost cancelled , and we obtain the local bare propagator of spin degrees of freedom,@xmath149considering the renormalization of the propagator @xmath101 by the corresponding boson self
energy corrections ( cf . ref .
@xcite ) , we obtain for the non - uniform susceptibility @xmath150 , \]]which yields eq .
( [ chiq ] ) of the main text ( we use also here that by symmetry @xmath151 ) . | applying the local density approximation ( lda ) and dynamical mean field theory ( dmft ) to paramagnetic @xmath0iron , we revisit a problem of theoretical description of its magnetic properties .
the analysis of local magnetic susceptibility shows that at sufficiently low temperatures @xmath1 k , both , @xmath2 and @xmath3 states equally contribute to the formation of the effective magnetic moment with spin @xmath4 .
the self - energy of @xmath3 states shows sizable deviations from fermi - liquid form , which accompanies earlier found non - quasiparticle form of @xmath2 states . by considering the non - uniform magnetic susceptibility
we find that the non - quasiparticle form of @xmath2 states is crucial for obtaining ferromagnetic instability in @xmath0-iron .
the main contribution to the exchange interaction , renormalized by the effects of electron interaction , comes from the hybridization between @xmath3 and @xmath2 states .
we furthermore suggest the effective spin - fermion model for @xmath0-iron , which allows us to estimate the exchange interaction from paramagnetic phase , which is in agreement with previous calculations in the ordered state within the lda approaches .
elemental iron in its low - temperature body - centered cubic ( bcc ) phase , which is stable below approximately 1200 k , provides unique example of itinerant magnetic @xmath5-electron systems , where formation of well - defined local magnetic moments can be expected .
indeed , the rhodes - wolfarth ratio @xmath6 for this substance is very close to one , which is characteristic feature of systems , containing ( almost ) localized @xmath5electrons ( @xmath7 corresponds to the magnetic moment , extracted from the curie
weiss law for magnetic susceptibility in the paramagnetic phase @xmath8 , and @xmath9 is the saturation moment , @xmath10 is a lande factor , @xmath11 denotes temperature ) . at the same time , the moment @xmath12 has a small fractional part , which is natural for the itinerant material .
this poses natural questions : which electrons mainly contribute to the local - moment spin degrees of freedom of @xmath0-iron ?
what is the appropriate physical model , that describes spin degrees of this substance ? attempting to answer the former question , goodenough suggestedgoodenough , that the @xmath2 electrons are localized , while @xmath3 electrons are itinerant .
this suggestion was later on refined in ref .
, pointing to a possibility , that only some fraction of @xmath2 electrons , contributing to formation of the peak of the density of states near the fermi level , named by the authors as giant van hove singularity , is localized .
( the intimate relation between peaks of density of states and electron localization was also previously pointed out in ref . ) . on contrary , there were statements made that @xmath13 of electrons are localized in iron@xcite .
on the model side , the thermodynamic properties of @xmath0-iron were described within the effective spin @xmath4 heisenberg model @xcite , assuming therefore that the main part of magnetic moment is localized , in agreement with the above - mentioned rhodes - wolfarth arguments .
use of the effective heisenberg model was justified from the ab
initio analysis of spin spiral energies yielding reasonable values of the exchange integrals @xcite .
these considerations however did not take into account strong electronic correlations in @xmath0iron , which important role was emphasized first in ref . .
previous calculations katanin2010,abrikosov2013 within the local density approximation ( lda ) , combined with the dynamical mean - field theory ( dmft ) revealed the presence of non - quasiparticle states formed by @xmath2 electrons , which were considered as a main source of local moment formation in iron , while @xmath3 states were assumed to be itinerant@xcite . at the same time
, magnetic properties of the same @xmath3 states also show some features of local - moment behavior . in particular
, the temperature dependence of inverse local spin susceptibility , which was calculated previously@xcite only at @xmath14 k because of the limitations of hirsch - fye method , is approximately linear , including the contribution of @xmath3 states ; the real part of @xmath3 contribution to dynamic local magnetic susceptibility has a peak at low frequencies , reflecting a possibility of partial local moment formation by @xmath3 states . studying this possibility requires investigation of electronic and magnetic properties at low temperatures , since the energy scale for partially formed local @xmath3 moments can be smaller than for @xmath2 states . although real substance orders ferromagnetically at low temperatures , in the present paper ( as in ref . )
we perform analysis of local properties of iron in the paramagnetic phase to reveal the mechanism of local moment formation . furthermore , we study non - local magnetic susceptibility in the low temperature range @xmath15 @xmath16 which allows us to analyze the mechanism of magnetic exchange . to this end
we use the state of art dynamical mean field theory ( dmft ) calculation with continous time quantum monte - carlo ( ct qmc ) solver@xcite , combined with the ab - initio local density approximation ( lda ) . from our low - temperature analysis
we argue , that @xmath3 electrons are almost equally contribute to the effective local magnetic moment , as the @xmath2 electrons , and play crucial role in the mechanism of magnetic exchange in iron .
in particular , the most important contribution to the exchange integrals comes from the hybridization of @xmath3 and @xmath2 states , which yields _ nearest - neighbour _ magnetic exchange interaction , which agrees well with the experimental data .
we perform the ab initio band structure calculations in lda approximation within tight binding linear muffin tin orbital atomic spheres approximation framework ; the von barth - hedin local exchange - correlation potential @xcite was used .
primitive reciprocal translation vectors were discretized into 12 points along each direction which leads to 72 * k*points in irreducible part of the brillouin zone . for dmft ( ct - qmc ) calculations ,
we use the hamiltonian of hubbard type with the kinetic term containing all @xmath17@xmath18@xmath5 states , being extracted from the lda solution , and the interaction part with density - density contributions for @xmath5 electrons only .
the coulomb interaction parameter value @xmath19 ev and the hund s parameter @xmath20 ev used in our work are the same as in earlier lda+dmft calculations lichtenstein_2001,katanin2010,igoshev2013 . to treat a problem of formation of local moments we consider paramagnetic phase , which is achieved by assuming spin - independent density of states , local self - energy and bath green function . for the purpose of extracting corresponding exchange parameters , we take in lda part physical value of the lattice parameter @xmath21 , corresponding to ferromagnetic state at room temperature .
we consider first the results for the orbital resolved temperature dependent local static spin susceptibility @xmath22 , where @xmath23 is the @xmath24projection of the spin of @xmath5electrons , belonging to the orbitals @xmath25 at a given lattice site @xmath26 , see fig .
[ fig : inverse_chi ] ( for completeness , we also show the total susceptibility @xmath27 which also includes the off - diagonal @xmath3-@xmath2 contribution ) . the temperature dependence of the static inverse local susceptibility is linear ( as was also observed in previous studies lichtenstein_2001,katanin2010,abrikosov2013,igoshev2013 ) , however being resolved with respect to orbital contributions ( see fig .
fig : inverse_chi ) it appears to manifest very different nature of @xmath2 and @xmath3 moments .
the inverse @xmath2 orbital contribution behaves approximately linearly with @xmath11 in a broad temperature rangekatanin2010,abrikosov2013 . at the same time , analyzing low - temperature behaviour , we find that @xmath28 demonstrates a crossover at @xmath29 k between two linear dependences with the low temperature part having higher slope ( i. e. smaller effective moment ) .
note that this feature was not obtained in previous study @xcite because of considering only temperature range @xmath14 k. the scale @xmath30 corresponds to the crossover to non - fermi - liquid behavior of @xmath3 states , see below . and @xmath3 orbital contributions .
dashed lines show linear behavior in different temperature intervals .
, scaledwidth=47.0% ] and @xmath31 in @xmath32iron , extracted from the temperature dependence of local susceptibility , together with the contribution of the @xmath2 and @xmath3 orbitals , scaledwidth=47.0% ] to get further insight into the local magnetic properties of @xmath0-iron , we consider the temperature dependence of the effective magnetic moment @xmath33 and the instantaneous average @xmath34 corresponding to different orbital states , see fig .
[ fig : moms_vs_t ] .
we find , that for @xmath2 electrons both moments saturate at temperatures @xmath1 k and remain approximately constant up to sufficiently low temperatures . comparing the value of the square of the moment @xmath35 , extracted from the curie - weiss law for local susceptibility , and the instantaneous average @xmath36 with the corresponding filling @xmath37 , we find that the major part of @xmath2 electrons determine the instantaneous average @xmath38 , and at least half of them contribute to the sufficiently long - living ( on the scale of @xmath39 ) local moments . at the same time , for @xmath3 electronic states the abovementioned crossover between the high - temperature value @xmath40 and the low temperature value @xmath41 is present , which , comparing to @xmath42 shows that at least @xmath43 of @xmath3 electrons participate in the effective local moment formation at low temperatures . yet , the corresponding low - temperature effective moments @xmath44 and @xmath45 are comparable ( each of them is approximately @xmath46 corresponding to the effective spin @xmath47 ) , showing important role of @xmath3 electrons in the formation of the total spin @xmath4 state . .
black solid lines illustrate the results of calculations at temperatures ( from top to bottom ) @xmath48 ev .
the green dot dashed line present fits to the the fermi - liquid dependence in the range @xmath49 ev , while blue dashed lines present fits to the non - fermi - liquid dependence ( see text ) .
dots denote matsubara frequencies @xmath50.,scaledwidth=44.0% ] although the self - energy calculations @xcite yield quasiparticle - like form of @xmath3 electron self - energy , the low - frequency and low - temperature dependence of self - energy shows pronounced deviations from the fermi - liquid behavior , see fig . [ fig : sigma ] . to analyse the frequency dependence of the self - energy on imaginary frequency axis , we fit the obtained results by the fermi - liquid dependence @xmath51\nu + \sigma ( t)\nu ^{2},$ ] where @xmath52 is the damping of electrons at the fermi level , @xmath53 is the temperature - dependent quasiparticle residue . alternatively , we consider the fit @xmath54 with some exponent @xmath55 .
the latter dependence corresponds to the non - fermi - liquid behavior of @xmath3 electrons .
the obtained results are presented in the table .
@xmath56 the linear - quadratic fits are applicable only at @xmath57 ev ; at sufficiently small @xmath58 they also do not fit the obtained results well .
we find that the spectral weight @xmath53 pronouncely decreases with decrease of temperature , and the coeffitient @xmath52 obviously does not obey the fermi - liquid dependence @xmath59 .
these observations show that sizable deviations from fermi - liquid picture can be expected .
the power - law fits yield much better agreement in a broad range of frequencies @xmath60 ev , describing at the same time correctly the low - frequency behavior .
the coefficients @xmath61 @xmath62 of these fits show very weak temperature dependence ( the contribution @xmath63 is almost negligible ) , while the damping @xmath64 and the exponent @xmath0 slightly decrease with temperature , being related by @xmath65 .
these observations imply that @xmath3 electronic subsystem is better described by non - fermi liquid behavior at low temperatures , which reflects its participation in the formation of local moments in @xmath0-iron .
remarkably , consideration of the three - band model in ref
. showed similar dependence of the self - energy @xmath66 due to hund exchange interaction , which allows to attribute the @xmath3 subsystem in iron as close to the " spin freesing transition , accroding to the terminology of ref . .
to get further insight into the formation of effective local moments and extract corresponding exchange integrals , we calculate the momentum dependence of particle - hole bubble @xmath67 , which is obtained using paramagnetic lda and lda+dmft electronic spectrum [ @xmath68 is the corresponding electronic green function for the transition from the orbital state @xmath69 to @xmath70 , @xmath71 is a fermionic matsubara frequency ; for more details on the calculation procedure see ref . ] . at @xmath72 k calculated in high symmetry directions of the brillouin zone .
the contributions @xmath73 , @xmath74 , @xmath75 , and the hybridization part @xmath76 are shown by black , red , green and blue lines , respectively .
solid ( dashed ) lines correspond to lda+dmft ( lda ) results .
the lda+dmft estimate for @xmath77 is shown by magenta short dashed line .
, scaledwidth=44.0% ] the results for lda and lda+dmft approaches at @xmath72 k are presented in the fig .
[ fig : chi : lda_vs_dmft ] ( we find that the lda+dmft results are almost temperature - independent at low @xmath11 ) . for the bubble , calculated using purely lda spectrum ( i.e. with the assumption that all electrons are itinerant ) , the maximum of @xmath78 is located at the point @xmath79 , while the ferromagnetic instability in @xmath0-iron requires maximum of @xmath78 at @xmath80 and low @xmath81 if one neglects the non - local vertex corrections .
one can observe , that the main contribution to this incorrect behavior of the bubble originates from the @xmath2 electron part , @xmath82 .
both @xmath82 and @xmath83 contributions are however strongly influenced by the account of the local self energy corrections to the green s function in dmft approach , which correspond physically to account of partial localization of @xmath5-electrons .
these corrections mainly change @xmath84 and shift the maximum of @xmath85 to @xmath86 point ( @xmath80 ) .
note that within lda+dmft , intra
orbital contributions to @xmath82 and @xmath87 are only weakly momentum - dependent ; they also behave similarly , varying counter phase . according to the general ideas of spin - fluctuation theory @xcite
, this weak momentum dependence can be ascribed to the formation of the effective moments from @xmath2 and @xmath3 states . in agreement with the abovediscussed consideration
, the @xmath84 contribution has even weaker dispersion than the @xmath88 part . at the same time ,
strongly dispersive @xmath89 contribution , which is assumed to correspond to the ( remaining ) itinerant degrees of freedom , provides the maximum of the resulting @xmath78 at @xmath80 and appears to be the main source of the stability of the ferromagnetic ordering in iron within lda+dmft approximation .
the obtained results do not change qualitatively for the other choice hubbard interactions ( as we have verified for @xmath90 and @xmath91 ev ) , see supplementary material @xcite . to see the quantitative implications of the described physical picture
, we consider the effective spin - fermion model @xmath92 c_{l^{\prime } \sigma } ( \mathrm{i}\nu _ { n } ) \notag\end{aligned}\]](@xmath93 is a bosonic matsubara frequency , @xmath94 combines site and orbital indices ) , describing interaction of itinerant electrons with ( almost ) _ local _ spin fluctuations ( in contrast to critical spin fluctuation in cuprates @xcite ) , see also ref .
@xcite .
we assume here that the coulomb and hund s interaction acting within @xmath2 and @xmath3 orbitals results in a formation of some common local moment ( field @xmath95 ) , while the remaining itinerant degrees of freedom are described by the field @xmath96 formed from the grassmann variables @xmath97 @xmath98 and @xmath99 are the hamiltonian and local self - energy corrections to the lda spectrum ( the latter is assumed to be local and therefore diagonal with respect to orbital indices ) .
the interaction between the two subsystems ( localized and itinerant ) , which are formed from the @xmath5electronic states , is driven by hund s constant coupling @xmath100 . considering the renormalization of the propagator @xmath101 by the corresponding boson self
energy corrections , we obtain for the non - uniform susceptibility ( see supplementary material @xcite ) @xmath102where @xmath103 is the local spin susceptibility and @xmath104 is the exchange interaction , which fulfills @xmath105 ( no spin self - interaction ) .
we find @xmath106 , @xmath107 $ ] is the intra - orbital part , while @xmath108 results from the hybridization of states of different symmetry .
the contribution @xmath109 is approximately twice smaller than @xmath110 and therefore the main contribution to the magnetic exchange comes from the hybridization of @xmath3 and @xmath2 states .
the whole momentum dependence of @xmath111 can be well captured by the nearest
neighbor approximation for effective exchange integrals only , @xmath112 while @xmath109 has more complicated momentum dependence . restricting ourselves by considering the contribution @xmath113 , ( we assume that the contribution @xmath109 is further suppressed by the non - local and vertex corrections ) , from fig . [
fig : inverse_chi ] we find at @xmath72 k the value @xmath114 ev .
this value , as well as the momentum dependence of @xmath111 agrees well with the result of s.v .
okatov et al .
@xcite . the obtained results together with @xmath115 ( see fig .
2 ) provide an estimate for the curie temperature ( we assume @xmath116 ) , which can be obtained from the divergence of @xmath117 : @xmath118and appears comparable with the result of full dmft calculation , and therefore shows that the above model is adequate for describing magnetic properties of the full @xmath119-band hubbard model .
( note that the overestimation of @xmath120 in dmft approach in comparison with the experimental data is due to density - density approximation for the coulomb interactionanisimov and ( to minor extent ) due to presence of non - local fluctuations , not accounted by dmft ) . neglecting longitudinal fluctuations of field @xmath95
we can map the model ( [ sf ] ) to an effective @xmath4 heisenberg model @xmath121 to estimate the spin wave spectrum : @xmath122we obtain the corresponding spin stiffness @xmath123@xmath124 in a good agreement with the experimental data @xmath125@xmath124 ( ref . ) . in conclusion
, we have considered the problem of the description of effective local moments in @xmath0-iron based on the electronic spectrum in paramagnetic phase within lda+dmft approximation .
we find that local moments are formed by both @xmath2 and @xmath3 orbital states , each of them contributing a half of the total moment @xmath126 for @xmath3 electronic states we find pronounced features of non - fermi - liquid behavior , which accompanies earlier observed non - quasiparticle form of @xmath2 states .
the local moment and itinerant states interact with itinerant states via hund interaction , yielding magnetic exchange between the local - moment states via the effective rkky type mechanism .
the obtained exchange integrals are well captured by the lda+dmft approach .
the main origin of the intersite interaction of these moments is attributed to the @xmath2-@xmath3 hybridization , which yields magnetic exchange , dominating on the nearest - neighbour sites .
contrary to the previous studieslichtenstein1987,gornostyrev , we do not however assume some magnetic ordering for the electronic system .
we also emphasize that non
local self energy corrections , as well as vertex corrections , missed in our investigation , can make the described physical picture more precise .
in particular , non - local effects allow for the non zero non - diagonal @xmath2@xmath3 self - energy matrix elements and therefore possibly renormalize the strength of exchange interaction , as well as the self - energy of @xmath3 electronic states .
the role of the vertex corrections , only roughly accounted in the considered approach , also requires additional study .
therefore further investigation using powerful theoretical techniques of dynamic vertex approximation @xcite , dual fermion@xcite , or other non - local approaches is of certain interest .
the authors are grateful to yu .
n. gornostyrev , a. v. korolev , and k. held for useful discussions .
the work of p. a. igoshev was supported by the russian foundation for basic research ( project no .
14 - 02 - 31603 ) and act 211 government of the russian federation 02.a03.21.0006 ; a. a. katanin acknowledges support of the program of `` dynasty '' foundation .
the calculations were performed using " uran supercomputer of imm ub ras .
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b * 75 * , 045118 ( 2007 ) ; a. toschi , g. rohringer , a. a. katanin , k. held , ann .
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see , e.g. , a. n. rubtsov , m. i. katsnelson , a. i. lichtenstein , a. georges , phys.rev .
b * 79 * 045133 ( 2009 ) . |
the work has been supported by the european community - access to research infrastructure action of the improving human potential programme , by the daad exchange programme ( ppp - polen ) , by the polish state committe for scientific research ( grants no .
2p03b07123 and pb1060/p03/2004/26 ) and by the research centre jlich . | due to the high sensitivity of the @xmath0 reaction to the nucleon nucleon potential , bremsstrahlung radiation is used as a tool to investigate details of the nucleon nucleon interaction .
such investigations can be performed at the cooler synchrotron cosy in the research centre jlich , by dint of the cosy11 detection system .
+ the results of the identification of bremsstrahlung radiation emitted via the @xmath1 reaction in data taken with a proton target and a deuteron beam are presented and discussed .
+ the installation of a neutron detector at the cosy-11 facility [ 1,2 ] enables to study a plethora of new reaction channels .
it opens wide possibilities not only to investigate the isospin dependence of the meson production [ 3 ] , but also to measure the bremsstrahlung radiation created in the collisions of nucleons .
the study of the latter process is interested since it is highly sensitive to the kind of the nucleon - nucleon potential , and hence may serve as a tool to discriminate between various existing potential models [ 4,5 ] .
although bremsstrahlung radiation has been studied since many years , it is still the subject of interest of many theoretical and experimental groups [ 4,5,6,7 ] .
+ at the cosy11 experiment a signal from @xmath2quanta was observed in the time of flight distribution for the neutral particles measured between the target and the neutral particle detector [ 2 ] .
this encouraged us to analyse the data in view of the bremsstrahlung radiation in a free @xmath3 and a quasi
free @xmath4 reactions .
data have been taken using a proton target and a deuteron beam with a momentum close to the threshold of the @xmath5 process .
events corresponding to the @xmath3 and @xmath6 reaction have been identified by measuring the outgoing charged as well as neutral ejectiles .
the protons and deuterons are detected by means of drift chambers and scintillator hodoscopes while neutrons and photons are registered in a scintillator
lead sandwich type detector .
the momentum vectors of the charged ejectiles are reconstructed by tracking back the trajectories to the target point [ 1 ] . in case of a neutron the time of flight between the target and the neutral particle detector together with the known position of the hitted detection unit enables to determine its four momentum vector [ 8 ] . + in order to identify the @xmath3 reaction events with two tracks in the drift chambers and a simultaneous signal in the neutron detector have been selected . in fig.1 ( left ) the squared mass of one particle is plotted versus the squared mass of the other registered particle .
based on this figure the measured reactions can be grouped according to the type of ejectiles .
thus reactions with two protons , proton and pion , proton and deuteron , and pion and deuteron can be clearly selected .
next the distribution of the time of flight between the target neutron detector was determined with requirement that one of the charged particles was identified as a proton and the other as a deuteron . due to the baryon number conservation , gamma quanta
are the only one possible source of a signal in a neutron detector .
indeed a clear peak around the time corresponding to the time of light of the light is visible ( see fig.1 right ) .
the gamma quanta may originate from bremsstrahlung reaction or from the decay of produced mesons eg . via the @xmath7 .
it is possible to distinguish between these hypothesis calculating the missing mass produced in the @xmath8 reaction .
fig.2 left shows the distribution of the squared missing mass as obtained for the @xmath8 reaction . a significant peak around 0 mev@xmath9/c@xmath10 the squared mass of a gamma quanta
constitute an evidence for events associated to the deuteron
proton bremsstrahlung .
in addition a broad structure at higher masses originating from two pions emmited from reaction @xmath11 or two gamma quanta from @xmath12 reaction is visible .
the extraction of the total cross section of the @xmath3 reaction requires the luminosity and acceptance determination , which will be performed in the near future .
the analysis of the @xmath13 reaction is more complicated , however in this case all three baryons , namely two protons and neutron can be measured in the drift chambers and in the neutron detector , respectively .
fig.2 ( right ) presents the time of flight with the condition that in coincidence with a neutral particle also two protons were identified . a clear signal originating from gamma quanta
is seen at a time value of 24 ns which coresponds to the velocity of light . using the missing mass technique , it might be possible to verify if gamma quanta originate from the direct @xmath13 reaction . at present
the data analysis is in progress . |
here we briefly outline basic steps and main results of the spin - wave calculations for the energy spectrum and the magnon relaxation rates of the @xmath143@xmath144 antiferromagnet on a honeycomb lattice .
the harmonic spin - wave analysis of the nearest - neighbor heisenberg honeycomb - lattice antiferromagnet can be found , for example , in @xcite .
geometry of exchange bonds of the considered model is schematically shown in fig .
[ suppl : lattice ] .
the unit cell of the antiferromagnetic structure coincides with the crystal unit cell and contains two oppositely aligned spins @xmath145 and @xmath146 in positions @xmath147 and @xmath148 .
the elementary translation vectors are defined as @xmath149 and @xmath150 .
the lattice constant in bani@xmath3(po@xmath4)@xmath3 is equal to @xmath151 .
the reciprocal lattice basis is @xmath152 and @xmath153 .
the volume of the brilouin zone is @xmath154 .
@xmath144 model in a honeycomb lattice .
] the spin hamiltonian includes heisenberg exchange interactions between first- and third - neighbor spins together with the single - ion anisotropy : @xmath155 \ . \nonumber\end{aligned}\ ] ] here @xmath156 denotes spin in the unit cell @xmath157 and so on .
the microscopic parameters for bani@xmath3(po@xmath4)@xmath3 ( @xmath158 ) were determined from the magnon dispersion as @xmath159 mev , @xmath160 mev , and @xmath161 mev @xcite .
the second - neighbor exchange was estimated to be much smaller @xmath162 mev and is neglected in the following .
applying the holstein - primakoff transformation for two antiferromagnetic sublattices and performing the fourier transformation @xmath163 we obtain the harmonic part of the boson hamiltonian @xmath164 \ , \nonumber\end{aligned}\ ] ] where we use the shorthand notations @xmath165 with @xmath166 and @xmath167 diagonalization of the quadratic form ( [ suppl : h2 ] ) with the help of the canonical bogolyubov transformation yields @xmath168 \ , \ ] ] where excitation energies are @xmath169 & & \varepsilon_\beta({\bf k } ) = s \sqrt { ( 3j_{13 } + |f_{\bf k}| ) ( 3j_{13 } - |f_{\bf k}| + 2d ) } \ .\end{aligned}\ ] ] the first magnon branch is gapless , @xmath170 , and reaches the maximum value of @xmath171 at @xmath172 $ ] with @xmath173 in the reciprocal lattice units .
the second branch describes optical magnons with a finite energy gap at @xmath174 @xmath175 the maximum of the optical branch @xmath176 is close to ( [ suppl : omax ] ) .
in the long - wavelength limit @xmath177 the energy of the acoustic branch has linear dispersion @xmath178 with the spin - wave velocity @xmath179 for the optical branch one finds @xmath180 with @xmath181 mev@xmath88 for bani@xmath3(po@xmath4)@xmath3 . for small @xmath182 the bogolyubov transformation
can be written explicitly in the following way .
first , we transform from the original holstein - primakoff bosons @xmath183 and @xmath184 to their linear combinations : @xmath185 the fourier transformed hamiltonian ( [ suppl : h2 ] ) takes the following form @xmath186 \ , .
\nonumber\end{aligned}\ ] ] second , the standard @xmath187@xmath188 transformation is applied separately for @xmath189 and @xmath190 bosons . in particular , for the acoustic branch , @xmath191 , we obtain @xmath192 where @xmath193 and @xmath194 . in the case of bani@xmath3(po@xmath4)@xmath3 the two dimensionless constants
are @xmath195 and @xmath196 .
similarly , for optical magnons with @xmath197 we obtain @xmath198 with @xmath199
for a collinear antiferromagnet the interaction between spin - waves is described by four - magnon terms in the bosonic hamiltonian .
the four - magnon terms of the exchange origin are expressed as @xmath200 where @xmath201 stands for @xmath202 etc .
the single - ion anisotropy contributes @xmath203 performing transformation from @xmath204 , @xmath205 to @xmath206 , @xmath207 we obtain various magnon - magnon terms .
the scattering of optical ( @xmath16 ) magnons on each other , which will be referred to as the roton - roton interaction , can be straightforwardly written as @xmath208 derivation of the roton - phonon interaction ( scattering of the optical magnon on the acoustic one , @xmath16 on @xmath15 ) is more involved and we obtain an estimate as @xmath209 the individual terms in the magnon - magnon interaction obtained from ( [ hj ] ) and ( [ hd ] ) applying the bogolyubov transformation are proportional to @xmath210 and diverge for scattering processes involving acoustic magnons , see ( [ suppl : uva ] )
. however , the leading @xmath211 and the subleading singularity @xmath212 cancel out in their net contribution and @xmath213 in agreement with the hydrodynamic approach @xcite . local modulation of magnetic coupling constants due to structural disorder , etc .
, will result in _ independent _ variations of @xmath134- and @xmath133-terms in magnon - magnon interaction in ( [ hj ] ) and ( [ hd ] ) .
thus , the resultant impurity - assisted magnon - magnon interaction will retain the same structure as the magnon - magnon interaction , with two important differences .
first , the momentum in such a scattering is not conserved , and , second , the variation of @xmath134 ( @xmath21 ) is associated only with ( [ hj ] ) and the variation @xmath22 will contain only ( [ hd ] ) part .
since such variations are independent , it suffices to consider one of them and treat the associated constant as a free parameter .
the most important consequence of this consideration is that , in the impurity scattering , there is no cancellation of the individual terms that are proportional to @xmath214 , compared to the case of magnon - magnon scattering in ( [ vrp ] ) discussed above where such a cancellation does take place .
thus , in the long - wavelength limit , @xmath51 , with a coefficient proportional to the impurity concentration and strength of the disorder .
the lowest - order diagram for the magnon self - energy calculated using matsubara technique is @xmath215 \nonumber\end{aligned}\ ] ] with @xmath216 . then the damping rate is @xmath217 \nonumber\\ & \times&\delta(\varepsilon_{\bf k } + \varepsilon_{\bf q } -\varepsilon_{\bf q ' } - \varepsilon_{\bf k'})\ , .
\label{gammak}\end{aligned}\ ] ] first , we consider the roton - roton scattering processes .
the low - temperature asymptote of ( [ gammak ] ) in this case is obtained by taking @xmath218 and keeping the leading exponentially small occupation factor .
then , for an optical magnon with @xmath174 in two dimensions @xmath219 performing integration in ( [ gamma01 ] ) and using parameters for bani@xmath3(po@xmath4)@xmath3 discussed above we obtain @xmath220 } \ . \label{gamma02rr}\ ] ] without going into details , there exist another channel of scattering that corresponds to a conversion of two rotons into two high - energy phonons , @xmath221 , which leads to the decay rate of the optical mode of the same exponential form as in ( [ gamma02rr ] ) with a numerical coefficient of the same order . | we demonstrate that local modulations of magnetic couplings have a profound effect on the temperature dependence of the relaxation rate of optical magnons in a wide class of antiferromagnets in which gapped excitations coexist with acoustic spin waves . in a two - dimensional collinear antiferromagnet with an easy - plane anisotropy ,
the disorder - induced relaxation rate of the gapped mode , @xmath0 , greatly exceeds the magnon - magnon damping , @xmath1 , negligible at low temperatures .
we measure the lifetime of gapped magnons in a prototype @xmath2 antiferromagnet bani@xmath3(po@xmath4)@xmath3 using a high - resolution neutron - resonance spin - echo technique and find experimental data in close accord with the theoretical prediction .
similarly strong effects of disorder in the three - dimensional case and in noncollinear antiferromagnets are discussed . _
introduction._the recent development of the neutron - resonance spin - echo technique has led to dramatic improvement of the energy resolution in neutron - scattering experiments @xcite . when applied to elementary excitations in magnetic insulators
, this technique allows one to measure magnon linewidth with the @xmath5ev accuracy compared to the mev resolution of a typical triple - axis spectrometer .
damping of quasiparticles depends fundamentally on the strength of their interactions with each other and with impurities , information not accessible directly by other measurements .
although theoretical studies of magnon damping in antiferromagnets ( afs ) go back to the 1970s @xcite , a comprehensive comparison between theory and experiment is still missing , mainly due to the lack of experimental data .
magnon - magnon scattering is traditionally viewed as the leading source of temperature - dependent magnon relaxation rates in afs @xcite .
another common relaxation mechanism in solids is the lattice disorder , which is responsible for a variety of the low - temperature effects , such as residual resistivity of metals @xcite and finite linewidth of antiferromagnetic resonances @xcite .
however , _ temperature - dependent _ effects of disorder are usually neglected because of the higher powers of @xmath6 in impurity - induced relaxation rates compared to leading scattering mechanisms and of the presumed dilute concentration and weakness of disorder .
the closest analogy is the resistivity of metals , in which the @xmath7 term is due to lattice imperfections and the temperature - dependent part is due to quasiparticle scattering . in this work ,
we demonstrate that scattering on the spatial modulations of magnetic couplings should completely dominate the low - temperature relaxation rate of gapped excitations in a wide class of afs .
such modulations , produced by random lattice distortions , yield scattering potential for propagating magnons and , at the same time , modify locally their interactions . for an illustration , we consider an example of the two - dimensional ( 2d ) easy - plane af with one acoustic and one gapped excitation branch .
in addition to potential scattering , responsible for a finite damping @xmath8 of optical magnons , see fig .
[ fig : diagrams](a ) , there exists an impurity - assisted temperature - dependent scattering of gapped magnons on thermally - excited acoustic spin waves , see fig .
[ fig : diagrams](c ) , which yields @xmath9 . despite the presumed smallness of impurity concentration @xmath10 , at low temperatures this mechanism dominates over the conventional magnon - magnon scattering , fig .
[ fig : diagrams](b ) , which carries a much higher power of temperature : @xmath11 .
we have performed resonant neutron spin - echo measurements with a few @xmath5ev resolution on a high - quality sample of bani@xmath3(po@xmath4)@xmath3 , a prototype 2d planar af @xcite .
we find that the theory describes very well the experimental data for the linewidth of optical magnons .
similar dominance of the impurity - assisted magnon - magnon scattering should persist in the 3d afs and is even more pronounced in the noncollinear afs .
we propose further experimental tests of this mechanism .
0.9 cm ) .,title="fig : " ] _ theory._we begin with the spin hamiltonian of a collinear af with an easy - plane anisotropy induced by the single - ion term @xmath12 : @xmath13 two examples are the nearest - neighbor afs on square and honeycomb lattices .
the latter model , with the non - frustrating third - neighbor exchange , is relevant to the spin-1 antiferromagnet @xmath14 @xcite discussed below . as a consequence of broken @xmath2 symmetry , excitation spectrum in the ordered antiferromagnetic state possesses acoustic ( @xmath15 ) and gapped ( @xmath16 ) magnon branches : @xmath17 see fig .
[ fig : diagrams](d ) for a sketch .
explicit expressions for @xmath18 , @xmath19 , and @xmath20 for bani@xmath3(po@xmath4)@xmath3 are provided in @xcite .
defects are present in all crystals .
while vacancies and substitutions may be eliminated in some materials , inhomogeneous lattice distortions remain an intrinsic source of disorder , inducing weak random variations @xmath21 and @xmath22 of microscopic parameters in the spin hamiltonian ( [ h ] ) @xcite .
both types of randomness have qualitatively the same effect on magnon lifetimes .
for example , local modification of the single - ion anisotropy @xmath23 generates scattering potential for magnons @xmath24 where @xmath25 , @xmath26 , and @xmath27 are the bogolyubov transformation parameters . for optical magnons at @xmath28 ,
the momentum dependence is not important , @xmath29 . for bond disorder ,
all expressions are the same with a substitution @xmath30 and an additional phase factor , which depends on bond orientation and disappears after impurity averaging . for the gapped magnons with @xmath31 , scattering amplitude in the second born approximation , fig .
[ fig : diagrams](a ) , averaged over spatial distribution of impurities is @xcite @xmath32 where @xmath10 is the impurity concentration , @xmath33 is the averaged impurity potential , and @xmath34 is the magnon bandwidth @xcite .
thus , in 2d , conventional impurity scattering results in a finite zero - temperature relaxation rate of the gapped magnons . at low temperatures , the principal scattering channel for optical magnons is due to collisions with the thermally excited acoustic spin waves with @xmath35 .
all other processes are either forbidden kinematically or exponentially suppressed . in this case
we can consider only @xmath36 terms in the magnon - magnon interaction : @xmath37 where the first and the second row correspond to the conventional and to the impurity - assisted magnon - magnon scattering , respectively , with @xmath38 .
the latter is of the _ same _ origin as the conventional impurity scattering in ( [ himp1 ] ) since @xmath22 and @xmath21 also modify locally interactions among magnons @xcite . in the one - loop approximation , ( [ hmm ] ) and ( [ 1h4imp ] )
yield the self - energies of figs .
[ fig : diagrams](b ) and ( c ) .
applying standard matsubara technique , relaxation rates can be expressed as @xmath39 where @xmath40 , @xmath41 , and @xmath42 is the bose factor .
there are two important differences between @xmath43 and @xmath44 in ( [ 1gmm ] ) and ( [ 1gimp ] ) .
first , the total momentum is not conserved for impurity scattering .
this relaxes kinematic constraints of the 4-magnon scattering processes , but requires instead integration over the extra independent momentum @xmath45 .
second and most crucial , interaction vertices @xmath46 and @xmath47 show very different long - wavelength behavior as @xmath48 , @xmath49 .
we calculate them using the approach similar to @xcite , and find that in the long - wavelength limit magnon - magnon interaction ( [ hmm ] ) is @xmath50 , in accordance with the hydrodynamic limit @xcite .
however , for the impurity - assisted scattering ( [ 1h4imp ] ) , interaction is @xmath51 .
this can be understood as a consequence of an effective long - range potential for acoustic magnons produced by the gaped magnon while in the vicinity of an impurity .
the leading @xmath6-dependence of @xmath52 and @xmath53 can be calculated now using ( [ wk ] ) and approximating interaction vertices with their long - wavelength expressions .
the main contribution to the integrals in ( [ 1gmm ] ) and ( [ 1gimp ] ) is determined by acoustic magnons with @xmath54 .
then , a straightforward power counting yields @xmath55 where @xmath56 @xcite .
thus , the inverse lifetime of an optical magnon is proportional to @xmath57 in 2d .
a generalization to higher dimensions gives @xmath58 .
the @xmath59-law for the relaxation rate of optical magnons in 3d afs was previously predicted in @xcite .
we note that for a given model , the effect of magnon - magnon scattering in ( [ 1gmm_est1 ] ) can be calculated using microscopic parameters , thus putting strict bounds on its magnitude . the same calculation for @xmath60 proceeds via the following integral : @xmath61 where @xmath62 with @xmath63 , @xmath64 , and we used the relation between @xmath65 in ( [ 1h4imp ] ) and @xmath66 in ( [ himp1 ] ) .
the nave power counting in ( [ 1gimp_est ] ) already gives @xmath67 , while a more careful consideration shows further enhancement of the scattering as the integrals formally diverge [ logarithmically ] in the @xmath68 region , demonstrating an important role of the long - wavelength magnons in 2d .
this divergence is similar to the one in the problem of finite @xmath69 ordering temperature in 2d and is regularized similarly by introducing low - energy cutoff .
the cutoff is either due to a 3d - crossover as in the case of some cuprates @xcite , or a weak in - plane anisotropy that induces small gap @xmath70 in the acoustic branch , the case directly relevant to the current work @xcite .
combining ( [ tau_0 ] ) and ( [ 1gimp_est ] ) we obtain impurity - induced relaxation rate of gapped magnons @xmath71 \ , , \end{aligned}\ ] ] where both @xmath72 and @xmath73 are proportional to @xmath10 and to the average strength of disorder @xmath74 . as a result , the impurity scattering leads to a relaxation rate that carries a significantly lower power of temperature than the magnon - magnon scattering mechanism . therefore , despite possible smallness of the combined impurity concentration and strength , it should dominate not only the @xmath7 lifetime of the gapped magnon , but also its temperature dependence in the entire low - temperature regime .
a qualitative prediction of our consideration is that @xmath72 and @xmath73 in ( [ 1gimp_est ] ) should be of the same order since both terms are related to disorder .
in addition , for samples of the same material of different quality , they must scale with the amount of structural disorder in a correlated way . in the 3d case , impurity - assisted mechanism ( [ 1gimp_est ] ) gives @xmath75 , still dominating the 3d magnon - magnon relaxation rate @xmath76 discussed above . _
experiment._the experimental part of our work is devoted to the neutron spin - echo measurements of the magnon lifetime in @xmath14 .
this material is a layered quasi-2d af with a honeycomb lattice of spin-1 ni@xmath77 ions and nel temperature @xmath78 k. a comprehensive review of the physical properties of @xmath14 is presented in @xcite .
its excitation spectrum has an optical branch with the gap @xmath79 k and an acoustic mode , as is sketched in fig .
[ fig : diagrams](d ) .
the fit of the magnon dispersion yields the following microscopic parameters : @xmath80 mev and @xmath81 mev are exchanges between first- and third - neighbor spins , and @xmath82 mev is the single - ion anisotropy .
the thermodynamic properties of bani@xmath3(po@xmath4)@xmath3 follow the 2d behavior down to @xmath83k and a small gap in the acoustic branch , @xmath84k , due to weak in - plane anisotropy is consistent with the value of the ordering temperature @xcite . for several representative spin - echo energies . ]
the spin - echo experiments were performed on the triple - axis spectrometer in22 ( ill , grenoble ) by using zeta neutron resonance spin - echo option @xcite . the incident neutron beam was polarized and the scattered beam analyzed from ( 111 ) reflection of @xmath85 heusler alloy focusing devices .
we used a fixed-@xmath86 configuration , with @xmath87 @xmath88 or @xmath89 @xmath88 .
different rf - flipper configurations were used in order to adapt the spin - echo time ( energy ) @xmath90 ( @xmath91 ) to the magnetic excitation lifetimes , typically in the range of @xmath92ps ( @xmath93ev ) . as for any spin - echo experiment @xcite , the measurement of the neutron polarization ( spin - echo amplitude ) after the scattering , @xmath94 , provides us with a direct access to the correlation function @xmath95 . for a spin - wave excitation described by a lorentzian function in energy of half width @xmath96
, one can show that @xmath97 , in which the prefactor @xmath98 depends on the spin - echo resolution . for our measurements
, we have used a @xmath99 single crystal of @xmath14 oriented with the @xmath100 and @xmath101 reciprocal axes in the scattering plane .
the spin - echo data were taken at the antiferromagnetic scattering vector @xmath102 and the energy transfer @xmath103 mev corresponding to the bottom of the dispersion curve of the gapped mode @xcite . in determining the spin - echo amplitudes ,
neutron intensities were corrected for the inelastic background , measured at the scattering vector @xmath104 and the energy transfer @xmath105 mev .
results of the temperature dependence of spin - echo amplitudes for several representative @xmath106 s are shown in fig .
[ fig : polarization ] .
solid lines are the fits of the spin - echo amplitudes with @xmath107 using relaxation rate in the functional form given by ( [ 1gmm_est1 ] ) and ( [ 1gimp_tot ] ) , @xmath108 , which we discuss next . using the full set of @xmath109 data , experimental results for @xmath110
are extracted from the fits of @xmath111 vs @xmath106 at fixed temperatures .
these results are presented in our fig .
[ fig : gamma ] together with the theoretical fits . _
comparison._the relaxation rate approaches the constant value of @xmath112 @xmath5ev at @xmath113 , in agreement with the expectation ( [ tau_0 ] ) for the gapped mode in 2d .
the low-@xmath6 dependence of the relaxation rate is following the power law much slower than @xmath57 .
the quality of the free - parameter fit of @xmath114 with just the @xmath57 law is not satisfactory for either @xmath110 or @xmath115 s in figs .
[ fig : gamma ] and [ fig : polarization ] , and the magnitude of @xmath116 also requires an unphysically large values of the magnon - magnon scattering parameter @xmath117 in ( [ 1gmm_est1 ] ) , exceeding theoretical estimates roughly tenfold . on the other hand ,
@xmath118 law gives much more satisfactory fits in the low- and intermediate-@xmath6 regime up to 12 k in both @xmath110 and @xmath115 , shown as a separate fit by the dotted line in fig .
[ fig : gamma ] .
the best fit of @xmath110 , given by solid line , is the sum of the magnon - magnon and impurity - scattering effects from ( [ 1gmm_est1 ] ) and ( [ 1gimp_tot ] ) , with the magnon - magnon and impurity - assisted parameters @xmath119 mev and @xmath120 @xmath5ev , respectively .
the same @xmath110 is used in all three curves of @xmath115 in fig .
[ fig : polarization ] , the original data from which experimental @xmath110 is extracted .
magnon bandwidth @xmath121 k and the low - energy cutoff @xmath122 k , equal to the gap in the acoustic branch , were used . of the optical magnon with @xmath123 in bani@xmath3(po@xmath4)@xmath3 .
full line is the best theoretical fit including all contributions with parameters described in the text .
dashed and dotted lines indicate separate contributions of magnon - magnon and impurity - assisted magnon - magnon scattering . ]
two remarks are in order concerning the role of the magnon - magnon relaxation rate used in fig .
[ fig : gamma ] .
first , fits of @xmath110 in fig .
[ fig : gamma ] also include a contribution from scattering off the thermally excited optical magnons , which is given by @xmath124 @xcite .
its contribution is roughly equal to that of the @xmath57-term ( [ 1gmm_est1 ] ) at @xmath125k ( @xmath126 ) , but diminishes faster at lower @xmath6 . in the fit of @xmath110
we use the value of @xmath127 @xmath5ev , about three times the theory estimate : @xmath128 @xmath5ev .
second , the theoretical estimate of the magnon - magnon interaction parameter in @xmath57 law ( [ 1gmm_est1 ] ) is @xmath129 mev , again factor 2.5 smaller than the one used in the fit ( @xmath119 mev ) . altogether , the magnon - magnon contribution to @xmath110 , shown by the dashed line and the corresponding color shading in fig .
[ fig : gamma ] , is likely a generous overestimate of its actual role in the relaxation .
still , the contribution of the impurity - assisted mechanism in @xmath110 is very strongly pronounced and is not explicable by the conventional scattering mechanisms .
for example , at 12k the impurity scattering accounts for at least 2/3 of the temperature - dependent part of @xmath110 .
the parameter of the impurity - assisted term in ( [ 1gimp_tot ] ) used in the fit is @xmath130ev , which is of the same order with the constant impurity term @xmath72 , meeting our expectations outlined above .
this is , again , the strong argument that both the constant and the @xmath6-dependent terms in the relaxation rate must have the same origin , giving further support to the consistency of our explanation of the data .
the values of @xmath73 and @xmath72 can not be determined theoretically as the impurity concentration and strength are , generally , unknown .
however , another consistency check is possible : the ratio of @xmath72 to a characteristic energy scale of the problem , @xmath131 , should give , according to ( [ tau_0 ] ) , an estimate of the cumulative measure of disorder concentration and its strength : @xmath132 .
this translates into a reasonable estimate of the disorder and its strength in bani@xmath3(po@xmath4)@xmath3 : modulation of magnetic couplings is equivalent to half of a percent of sites having @xmath22 ( @xmath21 ) of order @xmath133 ( @xmath134 ) .
the amount of structural distortion in bani@xmath3(po@xmath4)@xmath3 @xcite is consistent with the magnitude of such variations of magnetic couplings , given the strong spin - lattice coupling in this material . _
other systems._we propose that similar , and even stronger , effects of disorder in the relaxation rate must be present in the 2d noncollinear afs , in which magnon - magnon interactions acquire the so - called cubic interaction terms @xcite , absent in the collinear afs considered above .
the self - energies associated with such interaction are the same as in figs .
[ fig : diagrams](b ) and ( c ) , but with two intermediate lines instead of three . with the long - wavelength behavior of the impurity interaction to follow @xmath135 , as in the considered case , a qualitative consideration similar to ( [ 1gimp_est ] ) leads to : @xmath136 where @xmath137 , an even lower power of @xmath6 .
since the canting of spins can be induced by the external field , we propose an experimental investigation of the effect of such a field on the relaxation rate . for the 3d noncollinear afs
we predict @xmath138 .
recent neutron spin - echo experiment in a heisenberg - like af mnf@xmath3 @xcite have reported significant discrepancies between measured relaxation rates and predictions of the magnon - magnon scattering theory @xcite , precisely in the regime of low-@xmath6 and small-@xmath139 where the theory is assumed to be most reliable . although the current work concerns the dynamics of strongly gapped excitations and our results are not directly transferable to the case of mnf@xmath3
, we have , nevertheless , presented a general case in which the magnon - magnon scattering mechanism is completely overshadowed by impurity scattering , thus suggesting a similar consideration in other systems . _
conclusions._to conclude , we have presented strong evidence of the general situation in which temperature - dependence of the relaxation rate of a magnetic excitation is completely dominated by the effects induced by simple structural disorder .
our results are strongly supported by the available experimental data .
further theoretical and experimental studies are suggested .
this work was initiated at the max - planck institute for the physics of complex systems during the activities of the advanced study group program on `` unconventional magnetism in high fields , '' which we would like to thank for hospitality . the work of a. l. c. was supported by the doe under grant no .
de - fg02 - 04er46174 .
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* lifetime of gapped excitations in collinear quantum antiferromagnet : + supplemental information * + 0.35 cm a. l. chernyshev@xmath140 , m. e. zhitomirsky@xmath141 , n. martin@xmath141 , and l .- p .
regnault@xmath141 + 0.15 cm _
@xmath142department of physics , university of california , irvine , california 92697 , usa + @xmath141service de physique statistique , magntisme et supraconductivit , + umr - e9001 cea - inac / ujf , 17 rue des martyrs , 38054 grenoble cedex 9 , france _
+ ( dated : june 20 , 2012 ) + -0.1 cm |
in the standard model ( sm ) , @xmath3 is dominated by contributions from the gluonic and electroweak penguin ( ewp ) operators , @xmath4 and @xmath5 . in the @xmath6
chiral limit , the @xmath2 matrix elements of the ewp operators @xmath7 , are determined by two 4-quark vevs , @xmath8 and @xmath9 , which also determine the dimension @xmath1 part of the ope of the flavor @xmath10 v - a correlator difference @xmath11 @xcite , where the superscript @xmath12 denotes the sum of spin @xmath13 and @xmath14 components and , with @xmath15 the standard v or a @xmath10 current , the scalar correlators @xmath16 are defined via @xmath17 since @xmath18^{ope}_{d=6}$ ] is strongly dominated by the contribution involving @xmath9 , which vev also dominates the chiral limit @xmath5 matrix element , the extraction of @xmath18_{d=6}^{ope}$ ] is of considerable phenomenological interest , and a number of dispersive and finite energy sum rule ( fesr ) analyses have attempted it @xcite .
@xmath0 decay data plays a key role in these analyses since the spectral function of @xmath19 , @xmath20 , is directly measurable for @xmath21 in non - strange hadronic @xmath0 decays .
explicitly , in the sm , with @xmath22 a short - distance ew correction , @xmath23 , @xmath24 and @xmath25/ \gamma [ \tau^- \rightarrow \nu_\tau e^- { \bar \nu}_e ] $ ] , one has , for the continuum ( non-@xmath26-pole ) part of @xmath27 @xcite @xmath28 dispersive analyses employ the unsubtracted dispersion relation for @xmath19 and require either assumptions about the saturation of the dispersion integral within the range kinematically accessible in @xmath0 decays , or supplementary constraints on @xmath29 for @xmath30 , such as those provided by the weinberg sum rules @xcite and the dgmly @xmath26 electromagnetic ( em ) self - energy sum rule @xcite ( see , e.g. , ref .
@xcite for details ) .
higher dimension ( @xmath31 ) contributions to @xmath32 must also be considered .
these problems are avoided in the fesr approach , which relies on @xmath33 having no kinematic singularities and hence satisfying the fesr relation @xmath34 for any @xmath35 and any @xmath36 analytic in the region of the contour . for sufficiently large @xmath35 ,
the ope should become reliable on the rhs . choosing polynomial weights @xmath36 with degree @xmath37 strongly suppresses ope contributions with @xmath38 . for sub - asymptotic @xmath35 , ope breakdown , or duality violation ( dv )
is expected .
in fact , even for @xmath39 , sizeable @xmath35-dependent deviations between the lhs and ope versions of the rhs are found for the @xmath40 v and a analogues of eq .
[ fesrreln ] @xcite .
these are strongly suppressed for analogues employing pinched weights ( @xmath36 with a zero at @xmath41 ) @xcite , indicating that at scales @xmath42 dvs are localized to the vicinity of the timelike axis . with this in mind , the analysis of ref .
@xcite ( cgm ) employed doubly pinched weights , checking the @xmath35-dependence of the match between the weighted spectral integrals and optimized ope fit as a test of the self - consistency of the assumed neglect of residual dv contributions .
figure 1 shows the resulting residuals , @xmath43/\delta i^w_{opal}(s_0)$ ] , over an expanded @xmath35 range , for the two weights , @xmath44 and @xmath45 of the `` maximally safe '' cgm analysis based on opal data @xcite .
( we focus here on opal data due to a problem with the aleph covariance matrices @xcite which is the subject of ongoing reanalysis . )
@xmath46 are the lhs and rhss of eq .
[ fesrreln ] and @xmath47 the uncertainty on @xmath48 .
it is obvious that residual dvs , though not evident _ within errors _ above @xmath49 , become non - negligible below this point .
small residual dv contibutions are thus expected in the @xmath50 cgm fit window as well . lacking a model for dvs
, analyses such as cgm were unable to estimate the systematic uncertainty associated with neglecting these contributions .
in refs .
@xcite , a model for dv spectral contributions was developed .
the model builds on earlier work in refs .
@xcite and is motivated by large-@xmath51 and regge - based resonance spacing ideas .
the model leads to anstze @xmath52 , @xmath53 , for the v and a spectral functions , where the dv contributions have the form @xmath54 in refs .
@xcite the impact of dvs on previous v - a analyses was investigated using a _ single _ dv ansatz of the form eq .
[ dvmodelform ] for the v - a difference @xmath29 .
this involves the implicit additional assumption that @xmath55 and @xmath56 , allowing the @xmath57-parameter v - a difference to be re - written in the effective @xmath58-parameter form , eq .
[ dvmodelform ] .
we avoid this additional assumption and fit the v and a dv parameter sets separately , as part of a combined v , a fit which also determines the ope parameters @xmath59 , @xmath60 , and the relevant @xmath1 and @xmath57 v and a channel effective condensates .
we find central dv parameter fit values not in good accord with the expectations @xmath55 , @xmath56 .
our analysis employs @xmath36 up to degree @xmath61 , including @xmath40 , which is optimally sensitive to the dv contributions .
the resulting fits provide excellent matches between the opal spectral integrals and optimized ope+dv fit forms for all @xmath36 employed and all @xmath35 down to a fit window minimum @xmath62 .
though so far aimed at extracting @xmath59 , and not optimized for extracting @xmath63 v - a condensates , the analysis nonetheless provides preliminary results for these quantities . since the fits
provide a prediction for @xmath29 for @xmath64 , and hence also above @xmath65 , we can test our results against the weinberg and dgmly sum rules , which constraints have _ not _ been incorporated in performing the fits .
the first and second weinberg sum rules are written in a form with rhss equal to zero ; for the rhs of the dgmly sum rule we employ the @xmath66 chiral limit value @xmath67_{em } /3\alpha_{em}\
, = \ , -0.0109(15)\ { \rm gev}^4 $ ] @xcite .
the results of these tests are shown in figure 2 , with @xmath35 the point beyond which the fitted form of @xmath29 is employed in the relevant spectral integral .
below this point , experimental data are used .
the dotted and solid black lines in the third panel show the central dgmly sum rule rhs and error .
all three sum rules should be satisfied for all @xmath35 in our fit window .
this is evidently the case , giving us good confidence in the results for the fitted ope parameters as well .
as an illustration of our preliminary results , we quote the effective @xmath1 v - a condensate @xmath68 which results from an update of the cgm opal fit incorporating dvs and fitting @xmath69 , @xmath70 , and the @xmath71 , @xmath72 and @xmath73 ( @xmath74 ) fesrs with the cipt scheme for the truncated @xmath75 ope series and @xmath76 .
@xmath68 is defined by @xmath77^{ope}_{d=6}=c_6^{v - a}/q^6 $ ] .
we find @xmath78 , c.f .
the cgm no - dvs maximally safe analysis opal - based value @xmath79 .
values somewhat larger in magnitude , with larger errors , are obtained from analyses excluding @xmath80 , including those employing fopt for the @xmath75 series .
we emphasize that these results are preliminary , and that a dedicated v - a analysis , aimed at reducing the errors , is in progress .
readers noting the @xmath81 difference between the values quoted above and those obtained from the aleph - based analyses of cgm ( neglecting dvs ) and ref .
@xcite ( including dvs approximately ) should bear in mind that the aleph and opal @xmath82 data differ significantly in the upper part of the spectrum , with the opal data agreeing better with expectations based on cvc and recent preliminary babar and snd @xmath82 electroproduction data @xcite .
this work was supported by the natural sciences and engineering research council of canada , the us doe , micinn ( spain ) under grant fpa 2007 - 60323 , the spanish consolider ingenio 2010 program cpan ( csd2007 - 00042 ) , cicytfeder - fpa2008 - 01430 , sgr2005 - 00916 and the programa de movilidad pr2010 - 0284 .
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phys . j. _ * c55 * , 237 ( 2008 ) . | we discuss a preliminary study of the impact of duality violations on extractions from @xmath0 decay data of the @xmath1 vevs which determine chiral limit standard model @xmath2 matrix elements of the electroweak penguin operators . |
after this paper has been written , paper @xcite appeared , where ( among some other topics ) the addition law for energy - momentum was modified as compared to the one used in @xcite .
this was done to comply with the physical requirement that a set of particles with even sub - planckian energies can have an energy much exceeding the planck energy .
the modification was achieved by simply replacing the planck energy @xmath123 in our units ) for a system of @xmath115 particles with @xmath124 .
+ here we demonstrate that the modified addition law follows from our scheme , by simply adjusting one of our postulates ( postulate iii , ) .
the modification is as follows : we require that for a set of @xmath115 particles the upper bound on both energy and momentum ( normalized by planck energy @xmath0 ) is to be not @xmath125 , but @xmath115 .
this is equivalent to a postulate that the energy composition law for particles ( _ each having planck energy _ ) is a simple addition . in turn , postulate ( @xmath126)for one particle follows from that as a particular case of @xmath127 .
+ thus , if we use thus modified postulate in eqs.([11a],[11b ] ) , we obtain the following value of constant @xmath37 which now depends on the number of particles @xmath115 : @xmath128 as a result , the energy @xmath129 and momentum @xmath130 of a set of @xmath115 particles follow from eqs .
( [ 11a],[11b ] ) ( we restrict our attention to the positive values of @xmath42 ) : @xmath131 @xmath132 the inverse expressions are @xmath133 @xmath134 @xmath135 and @xmath136 represent the conventional sums of the respective individual quasi - energies @xmath137 ( momenta @xmath138 ) ( as in special relativity ) : @xmath139 the respective casimir is found from eqs.([a3 ] ) and ( [ a4 ] ) if we take the mass @xmath29 to be defined the same way in all the regions , from classical to planck s : @xmath144 the composition laws eqs.([a6 ] ) , ( [ a7 ] ) are reduced to the conventional addition laws not only if all the individual energies @xmath140 ( momenta @xmath141 ) are the same @xcite , but also if at least one of the values @xmath145 ( @xmath146 ) .
these laws take especially simple form for two single particles : @xmath147 99 j.kowalski-glikman and s.nowak , hep - th/0203040 j.lukierski and a.nowicki , hep - th/0203065 j.lukierski and a.nowicki , hep - th/0207022 j.rembielinski and k.smolinski , hep - th/0207031 g.amelino-camelia , gr - qc/0012051 ; int.j.mod.phys.*d*11:35-60,2002 g.amelino-camelia , hep - th/0012238 ; phys.lett.*b*510:255-263,2001 j.magueijo and l.smolin , hep - th/0112090 p.kosinski,j.lukierski,p.maslanka and j.sobczyk , hep - th/9412114 s.majid and h.ruegg,phys.lett . *
b313*,357(1993 ) n.r.bruno,g.amelino-camelia,j.kowalski-glikman,hep-th/0107039 j.lukierski , h.ruegg , w.j.zakrzewski , ann.of phys.,*243 * , 90 ( 1995 ) j.kowalski-glikman , hep - th/0107054 j.magueijo and l.smolin , gr - qc/0207085 m. visser , gr - qc/0205093 | we consider an alternative approach to double special - relativistic theories .
the point of departure is not @xmath0-deformed algebra ( or even group - theoretical considerations ) but rather 3 physical postulates defining particle s velocity , mass , and the upper bound on its energy in terms of the respective classical quantities . for a specific definition of particle s velocity
we obtain magueijo - smolin ( ms ) version of the double special - relativistic theory .
it is shown that this version follows from the @xmath0-poincare algebra by the appropriate choice of on the shell mass , such that it is always less or equal planck s mass .
the @xmath0-deformed hamiltonian is found which invalidates the recent arguments about unphysical predictions of the ms transformation . a recent research ( e.g.@xcite,@xcite,@xcite,@xcite,@xcite,@xcite,@xcite ) on the so - called double special relativity not only reexamined its relation to @xmath0-deformed kinematics , but in one specific example @xcite also subjected to criticism physical predictions of one of these theoretical constructs @xcite .
+ it should be mentioned that as early as in @xmath1 , j.lukierski with collaborators @xcite demonstrated that there exist an infinite set of transformations reducing the @xmath0-deformed casimir in majid - ruegg basis @xcite ( used in all the double - special relativistic theories , e.g.@xcite ) to the diagonal form .
in fact , it is possible to show that any of these transformations correspond to a different choice of what one can consider as a definition of the deformed mass .
this makes it difficult , without any additional assumptions , to choose a unique physical theory corresponding to the respective transformation .
this difficulty is emphasized @xcite by what looks like apparent non - physical predictions of one of these constructions @xcite .
+ here we revisit the latter work @xcite , more specifically its treatment of the energy - momentum domain , this time departing not from the group - theoretical point of view , but rather from certain physically justified restrictions ( postulates ) imposed on the classically - defined physical quantities , namely energy , mass , and velocity .
an analogous approach was used in @xcite for a more narrowly defined goal : a study of possible definitions of @xmath0-deformed velocities and their addition laws .
we begin by introducing the postulates defining \i ) the velocity of a particle , ii)its mass to be the same for any scale ( from classical to planck scale ) and therefore based on the relations provided by the momentum sector of classical relativity , iii)the existence of the upper bound ( the planck energy ) on the values of both energy and momentum .
we also retain the upper bound ( speed of light @xmath2 ) on a particle velocity .
+ in what follows we use units where @xmath3 , planck constant @xmath4 , and boltzmann constant @xmath5=1 .
we denote the planck energy ( momentum ) by @xmath0 which in these units is equal to the inverse of the planck length @xmath6 ( @xmath7 ) .
the classical relation between energy @xmath8 and momentum @xmath9 in these units has the following dimensionless form : @xmath10 where @xmath11 . and
@xmath12 is particle s mass .
+ quite analogously we introduce the dimensionless expressions for the physical energy @xmath13 and momentum @xmath14 ( different from the above energy @xmath15 and momentum @xmath16 ) applicable in the region of planck - scale physics @xmath17 following @xcite we write the general functional relation between the classical energy - momentum @xmath18 ( not physical anymore in the planck - scale phenomena ) and its planck - scale counterpart @xmath19 : @xmath20 where the functions @xmath21 and @xmath22 to be defined .
+ to find these functions we use the above postulates ( i)-(iii ) .
the dimensionless velocity of a particle @xmath23 ( compatible with its classical definition in terms of the energy - momentum ) is defined as follows @xmath24 where @xmath25 .
note that in this definition the velocity @xmath26 looks as the one used in the classical case , except that now this velocity @xmath27 while in the classical case @xmath28 next we use the second postulate ( ii ) which defines particle s mass @xmath29 to be _ the same _ in _ all the regions _ ( from classical to planck scale ) , and independent of the velocity definition ( [ 3a])-([3b ] ) .
@xmath30 finally we require ( postulate iii ) that @xmath31 where the equality signs correspond to @xmath32 + we begin with the velocity definition according to eq .
( [ 3a ] ) . upon substitution of this equation into eq.([2 ] ) we obtain @xmath33 this means that @xmath34 inserting eq.([7 ] ) into the definition of mass eq.([4 ] ) we arrive at the following differential equation : @xmath35 ^ 2=0\ ] ] its solution is : @xmath36 where the integration constant@xmath37 to be determined on the basis of the above postulates .
+ as a result , according to eqs.([2]),([6 ] ) the energy - momentum @xmath38 is : @xmath39 @xmath40 the value of the integration constant @xmath37 and the choice of the respective sign in the obtained solution ( [ 10a]),([10b ] ) are dictated by our postulate ( iii ) , eq .
( [ 5 ] ) .
+ to determine both , we notice that since in the classical limit @xmath41 the positive(negative ) values of @xmath15 should correspond to positive ( negative ) values of @xmath42 respectively .
this means the following : @xmath43 @xmath44 taking the limit @xmath45 of eq.([11a]),(eq . [ 11b ] ) and using our postulate iii ) ( eq.[5 ] ) we get @xmath46 inserting this value of @xmath37 into eqs.([10a]),([11a]),([11b ] ) we obtain the explicit expressions for @xmath47 and @xmath42 @xmath48 @xmath49 these expressions reproduce the results obtained in @xcite with the only difference that here @xmath42 is the antisymmetric function of @xmath15 in contradistinction to @xcite .
+ if we use the classical expressions for @xmath50 ( with the same @xmath26 and @xmath29 in all the regions ) @xmath51 and eqs.([10a]),([10b ] ) then we readily obtain ( restricting our attention to the positive region of @xmath42 ) the respective expressions ( cf.@xcite ) for @xmath52 : @xmath53 from ( [ add ] ) follows that the rest energy @xmath54 less than the mass @xmath29 : @xmath55 here the equality sign corresponds to the classical region @xmath56 + from expressions ( [ 13 ] ) , ( [ 14 ] ) we obtain the inversion formulas : @xmath57 @xmath58 if we use classical casimir and expressions ( [ 15 ] ) and ( [ 16 ] ) then the respective casimirs for the energy - momentum in the planck region are @xmath59 @xmath60 where ( @xmath61 ) corresponds to the positive values of @xmath42 and ( @xmath62 ) corresponds to negative values of @xmath42 . solving eqs.([17a]),([17b ] ) with respect to @xmath42 and choosing the correct signs ( according to the positive and negative values of @xmath42 , remembering that both @xmath63 ) we arrive at the following relation ; @xmath64 curves correspond to the values of masses @xmath65,width=226,height=226 ] @xmath66 where the upper(lower ) sign corresponds to @xmath67 respectively .
it is seen that the regions of the positive and negative values of @xmath68 are the same with accuracy to the sign .
the graph of @xmath68 is shown in fig.1 .
+ based on the relation between @xmath52 and @xmath69 [ eqs . ( [ 11a ] ) , ( [ 11b ] ) , ( [ 13]),([14 ] ) ] and on the expressions for classical lorentz boost of @xmath69 in the @xmath70-direction with a velocity @xmath71 ( in the units of @xmath72 )
, we can calculate in an elementary fashion the respective boost relations ( found by magueijo and smolin in @xcite with the help of group - theoretical analysis ) energy- momentum @xmath52 at the planck scale .
we write them in the dimensionless form : @xmath73 @xmath74 here @xmath75 is the kroenecker delta - function and @xmath76 .
since particle s velocity has been defined as @xmath77 , it is not surprising that eqs.([19a],[19b ] ) yield the velocity addition rule , coinciding with the classical relativistic rule : @xmath78 it was shown in @xcite that within the context of @xmath0-poinciana algebra various possible doubly - special relativity constructions can be viewed as different bases of this algebra . in particular , magueijo - smolin basis @xcite is one of such bases . in a more general scheme of things , j.lukierski and collaborators
@xcite demonstrated that all possible double special relativistic constructions differ by a suitable choice of what one defines as an effective mass .
+ here we show that the magueijo - smolin transformation ( obtained here in an elementary fashion with the help of simple physical postulates)contains an additional physical constraint on the mass . this transformation can be derived pro - forma from @xmath0-deformed algebra , and the result explicitly shows that in this case the particle mass @xmath79 . to demonstrate that we write the relations of the classical basis ( denoted here as @xmath80 ) by rearranging the formulas given in @xcite : @xmath81\equiv ae^{\overline{\pi}_0}[1-e^{-\overline{\pi}_0}cosh(\overline{\mu})]\ ] ] @xmath82 where @xmath37 is an arbitrary constant to be determined .
the respective casimirs are @xmath83 and @xmath84 + we can symmetrize expressions ( [ 20a ] ) , ( [ 20b ] ) by introducing the following quantities : @xmath85\ ] ] @xmath86 combining ( [ 23a ] ) , ( [ 23b ] ) and ( [ 20a ] ) , ( [ 20b ] ) , we obtain : @xmath87 @xmath88 by comparing eqs.([24a ] ) and ( [ 24b ] ) with eqs .
( [ 13 ] ) and ( [ 14 ] ) we immediately see that magueijo - smolin basis follows from @xmath0-deformed algebra if and only if @xmath89 in this case casimir ( [ 22 ] ) reads @xmath90 comparing eq.([26 ] ) with casimir given by eq.([17a ] ) @xcite we arrive at the conclusion that the mass @xmath29 used in the latter is @xmath91 in addition , if we use ( [ add2 ] ) then eq.([27 ] ) imposes the following condition on the value of the rest energy @xmath92 : @xmath93 + at the first glance this condition looks ( predicated on the restriction on particle s mass @xmath94 ) as overly restrictive . on the other hand , considering magueijo - smolin transform as a `` free - standing '' transformations we are not forced to have an upper bound on the rest energy @xmath54 in the planck region where @xmath95 ( that is one half of the upper bound on @xmath42 ) .
still , there is a strong argument in favor of adopting the upper bound on particle s mass .
if we would like to be consistent then it seems quite reasonable to expect that all the quantities in the region of planck scales to be bounded from above by planck energy @xmath0 , or bounded from below by planck length @xmath6 .
+ we have derived magueijo - smolin transformation without resorting to group - theoretical approach by simply defining particle velocity @xmath26 , its mass @xmath29 , and the upper bound on the magnitude of momentum - energy @xmath52 in terms of the respective classical quantities .
in particular , the velocity @xmath26 is defined as @xmath77 ( eq.[3a ] ) . if we substitute into this definition the relations between @xmath96 and the respective quantities @xmath97 , eqs .
( [ 23a ] ) , ( [ 23b ] ) ( used in the conventional treatment based on @xmath0-poincare algebra ) we arrive at the value of the velocity @xmath26 which is exactly the right group velocity @xmath98 ( obeying classical addition law ) introduced in @xcite : @xmath99 interestingly enough , the particle velocity is identical in 2 different bases : magueijo - smolin basis and the basis used in @xcite .
+ to complete our elementary treatment of magueijo - smolin transform , we address its critique expressed in @xcite .
it is argued there that a definition of the particle velocity according to hamilton equations results in a paradoxical situation where @xmath100 particles of different masses moving in an inertial frame with the same velocity will have different velocities when viewed from another inertial frame .
the fallacy of this conclusion is due to the fact that the authors of @xcite used a @xmath101-@xmath102 hamiltonian formalism . + it has been demonstrated ( e.g.,@xcite,@xcite ) that a velocity definition in a non - commutative space is dictated by an appropriate choice of a @xmath102 hamiltonian formalism ( see also @xcite )
to this end let us consider dimensionless relativistic phase space variables @xmath103 normalized by the appropriate planck scales and whose commutation relations are : @xmath104&=&\delta_{ij } , \nonumber \\ \lbrack\pi_0,\xi_0\rbrack & = & -(1-\pi_0 ) , \nonumber \\ \lbrack\pi_0,\xi_i\rbrack & = & 0 , \nonumber \\
\lbrack \xi_0,\xi_i\rbrack & = & \xi_i~ , \nonumber \\
\lbrack \xi_0,\pi_i\rbrack & = & -\pi_i , \nonumber \\ \lbrack\pi_{\alpha},\pi_{\nu}\rbrack & = & 0\end{aligned}\ ] ] the @xmath0-deformed hamilton equations then yield ( cf.@xcite ) : @xmath105 @xmath106 here one particle hamiltonian @xmath107 is taken to be the @xmath0-invariant casimir , eq . :
@xmath108 if we use this expression in the hamilton s equations ( [ 31a ] ) , ( [ 31b ] ) we obtain : @xmath109 from eqs.([32 ] ) immediately follows the expression for the velocity ( [ 3a ] ) which was postulated from the very beginning : @xmath110 + another seemingly unphysical prediction(s ) of magueijo - smolin ( ms ) basis , as was pointed out by j.rembielinski and k.smolinski @xcite , is connected with an apparent difficulty in formulating statistical mechanics based on ms basis .
it is argued that one - particle partition function is divergent when @xmath111 .
however this conclusion is based on an assumption that the temperature in the planck region is the same as in the classical region .
this is not true , since the existence of the upper limit on the energy immediately implies that there exist a relation between the temperature ( dimensionless ) @xmath112 in the planck region and its counterpart @xmath113 in the classical region analogous to the relations between energies in these two regions , eq .
( [ 11a ] ) . as a result , it is not difficult to demonstrate that the partition function ( expressed as an integral ) does not have singularities .
+ additional criticism of @xmath114 transformation is connected to the fact that for a large number @xmath115 of identical particles , each of energy @xmath116 their total internal energy in the thermodynamic limit ( @xmath117 ) does not depend on temperature . but this represents not a deficiency of the basis , but on the contrary , its advantage .
in fact , since the temperature is bounded from above by @xmath118 , in the limit of infinite number of particles , whose total energy tends to the respective upper boundary ( @xmath119 ) the respective temperature @xmath120 tend to its maximum that is to 1 , which explains an apparent absence of the dependence of the internal energy on temperature . in this case
the internal energy is simply equal to the temperature , and both are equal to unity ( in the chosen units ) .
+ in conclusion we would like to say that ms basis following from very simple and consistent physical postulates introduced here represents an attractive model for a description of phenomena which might be associated with planck scale physics .
in fact , the imposition of upper bound on the energy - momentum , and even mass ( if we adopt @xmath0-poinciana roots of the basis ) which are in agreement with a major postulate of planck scale phenomena , is the feature which is @xmath121 in any other bases .
still , there are some problems with this ( and to this matter , with any other @xmath0-deformed ) model(s ) . in particular , the commutation relation @xmath122 is not consistent with the well - known string uncertainty relation . |
let us consider the hamiltonian system @xmath5 with @xmath6 , called the _
potential_. system describes the motion of a particle in the plane submitted to the force field @xmath7 .
it always admits the so - called _ hamiltonian _ @xmath8 as a rational first integral .
the potential @xmath3 is called _ ( rationally ) integrable _ if system admits another rational first integral @xmath9 , functionally independent on @xmath10 . intuitively , the integrability of @xmath3 is equivalent to the fact that can be solved in explicit terms .
integrability is a rare phenomenon and it is in general a difficult task to determine whether a given potential is integrable or not . for _ homogeneous potentials _ in @xmath11 , _ necessary _ conditions for integrability
were given by morales - ramis @xcite and by morales - ramis - sim @xcite .
building on these works , we design in this article an algorithm which takes as input a _
family _ of rational homogeneous potentials @xmath12 depending on parameters @xmath13 and which computes a set of constraints on the parameter values @xmath14 that are necessary for the integrability of @xmath15 .
these constraints turn out to be of polynomial nature in @xmath16 .
there are several difficulties in this parameterized setting .
the first one is that the integrability constraints provided by the morales - ramis theory on which our whole approach relies , are expressed in terms of quantities ( eigenvalues of hessian matrices at darboux points , see section [ sec : preliminaries ] ) which are not easily accessible .
we circumvent this basic difficulty by using an equation that relates the eigenvalues , but this brings a new technical complication since the equation is of diophantine type .
a third difficulty is that the number of darboux points itself may depend on the parameters , leading to _ singular _ cases .
we follow a classical approach , inspired mostly by ideas in @xcite .
our contribution to the topic is effective and algorithmic , as we provide a complete , proven and implemented algorithm for the problem of computing necessary integrability conditions for planar parametrized homogeneous potentials , with precise output specifications .
our algorithm uses classical tools in computer algebra , such as polynomial ideal elimination based on grbner bases techniques .
an important feature is the use of ( complex ) polar coordinates to represent homogeneous potentials by univariate rational functions with parameters @xmath17 .
this change of representation considerably simplifies the computations and the proofs .
for instance , in polar representation , _ singular _ cases are those with non - generic multiplicity of the roots / poles of @xmath18 .
they are treated by our algorithm , which builds a tree containing each possible singular case .
this approach is related with comprehensive grbner bases @xcite , which are avoided here thanks to some a priori knowledge about singular cases . in summary ,
our strategy for computing necessary integrability conditions for @xmath3 consists in 4 steps : _ ( i ) _
rewrite @xmath3 in polar coordinates ; _
( ii ) _ set up a diophantine equation whose solutions belong to the so - called _ morales - ramis table _ ( that contains all possible eigenvalues of the hessian of @xmath3 at darboux points of @xmath3 ) ; _ ( iii ) _ solve this diophantine equation ; _ ( iv ) _ rewrite the condition of having prescribed eigenvalues at darboux points as polynomial conditions on @xmath19 .
some prior works used a similar strategy , but it was unclear which cases were possible to tackle , in particular for singular ones .
the approach was not fully automatized and this explains that results were only available for special families of potentials , for instance polynomials of small degree ( 3 or 4 ) @xcite , as the number of singular cases grows very fast ( already @xmath20 for polynomials of degree @xmath21 ) . by contrast , our treatment is unified and fully automated , and it allows not only to retrieve ( and sometimes correct ) known results , but more importantly , to treat potentials of degrees previously unreached ( up to 9 ) . by applying our algorithm to polynomial potentials
, we found three new cases admissible for integrability at degree @xmath21 ( but still not proved to be integrable ) , and various new families for higher degrees .
an even more striking application of our algorithm is the first complete proof of the non - integrability of the _ collinear three body problem _ , on which only partial results were known @xcite .
the direct approach that consists in searching first integrals @xcite is complementary to our ( non-)integrability analysis , as our algorithm helps either proving that the lists in @xcite are complete , or finding new unknown cases . .
( this is because the morales - ramis theory is much less powerful when @xmath22 . ) _ convention of notation : to avoid confusion , we will use bold letters for variables / parameters , and italic letters for parameter values_.
there exist strong integrability constraints ( see theorem [ thm : morales ] below ) .
they require to deal with darboux points , whose definition we now recall .
note that , by homogeneity , we could have chosen an arbitrary normalization non - zero constant on the right - hand side of . in the literature , this normalization constant is frequently chosen equal to @xmath26 @xcite .
however , our choice is deliberate , see the remark after theorem [ thm : morales ] . the following result ( which is an application of a more general criterion due to morales and ramis @xcite ) provides _ necessary _ conditions for integrability under the form of constraints on eigenvalues of hessian matrices at each darboux point .
it is the basic ingredient for numerous non - integrability proofs @xcite .
roughly , its main idea is as follows .
a darboux point leads to a straight line orbit of the dynamical system associated to @xmath3 , around which the system can be linearized .
if the whole system is integrable , then the linearized system , which in our case corresponds to a hypergeometric equation , is also integrable .
thus the integrability table of theorem [ thm : morales ] below is reminiscent of kimura s classification @xcite of solvable hypergeometric equations .
[ thm : morales ] ( morales - ramis @xcite ) let @xmath6 be a homogeneous rational function of homogeneity degree @xmath1 , and let @xmath27 be a darboux point of @xmath3 . if the potential @xmath3 is integrable , then for any eigenvalue @xmath28 of the hessian matrix of @xmath3 at @xmath29 , the pair @xmath30 belongs to the following table , for some @xmath31 . for polynomials of degree @xmath32 and @xmath33 ,
we retrieve known results ( leading to a complete classification of integrable homogeneous potentials of degree @xmath32 , and almost complete for degree @xmath33 ) . for @xmath34
, we obtain after simplification the following ideals @xmath35,[\a_4,\a_5],[36\,\a_5\a_1-\a_3 ^ 2,6\a_4\a_1-\a_3\a_2,6\a_2\a_5-\a_4\a_3],[44979\a_2 ^ 2-\\ 376712\a_3\a_1,66879684\a_5\a_1 - 75625\a_3 ^ 2,16719921\,\a_{{4}}\a_{{2}}-4708900\,{\a_{{3}}}^{2},\\ -376712\,\a_3\a_5 + 44979\,{\a_{{4}}}^{2},8178\,\a_{{4}}\a_{{1}}-275\,\a_{{3}}\a_{{2}},8178\,\a_{{2}}\a_{{5}}-275\,\a_{{4}}\a_{{3 } } ] , \\ [ -392\,\a_{{3}}\a_{{1}}+99\,{\a_{{2}}}^{2},484\,\a_{{5}}\a_{{1}}-{\a_{{3}}}^{2},1089\ , \a_{{4}}\a_{{2}}-196\,{\a_{{3}}}^{2},\\ -392\,\a_{{3}}\a_{{5}}+99\,{\a_{{4}}}^{2},22\,\a_{{4}}\a_{{1}}-\a_{{3}}\a_{{2}},22\,\a_{{2}}\a_{{5}}-\a_{{4}}\a_{{3 } } ] , \\ [ -40\,\a_{{3}}\a_{{1}}+7\,{\a_{{2}}}^{2},15876\,\a_{{5}}\a_{{1}}-25\,{\a_{{3}}}^{2},441\,\a_{{4}}\a_{{2}}-100\,{\a_{{3}}}^{2},\\ -40\a_3\a_5 + 7\a_4 ^ 2,126\,\a_{{4}}\a_{{1}}-5\,\a_{{3}}\a_{{2}},126\,\a_{{2}}\a_{{5}}-5\,\a_{{4}}\a_{{3 } } ] \end{split}\ ] ] the first two cases are the exceptional ones with @xmath36 , and the other cases lead indeed to integrable potentials .
these are exactly the conditions found in @xcite . at degree
@xmath21 , _ two non - trivial new potentials ( up to conjugation and rotation - dilatation ) are detected , not known to be integrable _ , but satisfying all integrability conditions .
their eigenvalue sets are @xmath37 .
the second has algebraic coefficients of degree @xmath38 , and the first is @xmath39 at degree @xmath40 and @xmath41 , the only possible cases are either already known , or @xmath36 , or they do not have darboux points .
thus for degree @xmath41 , the only cases whose integrability status is still unknown are up to rotation - dilatation @xmath42 and @xmath43 .
so we obtained a classification of integrable homogeneous polynomial potentials of degree @xmath41 . for degree @xmath44 and @xmath4 ,
some optimizations are necessary for the algorithm to be workable .
indeed , thanks to the fact that our family is invariant by rotation - dilatation , it is only necessary to consider functions @xmath45 with the coefficient @xmath46 and with the trailing coefficient of one polynomial factor equal to @xmath26 .
this removes two variables in the elimination ideal , and reduces by @xmath47 the hilbert dimension of the output . at degree
@xmath4 , we find _ three new cases satisfying all integrability conditions _ ; they are given by @xmath48 .
m. i. vigo - aguiar , m. e. sansaturio , and j. m. ferrndiz .
integrability of hamiltonians with polynomial potentials .
, 158(1):213224 , 2003 .
selected papers from the conference on computational and mathematical methods for science and engineering ( alicante , 2002 ) . | let @xmath0 be a rationally parametrized planar homogeneous potential of homogeneity degree @xmath1 .
we design an algorithm that computes polynomial _ necessary _ conditions on the parameters @xmath2 such that the dynamical system associated to the potential @xmath3 is integrable .
these conditions originate from those of the morales - ramis - sim integrability criterion near all darboux points .
the implementation of the algorithm allows to treat applications that were out of reach before , for instance concerning the non - integrability of polynomial potentials up to degree @xmath4 .
another striking application is the first complete proof of the non - integrability of the _ collinear three body problem_. * categories and subject descriptors : * + i.1.2 [ * computing methodologies * ] : symbolic and algebraic manipulations _ algebraic algorithms _ + * general terms : * algorithms , theory . + * keywords : * integrability , potentials , algorithms . |
we are grateful to the u.s .
department of energy for financial support . | this paper demonstrates that complex @xmath0-symmetric periodic potentials possess real band spectra
. however , there are significant qualitative differences in the band structure for these potentials when compared with conventional real periodic potentials . for example , while the potentials @xmath1 @xmath2 have infinitely many gaps , at the band edges there are periodic wave functions but no antiperiodic wave functions . numerical analysis and higher - order wkb techniques
are used to establish these results .
.5 cm for a quantum mechanical model having a periodic potential the schrdinger equation is @xmath3 where the potential @xmath4 is periodic with period @xmath5 : @xmath6 in conventional treatments of eq .
( [ e1 ] ) @xcite the periodic potential @xmath4 is assumed to be real . imposing the condition that the wave function @xmath7 be bounded leads to a real spectrum consisting of continuous bands separated by gaps .
there is an infinite number of bands and gaps , except for the special family of so - called _ finite - gap _ potentials such as the lam potentials @xcite . in this note
we extend the conventional analysis to include the case of complex periodic potentials .
we find that complex periodic potentials having @xmath0 symmetry exhibit _ real _ band spectra , despite the non - hermitian character of the schrdinger equation ( [ e1 ] ) .
( here , @xmath8 represents parity reflection and @xmath9 represents time reversal . ) potentials having this symmetry satisfy @xmath10^*=v(x ) .
\label{e3}\end{aligned}\ ] ] examples of such potentials are @xmath11 , @xmath12 , and @xmath13 .
in addition to the property that these potentials have real spectra , the band structure displays several novel features that are strikingly different from the case of real periodic potentials .
the work reported here was motivated by recent investigations of non - hermitian @xmath0-symmetric hamiltonian models having real discrete spectra .
one such class of models is defined by the hamiltonian @xcite @xmath14 despite the lack of conventional hermiticity , the spectrum of this hamiltonian is real , positive , and discrete ; each of the energy levels increases as a function of increasing @xmath15 .
it has been observed that the reality of the spectrum is a consequence of @xmath0 symmetry , which is a weaker condition than hermiticity .
this observation has also been used to construct new classes of quasi - exactly solvable quantum theories @xcite and to study new kinds of symmetry breaking in quantum field theory @xcite .
there have been many other instances of non - hermitian @xmath0-invariant hamiltonians in physics .
energies of solitons on a _ complex _ toda lattice have been found to be real @xcite .
hamiltonians rendered non - hermitian by an imaginary external field have been used to study population biology @xcite and to study delocalization transitions such as vortex flux - line depinning in type - ii superconductors @xcite . in these last two cases ,
initially real eigenvalues bifurcate into the complex plane due to the increasing external field , indicating the growth of populations or the unbinding of vortices .
we begin by summarizing the standard floquet analysis of the schrdinger equation ( [ e1 ] ) for the case where @xmath4 is real and periodic @xcite .
we define a _ fundamental pair _ of linearly independent solutions @xmath16 and @xmath17 satisfying the initial conditions @xmath18 any solution @xmath7 to eq .
( [ e1 ] ) is a linear combination of @xmath16 and @xmath17 .
it is then a straightforward algebraic exercise to show that @xmath7 is bounded provided that the _ discriminant _ @xmath19 , which is defined by @xmath20 satisfies the constraint @xmath21 to illustrate the features of the discriminant we consider a typical periodic potential , @xmath22 , for which the period @xmath23 . in fig .
[ f1 ] we plot @xmath19 as a function of @xmath24 .
note that @xmath19 is oscillatory and is well approximated by the function @xmath25 for large @xmath24 .
the crucial feature of @xmath19 , which can not be seen from this plot , is that its graph crosses the lines @xmath26 an infinite number of times ; each of the maxima of @xmath19 lies above @xmath27 and each of the minima lies below @xmath28 .
the regions of energy for which @xmath29 are called _ bands _ and the regions of energy for which @xmath30 are called _ gaps_. the gap size decreases exponentially as a function of @xmath24 .
the band edges at which @xmath31 correspond to periodic solutions to eq .
( [ e1 ] ) , @xmath32 , and the band edges at which @xmath33 correspond to antiperiodic solutions @xmath34 . now consider the calculation of the discriminant for the case of a _ complex _ periodic potential @xmath4 .
in general , a complex periodic potential will have no bounded solutions because the discriminant is typically complex . however , for complex @xmath0-symmetric periodic potentials , one can easily show that the discriminant @xmath19 is real when @xmath24 is real .
the @xmath0 symmetry is crucial here ; for a potential that is not @xmath0 symmetric [ one that does not satisfy eq .
( [ e3 ] ) ] , the discriminant is complex for all values of @xmath24 .
having established that complex @xmath0-symmetric periodic potentials have real discriminants , we can then apply the criterion in eq .
( [ e7 ] ) to locate the real energy bands within which the corresponding wave function @xmath7 is a bounded function .
we have computed the discriminants for the class of complex @xmath35-symmetric periodic potentials @xmath36 in figs .
[ f2]-[f7 ] we plot the discriminants for the cases @xmath37 . while these plots superficially resemble fig .
[ f1 ] for large @xmath24 , they exhibit new and intriguing features that are significantly different from the case of a real periodic potential .
the most obvious new feature is the appearance for @xmath38 of a local minimum of @xmath19 between @xmath28 and @xmath27 .
such a dip is rigorously forbidden in the case of real periodic potentials @xcite . the most dramatic differences between the discriminants for the complex @xmath35-symmetric periodic potentials in eq .
( [ e8 ] ) and real periodic potentials can not be easily seen in the figures .
we have performed a careful numerical study of the local minima and maxima of @xmath19 .
our study reveals that _ none of the local minima lies below _
@xmath28 .
this shows that there are _ no antiperiodic solutions _
@xmath7 to the schrdinger equation ( [ e1 ] ) .
nevertheless , all of the local maxima of @xmath19 lie above @xmath27 .
hence , there are an infinite number of band gaps in the spectrum and the band - edge wave functions are periodic . @xmath39 @xmath39 to perform this numerical analysis it is necessary to locate the positions of the local minima and maxima of @xmath19 to extremely high accuracy
. this can be done using wkb methods @xcite .
we take the energy @xmath24 to be large @xmath40 and define a small parameter @xmath15 by @xmath41 then we make an exponential _ ansatz _ for the wave function @xmath7 : @xmath42 . \label{e10}\end{aligned}\ ] ] substituting @xmath7 in eq .
( [ e10 ] ) into the schrdinger equation ( [ e1 ] ) gives a recursion relation for the functions @xmath43 : @xmath44 ^ 2&=&0,\nonumber\\ iq_0''(x)-2q_0'(x)q_1'(x)&=&0,\nonumber\\ iq_1''(x)-2q_0'(x)q_2'(x)-[q_1'(x)]^2-v(x)&=&0,\nonumber\\ iq_{n-1}''(x)-\sum_{j=0}^nq_j'(x)q_{n - j}'(x)&=&0\quad(n\geq3 ) .
\label{e11}\end{aligned}\ ] ] the solution to these equations is @xmath45,\nonumber\\
q_4(x)&=&\pm{1\over8}\left(v'(x)-v'(0)-\int_0^xdt\,v^2(t)\right),\nonumber\\ q_5(x)&=&{i\over16}\left[v''(x)-v''(0)-2v^2(x)+2v^2(0)\right],\nonumber\\ q_6(x)&=&\mp{1\over32}\left(v'''(x)-v'''(0)-5v(x)v'(x)+5v(0)v'(0 ) + \int_0^xdt\,[2v^3(t)-v(t)v''(t)]\right ) , \label{e12}\end{aligned}\ ] ] and so on .
note that @xmath43 is normalized so that @xmath46 .
in general , the formula for @xmath47 is @xmath48\quad(n\geq3 ) .
\label{e13}\end{aligned}\ ] ] in order to obtain a wkb formula for the discriminant @xmath19 in eq .
( [ e6 ] ) we need to evaluate @xmath43 at @xmath49 .
the periodicity of the potential @xmath4 simplifies the results considerably ; when @xmath50 is odd , @xmath51 and when @xmath50 is even , only the integrals in eq .
( [ e12 ] ) remain : @xmath52 , \label{e14}\end{aligned}\ ] ] and so on .
the wkb formula for the discriminant is particularly simple when the potential @xmath4 is @xmath0 symmetric : @xmath53 . \label{e15}\end{aligned}\ ] ] one obtains the same formula for potentials that are real and symmetric under parity @xmath8 . for the complex @xmath0-symmetric potentials @xmath4 in ( [ e8 ] ) the wkb formula for the discriminant in eq .
( [ e15 ] ) is @xmath54 .
\label{e16}\end{aligned}\ ] ] a similar wkb formula exists for the real odd - parity potentials @xmath55 : @xmath56 . \label{e17}\end{aligned}\ ] ] we can illustrate the extreme accuracy of these wkb approximations by comparing them with numerical computations of the discriminant .
for example , for @xmath57 at @xmath58 ( which corresponds to @xmath59 ) we find numerically that @xmath60 .
the first three orders of the wkb approximation taken from eq .
( [ e16 ] ) give @xmath61 , @xmath62 , and @xmath63 .
similarly , for @xmath64 at @xmath58 we find numerically that @xmath65 .
the first three orders of the wkb approximation taken from eq .
( [ e17 ] ) give the same values : @xmath66 , @xmath62 , @xmath63 .
despite this impressive precision , the wkb formulas ( [ e16 ] ) and ( [ e17 ] ) can not be used directly to answer the crucial question of whether there are band gaps because these approximations to the discriminant @xmath19 never cross the values @xmath26 .
the reason for this inadequacy of the wkb approximation is that the differences @xmath67 and @xmath68 are exponentially small when @xmath69 .
therefore , these differences are subdominant with respect to the wkb asymptotic series and are not accessible to any order in powers of @xmath15 . indeed
, the wkb series can only provide information about quantities with an _ algebraically _ small error , and not an exponentially small error .
we emphasize that the wkb approximation has this shortcoming only at the maxima and minima of the approximation . at other points
any exponential discrepancy is completely negligible compared with algebraic errors .
the wkb series is still an extremely useful ingredient in the numerical search for zeros of @xmath70 .
( these zeros are the dividing points between bands and gaps . )
our procedure is first to find the energies at which there are maxima and minima of the wkb approximation to the discriminant and then to evaluate , with high numerical precision , the actual value of the discriminant in a tiny neighborhood of each of these points . by doing this
we can determine whether or not the discriminant @xmath19 crosses the lines @xmath26 .
for the real periodic potentials @xmath71 our procedure confirms the rigorous theoretical result that every maximum of the discriminant lies above @xmath27 and every minimum lies below @xmath28 . consider , for example , the potential @xmath22 . from fig .
1 , it is clear that the first maximum lies above @xmath27 .
the first minimum occurs at @xmath72 , where the discriminant has the value @xmath73 .
the second maximum occurs at @xmath74 , where the discriminant is @xmath75 .
similar behavior is found for the other potentials in the class @xmath71 . in stark contrast , for the potentials @xmath76 , while the maxima of the discriminant lie above @xmath77 , the minima of the discriminant lie above @xmath28 .
thus , for these potentials there are no antiperiodic wave functions . as an example
, lengthy and delicate numerical analysis verifies that for the potential @xmath78 the first three maxima of the discriminant @xmath19 are located at @xmath79 , @xmath80 , and @xmath81 .
the value of the discriminant @xmath19 at these energies is @xmath75 , @xmath82 , and @xmath83 .
the first two minima of the discriminant are located at @xmath84 and @xmath85 and at these energies @xmath19 has the values @xmath86 and @xmath87 .
similar behavior is found for the other potentials in the class ( [ e8 ] ) .
we conclude by pointing out that from the expressions for @xmath88 in eq .
( [ e14 ] ) the wkb series truncates if the potential is a polynomial in @xmath13 .
for example , for the complex @xmath0-symmetric periodic potential @xmath89 the wkb series in eq .
( [ e15 ] ) truncates after the first term because @xmath90 vanishes for @xmath91 . for this case
the wkb approximation is exact and the discriminant is given by @xmath92 one can verify this result directly by solving the schrdinger equation ( [ e1 ] ) for this potential exactly ; the solution is a bessel function : @xmath93 . |
directional detection allows for unambiguous observation of dark matter ( dm ) even in presence of insidious backgrounds . when a weakly interacting massive particle ( wimp ) collides with a nucleus in the active mass of the detector , the direction of the nuclear recoil encodes the direction of the incident particle . for detectors consisting of a low - pressure gas ( about 50 torr ) ,
the typical length of such a recoil is 1 - 2 mm , which is sufficiently long to be reconstructed .
the simplest models of the distribution of wimps in our galaxy suggest that the orbital motion of the sun about the galactic center will cause an earth - bound observer to experience a wimp wind with speed 220 km / s ( the galacto - centric velocity of the sun ) , originating from the direction of the sun s motion . because the direction of this wind is inclined by 42@xmath1 with respect to the rotational axis of the earth , the average dm direction changes by almost 90@xmath1 every 12 hours @xcite . an ability to measure such a direction would allow for a powerful suppression of insidious backgrounds ( e.g. neutrons ) as well as a unique instrument to test local dm halo models .
our detector consists of a low - pressure tpc with optical readout .
the target gas is @xmath0 , whose spin 1/2 fluorine nuclei provide the ideal target material to detect spin - dependent interactions @xcite . in addition
, @xmath0 has high scintillation efficiency and low diffusion , and is ideal for underground detectors because it is non - toxic and non - flammable .
when an incoming wimp collides with a @xmath0 molecule at the design pressure of 50 torr , the emitted fluorine nucleus recoils 1 - 2 mm , ionizing the surrounding gas .
the primary electrons drift toward the amplification region , where charge multiplication takes place . to achieve 2d resolution ,
the amplification plane is built out of woven meshes @xcite . in the avalanche
, scintillation photons are produced together with the electrons in the ratio of 1:3 @xcite .
such photons are imaged by a ccd camera triggered by a pmt or electronic readout of the charge collected on the meshes .
the dmtpc detector is designed to measure the following quantities : * total light collected by the ccd , which is proportional to the energy of the nuclear recoil ; * length of the recoil track projected onto the amplification plane ; * length of the recoil track perpendicular to the amplification plane inferred from the width of the pmt signal ; * versus of the nuclear recoil ( `` head - tail '' ) as determined by the shape of the energy loss along the recoil track ( de / dx ) . at the typical energy of these recoils , de / dx decreases as the track slows down .
the simultaneous measurement of energy and length of the recoil effectively rejects electrons and @xmath2 tracks .
several prototypes ( figure 1 , top left ) have been built to prove the dmtpc detector concept .
alpha tracks from @xmath3am and low - energy neutrons from @xmath4cf are used to calibrate the device and measure its performance @xcite . for nuclear recoils of 100 kev , where the angular resolution is 15@xmath1 , we have achieved an energy resolution of @xmath5 10% .
typical gas gains are @xmath5 10@xmath6 - 10@xmath7 .
the intrinsic spatial resolution is of the order of 100 @xmath8 m , adequate to image recoils of 1 - 2 mm length with typical diffusion of 200 - 700 @xmath8 m .
the detector performance has been simulated using a combination of srim @xcite , casino @xcite , and geant4 @xcite .
the data - mc agreement is better than 10% .
a 10-liter detector @xcite has been built and is being commissioned in the laboratory .
underground operation is expected in early 2009 with the goal of studying backgrounds and place our first limits on spin - dependent interactions .
studies of the nuclear recoils induced by low - energy neutrons from @xmath4cf have demonstrated that the dmtpc detector can measure the energy , direction , and versus of recoiling nuclei @xcite .
figure 1 ( bottom left ) shows a typical nuclear recoil reconstructed in the dmtpc detector at a pressure of 75 torr .
the neutrons were traveling right to left .
the decreasing de / dx along the track direction is well visible , indicating the capability of determining the sense of the direction ( `` head - tail '' ) on an event - by - event basis .
mc studies indicate excellent head - tail discrimination can be obtained for nuclear recoils above 70 kev in cf@xmath9 at a pressure of 50 torr .
the dmtpc collaboration is designing a 1-m@xmath10 detector to be operated in an underground site .
this detector has two 1-m@xmath11 amplification planes . in the current design ,
each plane serves two 25-cm drift regions , and is imaged by 10 ccd cameras and 10 pmts . by running this device for one year at 100 torr
we will obtain an exposure of 100 kg - days . assuming a threshold of 50 kev and passive neutron shielding
, this device will allow us to set a limit on the spin - dependent cross section at @xmath12 , as shown in figure 1 ( right ) .
this high sensitivity is achieved despite the limited mass due to the excellent sensitivity that fluorine has to spin - dependent interactions @xcite and because directionality increases the sensitivity to dark matter by over one order of magnitude @xcite .
a larger detector with an active mass of a few hundred kg will explore a significant portion of the mssm parameter space .
the observation of directional wimp signal by this detector will allow us to test our understanding of the local dm halo model .
this detector is an ideal candidate for the dusel laboratory in south dakota .
this work is supported by the advanced detector research program of the u.s .
department of energy ( contract number 6916448 ) , the national science foundation , the reed award program , the ferry fund , the pappalardo fellowship program , the mit kavli institute for astrophysics and space research , and the mit physics department .
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d 77 , 043532 ( 2008 ) . | directional detection of dark matter allows for unambiguous direct detection of wimps as well as discrimination between various dark matter models in our galaxy .
the dmtpc detector is a low - pressure tpc with optical readout designed for directional direct detection of wimps . by using @xmath0 gas as the active material
, the detector also has excellent sensitivity to spin - dependent interactions of dark matter on protons . |
methanol masers in the @xmath0 line at 84521.21 mhz were found by batrla and menten ( 1988 ) and menten ( 1991 ) towards ngc 2264 , omc-2 , and dr 21 , but no extended survey in this line had been done .
the @xmath0 transition belongs to the class i ( menten , 1991 ) .
its excitation is similar to that of the @xmath2 and @xmath3 transitions .
since methanol masers emit in several lines of the same class , we expect the detection of a fairly large number of maser sources at 84.5 ghz .
their parameters should be taken into account when modeling maser sources .
therefore , we made a survey of known class i maser sources at 84.5 ghz .
the observations were carried out in may 1997 and march 2000 with the millimetre - wave telescope of the onsala space observatory . a sample of 13 sources at 84.5 ghz was observed in june 2000 with the 12-m nrao telescope at kitt - peak in remote mode from astro space center .
emission was detected in 51 of the 54 sources observed .
the spectra are markedly different from those of the strongest class i transition , @xmath4 at 44.1 ghz . at 44.1 ghz ,
most of the sources from our sample have bright and narrow maser features , whereas broad quasi - thermal components dominate at 84.5 ghz , and narrow ( @xmath5 km / s ) features are present in the spectra of only 17 of the 51 detected sources ( fig .
1 ) . however , it is possible that at least some of the quasi - thermal lines contain narrow maser components .
the shape of the 84.5 ghz spectra closely resembles the shape of the spectra of the same sources in the @xmath1 ( valtts et al .
1995 ) and @xmath3 ( slysh et al .
1999 ) transitions at 95.2 and 132.8 ghz , respectively .
the relationships between the integrated intensities of thermal lines at 84.5 , 95.2 and 132.8 ghz can be fitted by the equations @xmath6 and @xmath7 here @xmath8 is the main - beam brightness temperature .
the relative decrease of the line intensities at 132.8 , and especially at 95.2 ghz , is probably connected with the decrease of level population with increase of their energies : at a gas temperature of 35 k the population of the @xmath9 level is about 40% of the population of the @xmath10 level , making it possible to explain the relationships obtained .
note the detection of narrow features at 84.5 and 95.2 ghz towards the young bipolar outflow l 1157 . unlike other methanol masers , which are associated with high - luminosity young stellar objects ( above @xmath11 ) ,
this one is associated with an object of low luminocity ( @xmath12 ) .
slysh et al . ( 1999 ) showed that even quasi - thermal @xmath3 lines are typically inverted and their quasi - thermal appearance indicates that the line opacities are not large enough to cause significant narrowing . since the excitation of the @xmath0 transition is similar to that of the @xmath3 transition it is possible that the quasi - thermal @xmath0 lines are also inverted . to test this hypothesis , we determined the excitation temperature of the @xmath0 lines using the intensities of the @xmath13 lines at 157.2 ghz , measured by slysh et al .
the excitation temperatures were derived analytically using a simple method described by slysh et al .
we applied this method to 20 quasi - thermal sources , and for each , obtained negative excitation temperature between @xmath14 k and @xmath15 k , i.e. , the @xmath0 quasi - thermal lines proved to be strongly inverted .
the excitation temperatures derived in this way are distorted by a number of factors , such as the line opacities , influence of microwave background etc ( slysh et al . , 1999 ) .
therefore , we verified the results using a grid of lvg methanol models spanning the ranges @xmath16 @xmath17 in density , 10100 k in temperature , and @xmath18 @xmath17/(km / s pc@xmath19 ) in methanol density divided by the velocity gradient .
for each source , we selected the models corresponding to the observed ratios of the main - beam brightness temperatures of the @xmath0 line and the @xmath13 and @xmath20 lines , observed by slysh et al .
the results are as follows : for the majority of the sources , we found that only models with inversion of the @xmath0 transition or models with unlikely high methanol abundances satisfy the observed line ratios . in g29.95 - 0.02 , g34.26 + 0.15 ,
ngc 7538 , w 49n , and w 51e1/e2 , the observed intensity ratios can be obtained both in models with the inversion and in realistic models with positive excitation temperatures . however , since a number of models with inversion ( i.e. , same as those for the other 15 sources ) are applicable to these objects as well , it is not clear whether they are somehow different from the others or not .
thus , the quasi - thermal @xmath0 methanol lines , like the @xmath3 lines , are typically inverted .
this result confirms the plausibility of models in which compact class i masers appear in extended sources as a result of an appropriate velocity field ( see , e.g. , sobolev et al .
in the series of observations , performed in june 2000 with the 12-m nrao telescope at kitt - peak we tried to find linear polarization at 84.5 ghz towards 13 sources .
we expected that class i methanol masers may arise in a gas permeated by magnetic field and may exhibit a weak linear polarization similar to that of some h@xmath21o masers .
two polarization channels of the 3-mm receiver at kitt - peak can measure both senses of linear polarization simultaneously .
different brightness temperatures , measured in different channels would mean that the radiation is linearly polarized .
one can test whether the difference is a result of linear polarization by tracing the source during a sufficiently long time range .
owing to the diurnal rotation of the sky the direction of the polarization plane will vary , resulting in regular variations of the measured brightness temperatures in the two channels and hence , in a regular variation of the difference between them .
we failed to find any difference between channels in 12 sources and obtained the upper limits for the degree of linear polarization within the range 3%30% .
the only exception is a strong maser m 8e .
here we found a small difference between polarization channels , which might appear due to a weak ( @xmath22 ) linear polarization at 84.5 ghz .
unfortunately , this southern source ( @xmath23 ) can not be traced along a significant part of its diurnal trajectory from the northern hemisphere .
therefore , we could not detect any regular variation of the difference between channels and can not state that the difference is a result of linear polarization .
further polarization measurements of this source at 84.5 ghz are required .
the authors are grateful to the staff of the onsala space observatory and to the staff of the kitt peak telescope for providing help during the observations .
the work was done under a partial financial support of the russian foundation for basic research ( grant no . 95 - 02 - 05826 ) and intas ( grant no . 97 - 1451 ) .
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, booth r. , & winnberg , a. , 1995 , astronomy reports , 39 , 18 | fifty - one object in the @xmath0 methanol line at 84.5 ghz was detected during a survey of class i maser sources .
narrow maser features were found in 17 of these .
broad quasi - thermal lines were detected towards other sources .
one of the objects with narrow features , the young bipolar outflow l 1157 was also observed in the @xmath1 line at 95.2 ghz ; a narrow line was detected at this frequency .
analysis showed that the broad lines are usually inverted .
the quasi - thermal profiles imply that the line opacities are not larger than several units .
these results confirm the plausibility of models in which compact class i masers appear in extended sources as a result of an appropriate velocity field .
measurements of linear polarization at 84.5 ghz in 13 sources were made .
no polarization was found except a tentative detection of a weak polarization in m 8e .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
hard exclusive meson production in deep inelastic lepton scattering provides access to the unknown generalized parton distributions ( gpds ) of the nucleon @xcite . for such reactions
, it has been shown that for longitudinal virtual photons , the @xmath3 amplitude can be factorized into a hard lepton - scattering part and two soft parts which parameterize the structure of the nucleon by gpds and the structure of the produced meson by distribution amplitude @xcite .
gpds reflect the 3-dimensional structure of the nucleon and contain information about the total angular momentum carried by partons in the nucleon .
hard exclusive production of @xmath0 mesons is sensitive to the gpds @xmath4 and @xmath5 which are the ones related to the total angular momenta @xmath6 and @xmath7 of quarks and gluons in the nucleon @xcite .
the gpd @xmath4 is already somewhat constrained , while the gpd @xmath5 is still unknown . in the case of a transversely polarized target ,
the interference between the gpds @xmath4 and @xmath5 was shown to lead to a transverse target - spin asymmetry ( ttsa ) @xcite .
in contrast to the cross section measurements , the ttsa depends linearly on the helicity - flip distribution @xmath5 with no kinematic suppression of its contribution with respect to the other gpds . therefore the ttsa of exclusive @xmath0 production can constrain the total angular momenta @xmath6 and @xmath7 .
for an unpolarized ( u ) beam and a transversely ( t ) polarized target the ttsa @xmath8 is defined as @xmath9 where the target polarization @xmath10 is defined w.r.t . the lepton beam direction and
the angles @xmath11 and @xmath12 are the azimuthal angles of , respectively , the produced @xmath0 meson and the target spin vector around the virtual photon direction w.r.t . the lepton scattering plane ( see figure [ fig : angle ] ) @xcite .
the cross section of exclusive @xmath0 production can be factorized in terms of angular dependent and angle - independent parts : @xmath13 where @xmath14 is the bjorken scaling variable , @xmath15 is the squared virtual - photon four - momentum , @xmath16 . here
@xmath17 is the squared four - momentum transfer to the target and @xmath18 represents the minimum value of @xmath17 .
the complete expression for the cross section of @xmath0 production is given in @xcite .
the angular distribution @xmath19 can be written , @xmath15 and @xmath20 are omitted . ] in terms of asymmetries : @xmath21 where @xmath22 is the unpolarized asymmetry with @xmath23 , @xmath24 being the unpolarized angular distributions and @xmath25 is the transverse asymmetry with the transversely polarized angular distribution @xmath26 .
r0.45 since the factorization theorem is proven for longitudinal photons only @xcite , the asymmetry of @xmath0 mesons induced from longitudinal photons is of theoretical interest . under the assumption of @xmath2-channel helicity conservation ( schc ) , which implies that a longitudinal vector meson originates from a longitudinal photon ,
the longitudinal component of the asymmetry is obtained experimentally through the decay angular distribution of @xmath0 ( @xmath27 ) .
each @xmath0 helicity state ( l , t ) results in a characteristic dependence of the @xmath28 cross - section on the @xmath29 polar angle of @xmath30 in the @xmath0 rest frame @xcite .
the interference terms between different helicities of the @xmath0 production are canceled if the cross section is integrated over the @xmath31 azimuthal decay angle of @xmath30 in the @xmath0 rest frame .
the total angular distribution @xmath32 , including the dependence on the @xmath30 polar angle , can be written separately for longitudinal @xmath33 and transverse @xmath34 mesons : @xmath35 .
\nonumber\end{aligned}\ ] ]
the data were accumulated with the hermes forward spectrometer during the running period 2002 - 2005 . the @xmath1 gev positron ( electron ) beam was scattered off a transversely polarized hydrogen target with an average polarization of @xmath36
. events with exactly one positron ( electron ) and two oppositely charged hadron tracks were selected .
exclusive @xmath0 events were identified by requiring @xmath37 gev , where @xmath38 is the missing mass squared and @xmath39 is the proton mass . due to the experimental resolution and limited acceptance ,
semi - inclusive pion production can contribute to the exclusive sample ; this is the primary background .
it is well reproduced by the pythia simulation and is estimated to be of the order of @xmath40 .
the ttsa asymmetry is extracted by using the unbinned maximum likelihood method where all the moments @xcite of @xmath41 , @xmath42 and @xmath42 ( eqs . [ eq : wut ] , [ eq : wut_sep ] ) are fitted simultaneously . in this analysis , the angular distributions @xmath43 and the asymmetries @xmath44 of @xmath0 , @xmath33 and @xmath34
meson productions are defined by unpolarized spin density matrix elements ( sdmes ) @xcite previously measured by hermes @xcite .
r0.6 the only ttsa moment of @xmath0s produced from longitudinal photons that is related to the gpds @xmath4 and @xmath5 , is the @xmath45 moment . in figure
[ fig : a_ut ] the @xmath46 moment of the ttsa is presented .
the panels show from left to right the integrated value and the @xmath15 , @xmath14 and @xmath20 dependences of the asymmetry . for the @xmath14 and @xmath20 dependences ,
@xmath15 is required to be above @xmath47 gev@xmath48 .
the upper panels represent the @xmath0 total asymmetries , while the middle and the lower panels represent the longitudinal @xmath33 and transverse @xmath34 separated asymmetries , respectively .
the error bars represent the statistical uncertainties only , while the yellow bands indicate the systematic uncertainties due to the target polarization , the background subtraction procedure , the uncertainty resulting from the the unpolarized sdmes measurement as well as the influence of the beam polarization on the final result .
the @xmath14 and @xmath20 dependences of the @xmath46 moment for longitudinal @xmath0 mesons are compared to the theoretical calculations @xcite ( see figure [ fig : a_ut_theor ] ) .
the longitudinal component of @xmath46 moment of the asymmetry is related to : @xmath49 , where the @xmath50 , @xmath51 and @xmath52 , @xmath53 represent the quark and gluon gpds , respectively .
currently no model exists for the gluon gpd @xmath52 . in the present theoretical calculations
the gluon gpd @xmath5 is neglected .
however , @xmath52 is not expected to be large compared to the quark gpds @xcite .
no large contribution is expected from sea quarks in our @xmath14 range . as gpd @xmath50
is related to the total angular momentum @xmath54 and @xmath55 carried by @xmath56 and @xmath57 quarks , the @xmath46 moment of the asymmetry is sensitive to @xmath54 and @xmath55 .
the various curves in figure [ fig : a_ut_theor ] represent those calculations for @xmath58 , @xmath59 and @xmath60 and @xmath61 .
the @xmath61 choice is motivated by the results of recent lattice calculation @xcite .
the comparison of @xmath14 and @xmath20 dependences of the asymmetry with theoretical calculations indicates that the data favors positive @xmath54 values . and
@xmath20 dependences of @xmath46 moment of the ttsa of exclusive production of @xmath33 mesons compared to the model calculations .
the error bars represent the total error.,width=207 ] and @xmath20 dependences of @xmath46 moment of the ttsa of exclusive production of @xmath33 mesons compared to the model calculations .
the error bars represent the total error.,width=207 ]
the @xmath46 moment of the ttsa of exclusive @xmath0 meson production is measured on a hydrogen target .
the kinematic dependences as well as the integrated value of the asymmetry are presented . in particular , the longitudinal part of the asymmetry is compared to theoretical calculations .
the model suggests that the data favors positive @xmath54 values , which is in agreement with deeply virtual compton scattering results obtained from hermes data @xcite .
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915 ( 2006 ) 603 . | preliminary measurements are reported on the azimuthal single - spin asymmetry of exclusive @xmath0 mesons for a transversely polarized hydrogen target at hermes using the @xmath1 gev hera positron beam . within the generalized parton distribution ( gpd )
formalism , this asymmetry is sensitive to the total angular momentum of quarks and gluons in the nucleon . since the gpd formalism is only valid for mesons produced by longitudinal photons , the transverse target - spin asymmetry of longitudinal @xmath0 mesons
is extracted assuming @xmath2-channel helicity conservation and compared to theoretical calculations . |
completion of the knowledge of the generalized nuclear force , which includes not only the nucleon - nucleon ( nn ) interaction but also hyperon - nucleon ( yn ) and hyperon - hyperon ( yy ) interactions , brought the deeper understanding of atomic nuclei , structure of neutron stars and supernova explosions .
however it is hard to know the properties of the yn and yy interactions because their scattering data in free - space are scarce . recently
a method to extract the @xmath8 potential through the nbs wave function from lattice qcd simulations has been proposed in @xcite .
the obtained potential is found to have desirable features , such as attractive well at long and medium distances , and the central repulsive core at short distance @xcite .
further applications have been done in refs .
@xcite . in this work ,
we focus on the @xmath0 , @xmath1 b - b system to seek the @xmath9 interaction and to see the su(3)@xmath10 breaking effects of b - b interaction from lattice qcd simulation .
the @xmath11 baryon - baryon state consists of the @xmath9 , @xmath12 and @xmath13 components in terms of low - lying baryons .
mass differences of these components are quite small , and it causes the contamination of nbs wave function from excited states .
in sucn situation the source operator should be optimized to extract the energy eigen states through the variational method @xcite .
the equal - time nbs wave function @xmath14 for an energy eigen state with @xmath15 is extracted from the four point function , @xmath16 where @xmath17 is diagonalized wall - source operator .
the transition potential matrix of 3-states coupled channel equation can be acquired in a particle basis or a su(3 ) irreducible representation ( ir ) basis .
they are connected by unitary trandformation ( see in appendix b in ref .
the non - diagonal part of potential matrix in ir basis is a good measure of the su(3 ) breaking effect .
.hadron masses in unit of [ mev ] are listed . [ cols="^,^,^,^,^,^,^,^",options="header " , ] in this calculation we employ the 2 + 1-flavor full qcd gauge configurations of japan lattice data grid(jldg)/international lattice data grid(ildg ) .
they are generated by the cp - pacs and jlqcd collaborations with a renormalization - group improved gauge action and a non - perturbatively @xmath18 improved clover quark action at @xmath19 , corresponding to lattice spacings of @xmath20 @xcite .
we choose three ensembles of the @xmath21 lattice which means the spatial volume of about @xmath22 .
quark propagators are calculated from the spatial wall source at @xmath23 with the dirichlet boundary condition in temporal direction at @xmath24 .
the numerical computation is carried out at kek supercomputer system , blue gene / l .
the hadron masses are shown in table [ tab : gconf ] .
in figure [ fig : potall ] we compare the results of potential matrix in the ir basis calculated in different configuration sets .
we found the growth of repulstive core in the @xmath25 potential with decreasing the light quark mass .
the @xmath26 and @xmath27 transition potential are consistent with zero within error bar . on the other hand ,
it is noteworthy that the @xmath28 transition potential which is not allowed in the su(3 ) symmetric world is strengthen as the su(3)@xmath10 breaking gets larger .
we have investigated the @xmath29 bb state , which is known as the @xmath9 , @xmath12 and @xmath13 coupled state , from lattice qcd .
we have found a small transition potential between the singlet and octet state in terms of the su(3 ) ir basis .
such transition can not be allowed in the su(3 ) symmetric world .
this method could greatly assist us to complete the knowledge of not only the generalized nuclear force but also the interaction of hadrons including mesons , baryons and quarks .
* acknowledgements * : this work was supported by the large scale simulation program no.0923(fy2009 ) of high energy accelerator research organization ( kek ) , grant - in - aid of the ministry of education , science and technology , sports and culture ( nos . 20340047 , 22540268 , 19540261 ) and the grant - in - aid for scientific research on innovative areas ( no .
2004:20105001 , 20105003 ) .
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we prepare three types of baryon - baryon operators ( @xmath2 , @xmath3 and @xmath4 ) for the sink and construct three source operators diagonalizing the @xmath5 correlation matrix . combining of the prepared sink operators with the diagonalized source operators , we obtain nine effective nambu - bethe - salpeter ( nbs ) wave functions .
the @xmath5 potential matrix is calculated by solving the coupled - channel schrdinger equation .
the flavor @xmath6 breaking effects of the potential matrix are also discussed by comparing with the results of the @xmath6 limit calculation .
our numerical results are obtained from three sets of @xmath7 flavor qcd gauge configurations provided by the cp - pacs / jlqcd collaborations .
example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore |
while the cumulative evidence for neutrino oscillations is very striking , the final proof that the observed anomalies are actually due to neutrino oscillations is still outstanding . in particular ,
the current observations of atmospheric neutrinos @xcite are all consistent with the hypothesis of maximal @xmath2 oscillations , but do not yet exclude some alternative unconventional explanations @xcite .
the main physics goal of the monolith experiment @xcite is to establish the occurrence of neutrino oscillations in atmospheric neutrinos through the explicit observation of the full first oscillation swing in @xmath2 disappearance @xcite , and to investigate and presumably exclude alternative explanations .
this also yields a significantly improved measurement of the oscillation parameters with respect to previous measurements .
the monolith detector will be located at the gran sasso laboratory in italy , and the measurement of the oscillation pattern can be supplemented by measurements in the cern to gran sasso neutrino beam .
a proposal is currently in preparation @xcite .
if approved promptly , a first part of the detector could be operational towards the end of 2004 .
the physics results described in the following sections correspond to an exposure of 4 years with the full detector .
the goals quoted above can be achieved with a high - mass tracking calorimeter with a coarse structure and magnetic field .
a large modular structure has been chosen for the detector ( figure [ fig : module ] ) .
one module consists in a stack of 120 horizontal 8 cm thick iron planes with a surface area of @xmath3 , interleaved with 2 cm planes of sensitive elements .
the height of the detector is thus 12 meters .
thinner plates , 2 and 4 cm thick , were also considered in the past , however the 8 cm plate thickness resulted to be best compromise between physics result and detector costs .
the magnetic field configuration is also shown in figure [ fig : module ] ; iron plates are magnetized at a magnetic induction of @xmath4 t. the detector consists of two modules .
optionally , the downstream module could be complemented by an end cap of vertical planes to improve the performance for non - contained muons from the cngs beam .
the total mass of the detector exceeds 34 kt .
glass spark counters ( resistive plate chambers with glass electrodes ) have been chosen as active detector elements .
they provide two coordinates with a pitch of 3 cm , and a time resolution of 2 ns .
finally , an external veto made of scintillation counters reduces the background from cosmic ray muons .
in the two flavour approximation , the survival probability for neutrino oscillations in vacuum can be expressed by the well known formula @xmath5 where @xmath6 is the distance travelled in km , @xmath7 is the neutrino energy in gev , @xmath8 is the neutrino mixing angle , and @xmath0 is the difference of the mass square eigenvalues expressed in ev@xmath9 . [ cols="^,^ " , ]
provided that the neutrino oscillation hypothesis is confirmed , another goal of the experiment is to further investigate the nature of these oscillations . depending on the oscillation parameters , oscillations into active ( @xmath10 ) or sterile ( @xmath11 ) neutrinos can be distinguished through their different effects on the up / down ratio of neutral current ( nc)-like events , and/or through the presence or absence of matter effects yielding a distortion of the observed oscillation pattern as a function of energy and/or muon charge . even in the absence of sterile neutrinos ,
matter effects are present in the case of a small contribution from @xmath12 oscillations at the `` atmospheric '' @xmath0 .
the corresponding msw resonance might be observable @xcite as a localized @xmath2 rate suppression either in @xmath2 or in @xmath13 .
due to its ability of in situ measurement of the energy of every muon in the multi - tev range , monolith will also be a unique facility for pioneer investigations of cosmic ray muons in the unexplored 100 tev energy region .
the results of these studies will give information which is relevant for the solution of the problem of the knee in the cosmic ray energy spectrum .
other potential physics topics include studies of the primary atmospheric neutrino flux , the search for astrophysical point sources , and a search for a neutrino `` line '' from wimp annihilation in the center of the earth .
neutrino beams from future muon storage rings @xcite ( neutrino factories ) will be essentially pure beams of either @xmath14 or @xmath15 .
the occurence of @xmath16 or @xmath17 oscillations would therefore manifest itself via the appearance of wrong sign muons .
a massive magnetized iron detector like monolith , with good muon charge separation and momentum measurement , could therefore be well suited @xcite for the observation of such oscillations .
as pointed out in @xcite this kind of beam will in particular offer the possibility to measure the @xmath18 mixing angle , currently only constrained by the super - kamiokande and chooz results , and the sign of @xmath0 through matter effects . depending on which of the solar neutrino solutions is correct it might also open the way for the study of cp violation in the neutrino system .
interestingly , the optimization of detectors for the neutrino factory , focusing on wrong sign muon appearance measurements , has yielded a detector @xcite whose basic parameters are very similar to those of monolith .
this is true in particular when the source is far enough away to impinge at a sizeable angle from below ( horizontal geometry of monolith ) .
for instance , a beam from fermilab ( l=7300 km ) would impinge at an angle of 35@xmath19 , and be almost aligned with the gran sasso hall axis , and therefore perpendicular to the magnetic field axis .
the results obtained in the physics studies of ref .
@xcite concerning the measurements of @xmath20 , sign of @xmath0 , and cp violation therefore qualitatively apply to monolith used as a neutrino factory detector .
of course the potential timescale of a neutrino factory is quite different from the one of the current atmospheric neutrino program .
nevertheless , it might be interesting to consider that such a facility might become reality within the lifetime of the monolith project , and that its useful life might be extended accordingly .
monolith is a 34 kt magnetized iron tracking calorimeter proposed for atmospheric neutrino measurements at the gran sasso laboratory in italy .
its main goal is the proof of the neutrino oscillation hypothesis through the explicit observation of a sinusoidal oscillation pattern ( @xmath2 reappearance ) .
other goals include auxiliary measurements in the cern to gran sasso beam , and the investigation of potential @xmath12 and @xmath21 contributions . in the long term
, the detector could also be used in a potential neutrino factory beam .
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* b 547 * ( 1999 ) 21 . v. barger , s. geer and k. whisnant , hep - ph/9906487 . | 8.0 cm 5.0 cm monolith is a proposed massive ( 34 kt ) magnetized tracking calorimeter at the gran sasso laboratory in italy , optimized for the detection of atmospheric muon neutrinos .
the main goal is to establish ( or reject ) the neutrino oscillation hypothesis through an explicit observation of the full first oscillation swing .
the @xmath0 sensitivity range for this measurement comfortably covers the complete super - kamiokande allowed region .
other measurements include studies of matter effects and the nc / cc and @xmath1 ratio , the study of cosmic ray muons in the multi - tev range , and auxiliary measurements from the cern to gran sasso neutrino beam .
depending on approval , data taking with part of the detector could start in 2004 .
the detector and its performance are described , and its potential later use as a neutrino factory detector is addressed . -1.6 cm 16.5 cm -1 cm a. geiser , hamburg university for the monolith collaboration ( * m*assive * o*bservatory for * n*eutrino * o*scillations or * li*mits on * th*eir existence ) bologna , bonn , cnr torino , columbia , lnf frascati , hamburg , humboldt berlin , inr moscow , laquila , lnf frascati , lngs gran sasso , mephi moscow , milano , mnster , napoli , roma , torino , tunis -0.7 in 6.0 in 9.0 in |
a promising way to explain the late - time accelerated expansion of the universe is to assume that at large scales general relativity ( gr ) breaks down , and a more general action describes the gravitational field .
thus , in the latter context , infra - red modifications to gr have been extensively explored , where the consistency of various candidate models have been analysed ( see @xcite for a review ) .
note that the einstein field equation of gr was first derived from an action principle by hilbert , by adopting a linear function of the scalar curvature , @xmath0 , in the gravitational lagrangian density .
the physical motivations for these modifications of gravity were related to the possibility of a more realistic representation of the gravitational fields near curvature singularities and to create some first order approximation for the quantum theory of gravitational fields , and more recently in an attempt to explain the late - time cosmic acceleration . in this context , a more general modification of the hilbert - einstein gravitational lagrangian density involving an arbitrary function of the scalar invariant , @xmath1 , has been extensively explored in the literature , and recently a maximal extension of the hilbert - einstein action has been proposed @xcite .
the action of the maximal extension of the hilbert - einstein action is given by @xcite @xmath3 where @xmath4 is an arbitrary function of the ricci scalar @xmath0 , and of the lagrangian density corresponding to matter , @xmath5 .
the energy - momentum tensor of matter is defined as @xmath6 .
varying the action with respect to the metric @xmath7 , the gravitational field equation of @xmath8 gravity is provided by @xmath9 g_{\mu \nu } = \frac{1}{2 } f_{l_{m}}\left ( r , l_{m}\right ) t_{\mu \nu } \,.\end{aligned}\ ] ] for the hilbert - einstein lagrangian , @xmath10 , we recover the einstein field equations of gr , i.e. , @xmath11 . for @xmath12 , where @xmath13 , @xmath14 and @xmath15 are arbitrary functions of the ricci scalar and of the matter lagrangian density , respectively , we obtain the field equations of modified gravity with an arbitrary curvature - matter coupling @xcite .
an interesting application was explored in the context of @xmath16 gravity@xcite .
the @xmath2 models possess extremely interesting properties .
first , the covariant divergence of the energy - momentum tensor is non - zero , and is given by @xmath17 \frac{\partial l_{m}}{% \partial g^{\mu \nu } } \ , .
\label{noncons}\end{aligned}\ ] ] the requirement of the conservation of the energy - momentum tensor of matter , @xmath18 , provides the condition given by @xmath19 \partial l_{m}/ \partial g^{\mu \nu } = 0 $ ] .
secondly , the motion of test particles is non - geodesic , and takes place in the presence of an extra force . as a specific example , consider the case in which matter , assumed to be a perfect thermodynamic fluid , obeys a barotropic equation of state , with the thermodynamic pressure @xmath20 being a function of the rest mass density of the matter @xmath21 only , i.e. , @xmath22 , and consequently , the matter lagrangian density , becomes an arbitrary function of the energy density @xmath21 only , i.e. , @xmath23 ( for more details , we refer the reader to @xcite ) .
thus , the equation of motion of a test fluid is given by @xmath24 , where the extra - force @xmath25 is defined by @xmath26 \left ( u^{\mu } u^{\nu } -g^{\mu \nu } \right ) \,.\ ] ] note that @xmath25 is perpendicular to the four - velocity , @xmath27 , i.e. , @xmath28 .
the non - geodesic motion , due to the non - minimal couplings present in the model , implies the violation of the equivalence principle , which is highly constrained by solar system experimental tests .
however , it has recently been argued , from data of the abell cluster a586 , that the interaction between dark matter and dark energy implies the violation of the equivalence principle @xcite .
thus , it is possible to test these models with non - minimal couplings in the context of the violation of the equivalence principle .
it is also important to emphasize that the violation of the equivalence principle is also found as a low - energy feature of some compactified versions of higher - dimensional theories . in the newtonian limit of weak gravitational fields @xcite , the equation of motion of a test fluid in @xmath4 gravity
is given by @xmath29 where @xmath30 is the total acceleration of the system ; @xmath31 is the newtonian gravitational acceleration ; the term @xmath32 $ ] is identified with the hydrodynamic acceleration term in the perfect fluid euler equation .
now , by assuming that in the newtonian limit the function @xmath33 can be represented as @xmath34 , where @xmath35 , so that @xmath36 given by @xmath37\,,\ ] ] is a supplementary acceleration induced due to the modification of the action of the gravitational field .
in conclusion , the maximal extensions of gr , namely the @xmath2 gravity models open the possibility of going beyond the algebraic structure of the hilbert - einstein action . on the other hand ,
the field equations of @xmath2 gravity are equivalent to the field equations of the @xmath1 model in empty space - time , but differ from them , as well as from gr , in the presence of matter .
thus , the predictions of @xmath2 gravitational models could lead to some major differences , as compared to the predictions of standard gr , or other generalized gravity models , in several problems of current interest , such as cosmology , gravitational collapse or the generation of gravitational waves .
the study of these phenomena may also provide some specific signatures and effects , which could distinguish and discriminate between the various gravitational models .
in addition to this , in order to explore in more detail the connections between the @xmath2 theory and the cosmological evolution , it is necessary to build some explicit physical models .
fsnl acknowledges financial support of the fundao para a cincia e tecnologia through the grants cern / fp/123615/2011 and cern / fp/123618/2011 .
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b * 654 * , 165 ( 2007 ) . | we consider a maximal extension of the hilbert - einstein action and analyze several interesting features of the theory .
more specifically , the motion is non - geodesic and takes place in the presence of an extra force .
these models could lead to some major differences , as compared to the predictions of general relativity or other modified theories of gravity , in several problems of current interest , such as cosmology , gravitational collapse or the generation of gravitational waves .
thus , the study of these phenomena may also provide some specific signatures and effects , which could distinguish and discriminate between the various gravitational models . |
after the successful applications of lscher s method @xcite to the elastic scattering of _ elementary _ scalar and fermionic particles ( see , e.g. , @xcite ) , we have chosen the massive schwinger model ( qed@xmath0 ) with 2 flavours to determine scattering phases in meson - meson scattering .
similar to four - dimensional qcd , mesons occur because of confinement .
this two - dimensional model also exhibits charge screening and it possesses a nontrivial vacuum structure .
moreover , there exist analytical predictions which enable us to test the numerical results .
lscher s relation connects elastic scattering phases in infinite volume and two - particle energies in finite volumes . in 2 dimensions it has the simple form @xmath1 using the energy - momentum relation , @xmath2 can be calculated from the mass and the two - particle energies , which are accessible to monte carlo simulations .
the massive schwinger model with 2 flavours has the following continuum euclidean action : @xmath3 bosonization of the model leads in the strong coupling limit to the sine - gordon model , plus corrections @xcite . since the particle spectrum of the sine - gordon model
is known analytically , one can derive that the particle spectrum of the massive two - flavour schwinger model consists of a pseudoscalar isotriplet ( `` pion '' ) with g - parity g=+1 and a mass @xmath4 according to @xmath5 and a scalar isosinglet with g=+1 and mass @xmath6 @xcite . in the sine - gordon model
also the elastic scattering phases have been calculated @xcite and will form the basis for our numerical tests . from the corrections to the sine - gordon model only the `` @xmath7''-particle ( a pseudoscalar isosinglet , g=1 ) with mass @xmath8 is known @xcite . & & + & & + & & + @xmath9 & @xmath10 & @xmath11 & @xmath12 & @xmath13 & @xmath14 & @xmath12 & @xmath13 & @xmath14 & @xmath12 & @xmath13 & @xmath14 & @xmath12 & @xmath13 & @xmath14 & @xmath12 & @xmath13 & @xmath14 & @xmath12 & @xmath13 & @xmath14 + && & 0.05 & + & & 0.05 in ( 1,2 ) ( 0,0)(1,0)2(0,1)2 ( 0,0)(0,1)3(1,0)1 & & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & & & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & + & + &&+ & 0.05 & + & + & 0.05 in ( 1,2 ) ( 0,0)(1,0)2(0,1)2 ( 0,0)(0,1)3(1,0)1 & &+ & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & &+ & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & + & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & &+ & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & + & + + &+ & & 0.05 & & & 0.05 in ( 1,2 ) ( 0,0)(1,0)2(0,1)2 ( 0,0)(0,1)3(1,0)1 & + & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & & & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & + & + &+ & + & 0.05 & &+ & 0.05 in ( 1,2 ) ( 0,0)(1,0)2(0,1)2 ( 0,0)(0,1)3(1,0)1 & + & + & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & &+ & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & + & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & &+ & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & + & + + + & & & 0.05 & & & 0.05 & + & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & + & & 0.05 in ( 2,2 ) ( 0,0)(1,0)3(0,1)2 ( 0,0)(0,1)3(1,0)2 & & + + & &+ & 0.05 & &+ & 0.05 & + & + & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & &+ & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & + & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & + & + & 0.05 in ( 2,2 ) ( 0,0)(1,0)3(0,1)2 ( 0,0)(0,1)3(1,0)2 & &+ + + & + & & 0.05 & & & 0.05 & + & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & & & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & & & 0.05 in ( 2,2 ) ( 0,0)(1,0)3(0,1)2 ( 0,0)(0,1)3(1,0)2 & + & + + & + & + & 0.05 & &+ & 0.05 & + & + & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1
( 0,0)(0,1)2(1,0)4 & &+ & 0.05 in ( 4,1 ) ( 0,0)(1,0)5(0,1)1 ( 0,0)(0,1)2(1,0)4 & + & + & 0.05 in ( 3,2 ) ( 0,0)(1,0)2(0,1)2 ( 2,1)(1,0)2(0,1)1 ( 0,0)(0,1)1(1,0)1 ( 0,1)(0,1)2(1,0)3 & &+ & 0.05 in ( 2,2 ) ( 0,0)(1,0)3(0,1)2 ( 0,0)(0,1)3(1,0)2 & + & + + the lattice formulation of the schwinger model with staggered fermions and compact wilson action for the gauge field is given by : @xmath15 energy eigenstates are classified according to irreducible representations of the group of symmetry transformations leaving the time slices fixed .
the representation @xmath16 of the continuum time slice group ( cts ) is characterized by the representation @xmath12 of the su(2 ) and the quantum numbers @xmath13 and @xmath14 associated with parity and g - parity .
the representation @xmath17 of the lattice time slice group ( lts ) is characterized by the quantum numbers @xmath9 , @xmath10 and @xmath11 , which correspond to shift in space , inversion and charge conjugation on the lattice .
restriction of an irreducible cts representation to the subgroup lts will in general lead to reducible representations . for the one-(two-)particle operators , which transform according to the representations @xmath12 of rank 2 ( 4 ) , every lattice symmetry sector couples to two ( four ) continuum sectors , as shown in table [ tab : lts - cts ] .
[ fig : m_pi(m)-b2b4 ]
we first verified the analytical prediction for the relation of the pion mass to the bare mass of the fermions ( see fig .
[ fig : m_pi(m)-b2b4 ] ) .
we have good agreement between the analytical formula and our simulations : for @xmath18 = 4 we extract an exponent of 0.689(10 ) as compared to 2/3 of eq .
( [ eq : m_pi(m ) ] ) . the deviation between the measured points and the analytical curve decreases with increasing @xmath18 , which can be explained by the fact that the continuum limit corresponds to @xmath19 .
this is supported by additional measurements for higher values of @xmath18 , up to @xmath18 = 10 , for which the points tend towards the analytically predicted curve . [
fig : m_eff(m)-b7 ] in fig .
[ fig : m_eff(m)-b7 ] we show the particle content of the model found by us after the investigation of almost all lattice symmetry sectors .
unfortunately we are not yet able to identify numerically the analytically predicted singlet states mentioned above .
with increasing @xmath18 , a problem related to the topological properties of the model arises : the tunnelling rate between sectors of different topological charges decreases strongly , so that we are facing an ergodicity problem . to estimate its impact
we analyzed the dependence of the pion mass on the topological charge @xmath20 of the configurations by comparing measurements on configurations associated with different topological charges ( see fig .
[ fig : m_pi(q)+p(q)-b1m01 ] ) . within the error bars ,
no significant deviation is visible .
[ fig : m_pi(q)+p(q)-b1m01 ] because of the unexpected complexity of the one - particle spectrum for the massive schwinger model we have not yet been able to determine scattering phases satisfactorily .
helpful discussions with m. gckeler are gratefully acknowledged .
furthermore we wish to thank the hlrz jlich and the rechenzentrum of the rwth aachen for providing the necessary computer time .
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( 1979 ) 253 . | we discuss the possibility of extracting phase shifts from finite volume energies for meson - meson scattering , where the mesons are fermion - antifermion bound states of the massive schwinger model with su(2 ) flavour symmetry .
the existence of analytical strong coupling predictions for the mass spectrum and for the scattering phases makes it possible to test the reliability of numerical results . |
this work falls into a general framework which consists of observing the behavior of patterns and structures that can be formed after instability onset in an evaporating liquid layer . in previous work , we studied theoretical instability thresholds in pure fluids [ 1,2 ] and in binary mixtures [ 3,4 ] .
what is of interest here , is a two - dimensional numerical simulation study of the transient temperature and fluid motion in the liquid for a liquid evaporating into a nitrogen gas flow .
the chosen liquid is hfe7100 ( an electronic liquid produced by 3 m ) .
the numerical ( cfd ) simulations are performed using the software comsol ( finite elements method ) . the evaporation causes the instability and the gas flow evacuates the liquid vapor .
the setup used for this numerical simulation is represented in fig . [ scheme ] and is inspired from the cimex experimental setup of esa [ 5 ] .
the gas flow is maintained at 100 ml / min in a channel of 3 mm height , while three different liquid thicknesses are considered : 2 , 4 and 8 mm .
the width of the whole setup is 50 mm .
the cover between the liquid and gas channel is @xmath0 thick . at the middle of this cover
, there is an opening with a width of 10.6 mm , allowing contact between the liquid and gas channel .
these items are taken into the geometry of the numerical software comsol .
the boundaries of the whole system are kept at an ambient temperature and pressure of respectively 298 k and 1 atm , except for the gas channel outlet where only the ambient pressure is respected . also , the whole system is surrounded by walls except for the gas flow inlet and outlet .
the interface is kept at a constant height , since in the esa experimental setup the liquid is to be replenished at the same rate as the evaporation rate . at the interface , flux conservation is maintained and a tangential stress balance is considered .
furthermore , a no - slip condition is assumed at the interface .
the assumption of local thermodynamic equilibrium at the interface allows us the use of raoult s law , in which the temperature dependence of the saturation pressure is determined via the clausius - clapeyron relation .
the results present the temperature in the liquid and gas phase as well as the fluid motion in the liquid ( caused by the evolution of the temperature via surface - tension and buoyancy effects ) by means of streamlines as a function of time .
the real total elapsed time is 10 seconds .
two videos are shown , presenting the same results in the following urls : 1 .
link : doi[video 1 - high resolution ] 2 .
link : doi[video 2 - low resolution ] note that in the videos the inner streamlines represent the highest velocity values .
the red color represents the highest observed temperature ( that of the ambient one ) , 298 k. the blue color represents the lowest observed temperature , around 285 k.
from the results in the videos we can observe that first several small rolls are formed near the surface , caused by the surface - tension effect as fig .
[ comparisont1 ] shows for the three liquid layer thicknesses at time @xmath1 . due to buoyancy and as time proceeds ,
the rolls grow towards the bottom of the liquid layer .
then the rolls also grow in horizontal direction merging with each other until a steady configuration is obtained . for a higher liquid layer thickness , the merging occurs earlier and less rolls are left .
furthermore , the temperature gradients decrease as the liquid thickness increases , which is caused by the higher mixing efficiency when the liquid is less confined . moreover , the rolls extend more horizontally under the cover towards the side walls as the liquid layer thickness increases . for smaller liquid layer thicknesses ,
the rolls reach the bottom where a constant temperature of 298 k is maintained . therefore the rolls stay concentrated close to the interface . as the liquid layer thickness increases , the rolls have more time to increase in size towards the side walls before they reach the bottom of the liquid layer .
[ comparisont10 ] shows this at the time @xmath2 .
this work yields valuable information about the supercritical instability behavior of an evaporating liquid and the qualitative influence of its confinement by means of fluid dynamics .
the authors gratefully acknowledge financial support of belspo and esa .
[ 1 ] b. haut and p. colinet , j. colloid interface sci . , 285 : 296 - 305 , 2005 . [ 2 ] f. chauvet , s. dehaeck and p. colinet , europhys .
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[ 5 ] esa , http://www.esa.int/specials/hsf_research/semlvk0yduf_0.html[cimex experimental setup ] , accessed 12 octobre 2012 | this work presents fluid dynamics videos obtained via numerical ( cfd ) calculations using comsol ( finite elements method ) software , showing the evaporation of hfe7100 ( 3 m company refrigerant ) into a nitrogen gas flow along the liquid interface .
the overall temperature evolution and liquid motion , which is caused by surface - tension ( marangoni ) and buoyancy ( rayleigh ) instability mechanisms , are shown as well .
flow behavior in the liquid caused by the aforementioned instability mechanisms can be nicely seen .
finally , these observations are made for three liquid thicknesses in order to appreciate the qualitative influence of confinement . |
j. bae is supported in part by the hanyang university fellowship and y. kwon is supported in part by the fund of hanyang university . | it is questionable that grover algorithm may be more valuable than a classical one , when a partial information is given in a unstructured database . in this letter , to consider quantum search when a partial information is given , we replace the fourier transform in the grover algorithm with the haar wavelet transform .
we then , given a partial information @xmath0 to a unstructured database of size @xmath1 , show that there is the improved speedup , @xmath2 .
suppose that we have a problem of finding a desired one of unstructured @xmath1 items .
it is known that a classical search algrithm may take @xmath3 times , but the fast quantum search algorithm provides the quadratic speedup , @xmath4.@xcite the quantum algorithm whose central idea is amplitude amplification was first provided by grover in 1996.@xcite@xcite it is well - known that grover algorithm is 1)optimal in the context of applying unitary operators repeatdly and 2)efficient in searching a target of a unstructured database .
however , it is not evident that , when a partial information is given , the grover algorithm is still more valuable than a classical one . in this letter , we provide the quantum search algorithm which is able to benefit from a partial information .
the key building block in our construction is the ( haar ) wavelet transform instead of the fourier transform in the grover algorithm .
+ let us first consider the grover algorithm .
a bijection between a database and quantum states is necessary before applying the grover algorithm .
if a superposition of @xmath1 states is initially prepared , the grover algorithm amplifies the amplitude of the target state up to around one , while those of other states dwindle down to nearly zeros .
the amplitude amplification is performed by two inversion operations : inversion about the target by the oracle and inversion about the initial state by the fourier transform .
noting the fact that two simultaneous reflections about two mirrors crossing by an angle @xmath5 induce @xmath6 rotation , one may imagine that the inversions in the grover algorithm rotate the initial state around the target state.@xcite if the target state and the initial state are denoted by @xmath7 and @xmath8 respectively,(here the initial state is prepared by the fourier transform of a state @xmath9 , i.e. @xmath10 ) the inversion operators is expressed as @xmath11 since @xmath12 , the grover operator is written as @xmath13 then , after applying the operator @xmath4 times , the final state comes to @xmath14 , which is @xmath15 , @xmath16 .
the query complexity of this algorithm , the number of callings of the oracle , is therefore @xmath4 .
we here note that the running time has nothing to do with the choice of @xmath9 . + to consider the partial information , let us think about the following situation .
+ _ suppose that hanyang university library has @xmath1(@xmath17 , for some @xmath18 ) books .
each book has a code number identifying itself .
recently , the library decides to label new code numbers to each book since a better way to classify books has provided .
a labelling machine is applied to the tedious job .
each code is composed of @xmath19 numbers .
the first numbers must be @xmath20 , since they stands for the region .
and hanyang university is in south korea , so the second number is @xmath20.the other numbers stand for the category each book is included .
an earlier number means a larger category .
the rules of labeling a code number is that the @xmath21-th number , @xmath22 , is in @xmath23 $ ] for @xmath24 .
the following codes are a good example , _
@xmath25 the first code means @xmath26 and the next one @xmath27 .
the first two numbers @xmath28 stands for the region , and hanyang university . to aid the searching a book in the library
, the library also has implemented the grover algorithm in a quantum computer .
+ after the labelling is completed , one discovers a fault in the machine .
therefore , the library decides to do labelling again , fixing the fault in the labelling machine .
they then recommend to apply the grover algorithm to whom may be concerned to search a book , during labelling .
+ dr .
lee , a postdoc in physics , has to submit his research paper by tomorrow @xmath29 a.m. it is now 6 p.m. he wish to fill the reference section in the paper , but the library in mess blocks his work .
the director of the library recommends him to try the grover algorithm , but it was calculated , based on the number of books @xmath1 , that @xmath30 hours is the running time of the algorithm .
therefore , he concludes that the grover algorithm can not help him . at that moment
, he gets a call from the library that the only @xmath21-th number of all code numbers is correct .
+ it is sure that the grover algorithm can not complete the search task in time , since it takes over @xmath30 hours .
the only thing that dr .
lee can use in order to overcome his hopeless situation , is the fact that only the @xmath21-th number was correctly labelled .
the partial information may save his problem .
however , the grover algorithm can not benefit from the partial information of this problem . +
we here introduce the fast wavelet quantum search algorithm(wqsa ) , which is a modification of the grover algorithm by replacing the fourier transform with the haar wavelet transform , to resolve the situation of dr .
lee .
let us note that to apply the following operator @xmath31 is one iteration of the wqsa .
the haar wavelet transform @xmath32 is represented @xmath33 where @xmath34.\end{aligned}\ ] ] and @xmath35 the haar 1-level decomposition operator as follows ; @xmath36_{2^k \times 2^k}\end{aligned}\ ] ] we have used @xmath37 as the @xmath38 unit matrix and @xmath39 as the @xmath40 zero matrix .
it is clear that the wavelet transform @xmath32 is unitary since the operator @xmath41 is unitary .
+ since the operator is composed of the wavelet transform , consistently , the initial state is prepared by applying the inverse wavelet transform @xmath42 to a state @xmath9 , i.e. , the initial state is now @xmath43 .
the power of our wqsa appears in the initialization procedure .
it is quite remarkable that the state @xmath44 is a superposition of @xmath45 states , where @xmath46(@xmath21 is given by @xmath47 ) , while the state @xmath48 is a superposition of @xmath1 states .
then it is expected that the running time is @xmath2 .
choosing the initial state as @xmath44 , @xmath49 when the target state exists in the restricted domain of the @xmath45 states , we look forward to an improved speedup with the partial information .
since @xmath50 , by setting @xmath51 , @xmath52 and @xmath24 , and @xmath53 , the state @xmath44 is explicitly , @xmath54 the following diagram shows the set of states composing @xmath44 . .
the @xmath55axis runs from @xmath56 to @xmath57 .
when the initial state is @xmath58 or @xmath59 , the running time is the same to that of the grover algorithm since the lowest two retangulars include all states.,scaledwidth=40.0% ] we thus arrive at the following proposition .
suppose that we solve the problem of finding a desired one in the set @xmath60 .
given a partial information that the target state is in the subset @xmath61 , we complete the search task in @xmath62 times by choosing the initial state as @xmath63 .
proof ) let the target state @xmath64 . let us take the initial state as @xmath65 .
it suffices to show that it takes @xmath62 times for the wqsa to find the target state with the following setting .
+ let @xmath66 .
the wavelet quantum search operator is @xmath31 where @xmath32 is the haar wavelet transform .
applying the operator @xmath42 to the @xmath9 , we have the initial state @xmath67 and the state @xmath68 iterations of the operator @xmath69 create the following state , @xmath70 iterations is @xmath71 , where @xmath72 and @xmath73 .
hence , we have shown that the total number of iterations is @xmath62 . if we denote @xmath74 and @xmath46 , then the running time is written as @xmath2 q.e.d .
+ let us revisit the dr .
lee s problem.the partial information that the @xmath21-th number @xmath22 is correctly labelled leads dr .
lee to apply the wqsa so that the reference section is filled in time .
however note that there is no improvement in running time when the intial state is @xmath58 or @xmath59 since , in those cases , the initial state is still a superposition of @xmath1 states .
therfore , from the proposition , we know that he can complete the submission in time if the @xmath21 is larger than @xmath75 .
+ we have exerted how to utilize a partial information , in order to enhance quantum search .
our construction provides a way for quantum search to benefit from a partial information .
since the running time of the grover algorithm has nothing to do with the choice of unitary operator , the complexity of the wqsa is the same to the grover algorithm .
however , we have obtained the speedup @xmath2 by preparing the initial state as @xmath44 .
the running time of the wqsa depends on the choice of @xmath47 , while that of the grover algorithm does not .
this is because the state @xmath44 is a superpositin of states in the restricted domain of @xmath45 states .
the speedup is indeed originated in the initialization .
+ finally , let us discuss the haar wavelet basis .
although other wavelet transforms may be applied to the wqsa , we chose the haar wavelet transform .
it is observed that the first half of the haar wavelet basis differs with the second half of the wavelet basis on the phase @xmath76 .
this implies that destructive and constructive interference between states accepts a set of states containing the target and rejects the other states . in this sense , other known wavelet basis , e.g. daubechies s ,
are not appropriate to play the role of seclecting a subset of the @xmath1 states . |
traditional methods for visual cryptography have been established , are consistent and easily understood .
unfortunately , these methods exist for black and white pictures only , leaving the encryption of colour images wanting . while there are a handful of attempts at bringing colour to visual cryptography
, it is still an open field with implementations of varying efficiency . in this paper
, we will establish some basic standards for encrypting colour pictures , as well as a simple , yet efficient method for encryption based upon those rules . while black and white pictures are fairly easy to work with due to their simple nature , colour pictures contain much more information and possibly details that may not be lost in the process .
this leads to a need for the static that normally appears in the decryption of black and white pictures to have to be absent[1 ] .
however , a partial reconstruction of the picture ( such as having less than all the necessary parts for full restoration ) may not hint at what the final image is meant to be .
in addition to the standard of security for the traditional black and white pictures , we set the following points as mandatory for encryption of colour images . * full restoration upon decryption . * no indication as to the original image , whether by eye or any other method , when combining a subset of all available parts .
* usability for any type of image , whether that image contains a mixture of colours , is black and white or is simply one single colour . *
destruction of intermediary steps in the encryption process .
our method of encryption is , due to the process of creating images within visual cryptography and the expanse of computer use , based around the rgb colour model for computers and other , similar devices .
this does not prevent implementation of this process with any other model as long as the information is stored as bits .
the encryption is fairly straightforward and can be easily understood as well as implemented .
although it is easy to handle , it is efficient , provides the necessary security and fulfills every point previously stated . for the process , the thought was to work on the bitwise level that represents the colours themselves ; in this case , the rgb values are used . as each pixel
is processed , two random values are generated ; the first one is compared to the rgb value of the current pixel and it is then separated into two values : an rgb value with the bits that were set in both the original as well as the first random value , and another one with the set bits left over from the original . next , the second random value is compared to the two new results from the previous step .
if both values are not set while the bit at the same position in the random value is , those bits for the values from the previous step are set .
these steps are repeated for every pixel and then the encryption is finished .
decryption is easily done via a bitwise xor of the rgb values of the two resulting pictures and we effectively have a one - time pad implementation on the colour values of an image .
the random values from the process of encryption are discarded alongside any other values we might have produced .
the encryption algorithm will `` split '' the original image into two so called _ shadow images_. let @xmath0 denote one pixel in the original image , and let @xmath1 and @xmath2 denote the corresponding pixels in the shadow images , respectively . here
@xmath0 , @xmath1 , and @xmath2 are vectors , representing the channels used , e.g. red , green and blue in the rgb colour model . the calculations during the encryption are carried out both bitwise and channel - wise .
@xmath3 @xmath4 @xmath5 @xmath6 we illustrate the encryption with an example .
assume that we want to encrypt the image in figure [ fig : ex1 ] .
then if we apply the algorithm , it may result in the two shadow images in figure [ fig : ex2]remember that the algorithm is probabilistic . to restore the original image , we compute @xmath7 for each pixel .
the result will give us back the original image , without any loss of quality , that is , figure [ fig : ex1 ] .
as with both visual cryptography and the one time pad , this method offers complete security as there is neither a repetition to be found , nor is a brute force attack possible as every possible result within the picture s resolution will show up .
this method does not only fulfill the standards we previously set , it even leaves the resolution of the original image intact .
of course , it should be noted that for this encryption to work to its full potential , the results must be saved as a lossless image type . in the event that one would wish to separate the original into more than two pictures , reapplying this process to the results until a satisfactory amount is reached is all one needs to do .
it could be argued that all this encryption would need is random values generated and applied with a bitwise xor to the original image , leaving the randomly generated sequence as one of the resulting images and the result of the bitwise xor as the other .
while this could be done , let us take a look at the absolute worst case scenario , disregarding the possibilities that an attacker knows the original or has access to all parts of the picture .
the scenario in mind would be in the highly unlikely event that an attacker would have an intimate enough knowledge of the encryption process to know exactly how it is implemented as well as knowing exactly which random values were generated .
if the method of encryption would be nothing more than the simplified version suggested , then having the result of the bitwise xor in your possession would be enough to get the original as being able to predict the exact pseudo - random values would mean that you effectively have the key .
this is not the case for the method we propose as depending on the random values and how they interact with the original data , only some bits could possibly be decided , as shown in table [ tab : values ] .
there are four possible cases for the pair @xmath8 .
each case can be divided into two subcases , where each corresponds to the possible value @xmath9 of @xmath0 . without loss of generality , we consider the cases on bit - level . * 5c case & @xmath10 & @xmath11 & @xmath9 & @xmath0 + 1 & 0 & 0 & 0 & + 2 & 0 & 0 & 1 & 1 + 3 & 0 & 1 & 0 & 1 + 4 & 0 & 1 & 1 &
+ 5 & 1 & 0 & 0 & + 6 & 1 & 0 & 1 & 1 + 7 & 1 & 1 & 0 & 1 + 8 & 1 & 1 & 1 & + as seen , even in the case of knowing the generated pseudo - random values , half the possible combinations lack a value , thus mitigating such an attack .
the method of encryption presented here could also be applied to the one time pad due to the likeness of them , so providing the extra bit of security by mitigating this most unlikely of scenarios .
the reasoning for the received original value presented in the above table is shown with simple boolean algebra .
the equations used are the ones presented in the pseudocode , also presented here for ease of following .
keep in mind that we do not know which one of the values we have and thus not what the other one could be .
[ [ case-1-and-2 ] ] * case 1 and 2 * + + + + + + + + + + + + + + here is @xmath12 and @xmath13 . while we know for sure that at least one of the values must be @xmath14 , the other could be either possible value .
this means that if our available result ( @xmath9 ) is @xmath14 , we have no way of knowing which value we have in our possession , which in turn means that @xmath1 and @xmath2 are equal in terms of possibility .
thus , since the original value could be either for @xmath1 , it remains undetermined .
if , on the other hand , our available value is @xmath15 , then we can logically conclude that it is @xmath2 that we are dealing with and we only have to complete the following equation : @xmath16 and therefore @xmath17 .
[ [ case-3-and-4 ] ] * case 3 and 4 * + + + + + + + + + + + + + + here is @xmath18 and @xmath19 . as per the same logic as in the previous one : if the available result is the same as the one we know must exist ( in this case one ) , then we can not tell which equation it is we have .
if it is the opposing value , then we can in this case rule out @xmath2 and calculate the equation : @xmath20 and hence @xmath17 .
[ [ case-5-and-6 ] ] * case 5 and 6 * + + + + + + + + + + + + + + here is @xmath21 and @xmath22 .
following the previous logical steps gives us an unknown for the available result of @xmath14 , but the following result for @xmath15 is @xmath17 .
[ [ case-7-and-8 ] ] * case 7 and 8 * + + + + + + + + + + + + + + here is @xmath23 and @xmath24 .
once again we can not say for sure which case is before us if our available result is the same as the one we know with certainty to exist , but in the case of a differing result , we know the following : @xmath25 and @xmath17 .
we would like to thank robert nyqvist for : | while strictly black and white images have been the basis for visual cryptography , there has been a lack of an easily implemented format for colour images .
this paper establishes a simple , yet secure way of implementing visual cryptography with colour , assuming a binary data representation . |
this work was supported by the national natural science foundation of china under grant no . 11104159 , scientific research foundation of nanjing university of posts and telecommunications under grant no .
ny211008 , university natural science research foundation of jiangsu province under grant no .
11kja510002 , the open research fund of key lab of broadband wireless communication and sensor network technology ( nanjing university of posts and telecommunications ) , ministry of education , china , and a project funded by the priority academic program development of jiangsu higher education institutions .
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lett . a * 375 * , 396 ( 2011 ) . | we present an efficient entanglement concentration protocol ( ecp ) for mobile electrons with charge detection .
this protocol is quite different from other ecps for one can obtain a maximally entangled pair from a pair of less - entangled state and a single mobile electron with a certain probability . with the help of charge detection , it can be repeated to reach a higher success probability .
it also does not need to know the coefficient of the original less - entangled states .
all these advantages may make this protocol useful in current distributed quantum information processing .
entanglement plays an important role in the current quantum communication @xcite and distributed quantum information processing field @xcite . for most of the practical quantum communication and computation protocols ,
people need to share a maximally entangled state with each other .
however , the entanglement resource is fragile , for the maximally entangled state may be degraded into a mixed state or become a less - entangled state when it interacts with the noisy environment .
people usually resort to the entanglement purification @xcite to increase the fidelity of the mixed state and the entanglement concentration @xcite which will be detailed here to recover the less - entangled state to a maximally entangled state .
currently , most of the protocols for purification and concentration are focused on optical systems @xcite , for during the transmission , the photons have weak interaction with the environment . on the other hand
, there is another candidate for the flying qubit , that is the mobile electron .
a strong interaction between different electrons makes them feasible to interact flying electron spins with other solid electron spins , since the coulomb interaction between each electrons is strongly screened . in the recent years
, the investigation about the flying electron qubits becomes an active study area @xcite . in 2004 , beenakker _
et al .
_ broke through the obstacle of the no - go theorem with the help of charge detection and constructed a controlled - not(cnot ) gate using beam splitters and spin rotations near deterministically @xcite . with the help of charge detector
, people can construct the charge qubit @xcite , perform entanglement purification @xcite , construct entangled spins @xcite , and prepare a multipartite entanglement analyzer and cluster states @xcite . especially , the flying qubit can also be used in the one dimensional system and create entanglement between two distant matter qubits .
recently , matsuzaki and jefferson proposed a protocol for distributed quantum information processing with mobile electrons @xcite . in their protocol , they used mobile electron spins as the mediators of the interaction between the static qubits at each node and finally created a high quality entanglement between each node .
unfortunately , the distributed quantum entanglement may also be degraded into the less - entangled state when it is coupled with the noisy environment .
on the other hand , with current technology , it is difficult to operate each flying quibts perfectly , which can also lead the ideal maximally entangled state to be degraded @xcite . and reflect spin down @xmath0 .
the charge detector ( c ) can distinguish the charge number 1 from 0 and 2 , but can not distinguish the number 0 and 2 .
d is the detector.,width=302 ] entanglement concentration is a powerful tool to recover a less - entangled state into a maximally entangled one with only local operation and classical communication .
the first entanglement concentration protocol ( ecp ) was proposed by bennett _
et al . _ in 1996 @xcite .
this method is called schmidt projection method , in which they need the collective measurement and need to know the exact coefficient of the initial entangled state . in 2001 , zhao _ et al . _ and yamamoto _ et al . _
proposed two similar simplified ecps with linear optical elements based on the schmidt projection method respectively .
both ecps have been realized experimentally @xcite . in 2009
, we proposed an ecp based on electrons @xcite .
almost all the current ecps need two pairs of less - entangled states , but after performing each ecp , at most one pair of maximally entangled state can be obtained with a certain success probability .
actually , using two copies of less - entangled pairs to obtain one maximally entangled pair is not the optimal way . in this paper , we show that we can perform the ecp with the same success probability by using only one pair of less - entangled state and a single electron .
compared with the previous ecps , this protocol requires less less - entangled resources . moreover , analogized with the ref .
@xcite , we adopt the charge detectors and polarization beam splitter ( pbs ) to reconstruct our protocol , which makes it have a higher success probability than those protocols with linear optics .
this protocol can also be used to concentrate the multipartite entangled system .
all these advantages may make this protocol more useful in current quantum communication and distributed quantum information processing . before we start to explain our ecp
, we first introduce the charge detector ( c ) which is a key element shown in fig .
1 . the charge detector can distinguish the occupation number 1 from the occupation number 0 and 2 .
however , it can not distinguish between the occupation number 0 and 2 @xcite , so in both two cases , we define the charge detector will show 0 for simple . in fig.1 , we suppose the source @xmath1 emits a pair of less - entangled state of the form @xmath2 . @xmath3 and @xmath0 are spin up and spin down respectively .
meanwhile , the source @xmath4 emits a single electron to bob of the form @xmath5 and @xmath6 and alice only receives one electron from @xmath7 .
bob first performs a bit - flip operation and makes @xmath8 become @xmath9 then bob lets his two electrons pass through the pbs , which fully transmits @xmath3 and reflects @xmath0 .
the @xmath10 becomes @xmath11 from above equation , one can find that the item @xmath12 means that the two electrons in bob s location are both in the spatial mode @xmath13 while the item @xmath14 means that the two electrons are both in the mode @xmath15 .
however , both the items @xmath16 and @xmath17 mean that the two electrons are in the modes @xmath15 and @xmath13 , respectively .
therefore , the charge detector will show 0 if the original state collapses to @xmath12 or @xmath14 , and it will show 1 if the original state collapses to @xmath18 the probability of obtaining the state of eq .
( [ threephoton ] ) is @xmath19 . obviously , it is the three - electron maximally entangled state .
it is easy to get a two - electron maximally entangled state from eq .
( [ threephoton ] ) .
bob needs to perform a hadamard operation on his electron in the mode @xmath13 .
it makes @xmath20 ) becomes @xmath21\nonumber\\ & = & \frac{1}{2}[(|\uparrow\rangle_{a1}|\uparrow\rangle_{c1}+|\downarrow\rangle_{a1}|\downarrow\rangle_{c1})|\uparrow\rangle_{c2}\nonumber\\ & + & ( |\uparrow\rangle_{a1}|\uparrow\rangle_{c1}-|\downarrow\rangle_{a1}|\downarrow\rangle_{c1})|\downarrow\rangle_{c2}].\end{aligned}\ ] ] then the last step for bob is to measure the spin in the basis @xmath22 . from above equation , if the measurement result is @xmath23 , the electron pair in the modes @xmath24 will become @xmath25 , the electron pair in the modes @xmath24 will become @xmath26 .
if they share the pair @xmath27 , bob will tell alice that the protocol is successful and asks alice to retain her electron . in this way
, they can share a maximally entangled state from a less - entangled state with the success probability of @xmath19 . from above description , bob chooses the case that the charge detector s result is 1 and discards the case of 0 .
it is essentially the partially parity check gate which picks up the even parity states @xmath28 and @xmath29 but discards the odd parity states @xmath30 and @xmath31 . in this case , the function of pbs is similar as it is in the optical systems @xcite . in refs .
@xcite , they need to check that both the output modes of the optical pbs contain exactly and only contain one photon .
it is so called the post - selection principle . therefore , even if they successfully perform their ecps , the maximally entangled state would be destroyed by the single photon detector .
the maximally entangled photon pair can not be remained for further application . in this protocol
, bob can judge the successful case from the charge detection results .
the charge qubit carries both the spin degree of freedom and the charge degree of freedom . as charge and spin
are commute and a measurement of charge leaves the spin qubit unaffected , the charge detection does not affect the entangled state of the electrons .
actually , the charge detector and pbs are more powerful than it has been described above , for the discarded items are essentially the lesser - entangled state which can be reconcentrated in a second step . that is to say , we can not only pick up the even parity states , but also pick up the odd parity states . in fig .
2 , we add another pbs say pbs@xmath32 to reconstruct our ecp .
we denote the whole setup p gate shown in fig .
2 . if the charge detector s result is 0 , the original state will collapse to @xmath33 it means that after passing through the pbs@xmath34 , both the two electrons are in the same spatial mode , while with the help of pbs@xmath32 , they are coupled into latexmath:[\[\begin{aligned } it means that the two electrons in bob s location are in the different spatial modes , say @xmath15 and @xmath13 , respectively . then after performing the hadamard operation and measuring the spin of the electron on the mode @xmath13 , they can get latexmath:[\[\begin{aligned } if the measurement result is @xmath3 .
they can get latexmath:[\[\begin{aligned } if the measurement result is @xmath0 . both eqs .
( [ less1 ] ) and ( [ less2 ] ) are lesser - entangled states .
they can be reconcentrated in the next step . briefly speaking ,
if they obtain @xmath38 , bob needs to choose another single electron of the form @xmath39 , it becomes @xmath40 obviously , if the charge detection c=1 , they can obtain the same three - electron state as described in eq .
( [ threephoton ] ) with a probability of @xmath41 .
otherwise , if c=0 , the remained state is a lesser - entangled state and can be reconcentrated in a third round . in this way
, they can repeat this protocol to get a higher success probability than other protocols .
particles in the multipartite ghz state from the source @xmath1 are sent to to @xmath42 parties , say , alice , bob , charlie , etc .
the source @xmath4 also emits a single electron to bob .
the p is the parity check gate shown in fig.2 .
it comprises the pbs@xmath34 , charge detector c and pbs@xmath32 . only bob needs to perform this concentration.,width=302 ]
it is straightforward to extend this protocol to multi - partite pure entangled state systems .
an @xmath42-electron less - entangled system can be described as latexmath:[\[\begin{aligned } the @xmath42 electrons are emitted from @xmath1 and sent to @xmath42 parties , say , alice , bob , charlie , etc , as shown in fig .
3 .
alice gets the electron of number 1 in the spatial mode @xmath7 .
bob gets number 2 in the spatial mode @xmath44 and charlie gets the number 3 , etc .
the source of @xmath4 also emits a single electron to bob with the same form of eq .
( [ single ] ) . after rotating it by @xmath45
, the composite system can be described as @xmath46 subsequently , the electrons in the spatial modes @xmath44 and @xmath47 in bob s location pass through the @xmath48 gate . if the charge detector s result is @xmath49 , the eq .
( [ multi ] ) will collapse to @xmath50 with the probability of @xmath19 .
finally , bob performs a hardamard operation , and measures the electron in the mode @xmath13 in the basis @xmath51 . if the measurement result is @xmath3 , they will get @xmath52 and if the measurement result is @xmath0 , they will get @xmath53 both eqs .
( [ multi1 ] ) and ( [ multi2 ] ) are the @xmath42-electron maximally entangled states . otherwise , if the charge detector s result is @xmath54 , then eq .
( [ multi ] ) becomes @xmath55 after performing the hadamard operation and measuring the electron in c2 mode in the @xmath56 basis , the above state becomes @xmath57 compared with eq .
( [ nparticle ] ) , it is also a multipartite less - entangled state which can be reconcentrated into a maximally entangled state .
+ or - is decided by the measurement result @xmath3 or @xmath0 , respectively .
so far , we have fully described our ecp .
it is interesting to compare this protocol with ref .
@xcite . in ref .
@xcite , we resort two copies of less - entangled pairs to perform the concentration .
we can get one pair of maximally entangled state with the success probability of @xmath19 . in this protocol
, we use only one pair of less - entangled state and a single electron which can reach the same success probability with ref .
@xcite .
moreover , during the whole protocol , only one - way classical communication is required .
that is alice only needs to receive the information from the bob s measurement and to judge whether the protocol is successful or fail .
if the protocol is a failure , alice needs to do nothing .
if the protocol is successful , bob will tell alice the remaining state is @xmath58 or @xmath59 according to his measurement . in previous protocols
@xcite , all of the parties have to participate the whole procedure , to measure their electrons and check their results to each other to judge the remained state if the protocol is successful .
so this protocol is much more simple , especially when it is used to concentration multi - partite system , for only one of the parties needs to perform the protocol and then report his results to others . finally , let us briefly discuss the key ingredient of this protocol here , that is charge detector @xcite .
it has been realized in a two - dimensional electron gas .
it was reported that currently achievable time resolution for charge detection is @xmath60 @xcite . in a semiconductor
it was reported that the resolution required for ballistic electrons is less than 5 ps @xcite .
compared with flying qubit , it may be more practical to use isolated electrons in an array of quantum dots , as pointed by ref . @xcite . in conclusion
, we have proposed an mobile electron ecp based on charge detection .
compared with other protocols , it has several advantages : first , it dose not require the post - selection principle , and can be repeated to reach a higher efficiency than those based on linear optical elements ; second , only one pair of less - entangled state and one - way classical communication are required , which make this protocol more economic and simple than others .
all these advantages make this ecp more useful in current quantum communication and distributed quantum information processing . |
diffractive events in @xmath0 collisions are characterized by the presence of a leading proton or antiproton which remains intact , and/or a rapidity gap , defined as a pseudorapidity of a particle is defined as @xmath1 , where @xmath2 is the polar angle of the particle with respect to the proton beam direction . ]
region devoid of particles .
diffractive events involving hard processes ( `` hard diffraction '' ) , such as production of high @xmath3 jets ( see fig . [
fig : diff_diagram ] ) , have been studied extensively to understand the nature of the exchanged object , the pomeron , which in qcd is a color singlet entity with vacuum quantum numbers .
one of the most interesting questions in hard diffractive processes is whether or not they obey qcd factorization , in other words , whether the pomeron has a universal , process independent , parton distribution function ( pdf ) .
results on diffractive deep inelastic scattering ( ddis ) from the @xmath4 collider hera show that qcd factorization holds in ddis
. however , single diffractive ( sd ) rates of @xmath5-boson @xcite , dijet @xcite , @xmath6-quark @xcite and @xmath7 @xcite production relative to non - diffractive ones measured at cdf are @xmath8(10 ) lower than expectations from pdfs determined at hera , indicating a severe breakdown of factorization in hard diffraction between tevatron and hera .
the suppression factor at the tevatron relative to hera is approximately equal in magnitude to that measured in soft diffraction cross sections relative to regge theory predictions based on regge factorization .
the suppression relative to predictions based on ddis pdfs is illustrated in fig .
[ fig : sd_jj ] , which shows the `` diffractive structure function '' @xmath9 measured at cdf by using diffractive dijet data with a leading antiproton detected in roman pots @xcite .
the @xmath10 ( integrated over antiproton momentum loss @xmath11 and four momentum transfer squared @xmath12 ) was obtained as a function of @xmath13 , the momentum fraction of the parton in the pomeron , @xmath14 ( @xmath15 is @xmath16-bjorken of the parton in the antiproton , see fig .
[ fig : sd_jj ] ) , by measuring the ratio of diffractive to non - diffractive dijet rates and using the known leading order pdfs of the proton .
the measured suppression of @xmath9 relative to the expectation from the h1 pdfs is approximately equal to that observed in soft diffraction .
cdf has also studied dijet events with a double pomeron exchange ( dpe ) topology ( fig .
[ fig : diff_diagram ] ) using the roman pot trigger sample at @xmath17 gev @xcite . by measuring the ratio of dpe to sd dijet rates ( @xmath18 ) and comparing it with that of sd to nd rates ( @xmath19 ) ,
a breakdown of qcd factorization was observed as a discrepancy of the double ratio @xmath20 from unity .
in run ii , being currently under way , cdf plans to study various topics on diffraction , including @xmath21 and @xmath11 dependence of @xmath9 in sd , gap width dependence of @xmath9 in dpe , production of exclusive dijet , heavy flavor and low mass states in dpe , and dijets with a large gap in - between jets .
two recently installed `` miniplug '' ( mp ) calorimeters cover the region @xmath22 , and 7 stations of scintillation counters , called beam shower counters ( bsc ) , mounted around the beam pipe , extend the coverage to the very forward region of @xmath23 . the roman pots ( rp ) used in run
i were re - installed and are being operated to trigger on leading antiprotons in the kinematic range @xmath24 and @xmath25 gev@xmath26 .
= 3.5 cm = 6.0 cm
triggering on a leading antiproton in the rp in conjunction with at least one calorimeter tower with @xmath27 gev , a study of diffractive dijet events has been performed . from a sample of 352k triggered events , about 15k sd dijet events with dijets of corrected @xmath27 gev in the range @xmath24
were obtained .
the @xmath11 ( fractional momentum loss of antiproton ) was measured by using all calorimeter information . using a non - diffractive dijet sample triggered on the same calorimeter tower requirement ,
the ratio of diffractive to non - diffractive dijet rates was measured as a function of @xmath16-bjorken of the parton in the antiproton , as shown in fig .
[ fig : r_xbj ] .
this figure shows that ( i ) the ratio observed with run ii data in approximately the same kinematic region as in run i reproduces the run i results , and ( ii ) there is no appreciable @xmath11 dependence in the ratio , as already seen in run i. measurement of the @xmath11 dependence at still lower @xmath11 values ( @xmath28 ) is one of our run ii goals and is being currently under study .
preliminary results of the @xmath21 dependence of the ratio , where @xmath21 is defined as the square of average value of the mean dijet @xmath3 , are shown in fig .
[ fig : r_xbj ] .
no significant @xmath21 dependence is observed , indicating that the pomeron evolves with @xmath21 in a similar way as the proton .
for a study of dpe dijets in run ii , a dedicated trigger has been implemented that requires a rapidity gap in the bsc in the outgoing proton direction in addition to the presence of a leading antiproton in the rp and a single calorimeter tower of @xmath27 gev .
the requirement of a bsc gap on the proton side enhances the dpe signal , as can be seen in the two - dimensional lego plot of mp versus bsc hit multiplicity of sd dijet events ( fig .
[ fig : dpe ] ) .
offline , requiring in addition a gap in the proton - side mp , we obtained about 16k dijet events ( about 100 times more data than in run i ) , which are qualitatively consistent with dpe dijets .
figure [ fig : dpe ] ( middle and right ) shows the @xmath3 , mean @xmath29 and azimuthal angle difference @xmath30 of the two leading jets for the dpe candidate events ( points ) .
as seen in run i dpe data , the @xmath3 distributions look similar to those of sd dijets ( histograms ) , while the mean @xmath29 and @xmath30 show that the dpe dijets are more central and more back - to - back .
et al . _ ,
78 * , 2698 ( 1997 ) .
et al . _ ,
79 * , 2636 ( 1997 ) .
t. affolder _
et al . _ ,
* 84 * , 232 ( 2000 ) .
t. affolder _
et al . _ ,
lett . * 87 * , 241802 ( 2001 ) .
t. affolder _
et al . _ ,
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t. acosta _
et al . _ ,
lett . * 88 * ,
151802 ( 2002 ) . t. affolder _
et al . _ ,
lett . * 85 * , 4215 ( 2000 ) . | we present results on hard diffraction obtained by the cdf collaboration in run ii proton - antiproton collisions at the fermilab tevatron .
run i cdf results on hard diffraction are also reviewed . |
in the main body of the paper , we focus on the dynamics of the skyrmion density as the important quantity to describe skyrmions or antiskyrmions , respectively .
still , these objects have an internal magnetic structure given by the magnetization @xmath14 .
in particular , different kinds of dzyaloshinskii - moriya interactions ( dmi ) may stabilize different types of skyrmions . in this appendix
, we show exemplary magnetic structures for * bulk dmi given by the hamiltonian @xmath98 $ ] which stabilizes bloch - like skyrmions ( cf .
[ fig::bdmi ] and movie `` ` sk_density_vs_time_bulkdmi.avi ` '' ) , * interfacial dmi given by the hamiltonian @xmath99 $ ] which stabilizes nel - like skyrmions ( cf .
[ fig::idmi ] and movie `` ` sk_density_vs_time_interfacialdmi.avi ` '' ) , and , * no dmi with means stabilization neither of bloch - like nor of nel - like skyrmions ( cf .
[ fig::zdmi ] and movie `` ` sk_density_vs_time_zerodmi.avi ` '' ) .
all figures are snapshots taken from movies which we also provide as supplemental material online in the `` other formats '' option on the article s arxiv page . even though the explicit magnetic structures differ for the according dmi , no qualitative changes for the pair creation process , as described in the main article ,
were observed .
+ we have used the same parameter set as before .
the calculations were performed on a @xmath66 square lattice with periodic boundary conditions , external magnetic field @xmath68 , spin velocity @xmath100 m/s , gilbert damping @xmath101 and non - adiabaticity @xmath102 . to create initial fluctuations of the skyrmion density , a tiny modulation to the magnetic field pointing in the @xmath71-direction , i.e. , @xmath72 $ ] and
@xmath73 has been added to the external field .
+ 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 \doibase http://dx.doi.org/10.1016/0029-5582(62)90775-7 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1103/physrevb.74.085308 [ * * , ( ) ] `` , '' in link:\doibase 10.1007/978 - 1 - 4684 - 9449 - 5_6 [ _ _ ] ( , , ) pp . @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop ( ) @noop * * ( ) @noop * * , ( ) @noop * * , ( ) @noop * * ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) \doibase http://dx.doi.org/10.1016/j.jmaa.2007.01.013 [ * * , ( ) ] @noop * * , ( ) @noop * * ( ) @noop | magnetic skyrmions can be considered as topologically protected quasiparticles . due to their stability , their small size , and the possibility to move them by low electric currents they are promising candidates for spintronic devices . leaving the topological protection untouched ,
it is possible to create skyrmion - antiskyrmion pairs , as long as the total skyrmion number remains unchanged .
we derive a skyrmion equation of motion which reveals how spin - polarized charge currents create skyrmion - antiskyrmion pairs .
it allows to identify general prerequisites for the pair creation process .
we corroborate these general principles by numerical simulations . on a lattice , where topological protection becomes imperfect ,
the antiskyrmion partner of the pairs is annihilated and only the skyrmion survives .
this eventually changes the total skyrmion number and yields a new way of creating and controlling skyrmions .
magnetic skyrmions ( sks ) are vortex - like localized magnetization configurations @xcite which have been predicted @xcite before they were discovered experimentally @xcite in magnetic layers with a strong spin - orbit interaction @xcite . despite their size being much smaller @xcite than , for example ,
that of topologically trivial magnetic bubbles , their thermodynamic stability is amazing @xcite .
this is a consequence of the particular magnetic configuration which can be characterized by a topological sk number @xmath0 .
it can take integer values only and therefore can not be changed continuously @xcite .
this feature protects magnetic sks against typical drawbacks of solid state systems such as disorder or imperfect fabrication @xcite .
together with the property of easy repositioning by rather tiny in - plane electrical currents @xcite , this makes diluted sks attractive candidates for future racetrack memory devices @xcite .
creation of sks has been reported in the vicinity of notches @xcite or by sweeping the back ground magnetic field @xcite . controlled creation and annihilation of individual sks has been demonstrated @xcite . with in - plane electrical currents @xcite the density of sks adjusts to the respective equilibrium value when ,
for example , the strength of the externally applied zeeman magnetic field is varied in time .
this process must overcome topological stability .
the precise mechanism of sk creation remained , however , unexplored . in this work ,
we derive a sk equation of motion which reveals the details of the process how sk - numbers @xmath0 change by an applied in - plane current .
we find this to happen in three steps .
first , a skyrmion - antiskyrmion ( sk - ask ) pair is created @xcite , triggered by small spatial fluctuations of the magnetization .
pair creation does not change the total sk - number @xmath0 , since the sk and the ask have non - zero equal @xmath0 of opposite sign , respectively . then , in a second step , sk and ask get spatially separated by the dynamics we describe below .
the sk equation of motion reveals the relevant terms at work which are not captured by the common thiele approximation @xcite . finally ,
the ask , being no stable solution for a given zeeman- and dzyaloshinsky - moriya interaction strength , decays due to gilbert damping .
it is this last dissipative step which is ultimately responsible for changing @xmath0 .
all general findings are confirmed by extended numerical simulations .
the two - dimensional magnetization configuration @xmath1 of a single current - driven sk evolves in time according to the landau - lifshitz - gilbert ( llg ) equation @xcite @xmath2 where @xmath3 is a normalized vector field .
all interactions of the hamiltonian @xmath4 describing the system are contained in the effective field @xmath5 .
below , in eq .
( [ latticemodel ] ) , we specify the hamiltonian for a lattice model , but its detailed form is not relevant for the following consideration .
@xmath6 already contains the gyromagnetic ratio and we set @xmath7 .
further important parameters are the gilbert damping constant @xmath8 and the non - adiabaticity parameter @xmath9 . in this work
, we focus specifically on the impact of spin - polarized electronic currents @xmath10 @xcite flowing homogeneously in space and time in the magnetic plane with spin polarization @xmath11 and lattice constant @xmath12 , proportional to an electronic charge current density @xmath13 . with the vector field @xmath14
, we then define the sk density @xmath15\;,\ ] ] and the spatial integral which yields the quantized skyrmion number @xmath16 in fact , this homotopy invariant completely characterizes sks and is the degree of the vector field @xmath17 @xcite . for convenience , we take the direction of the spin current @xmath18 as reference direction , @xmath19 and @xmath20 .
while the topological invariant @xmath0 is conserved in time at low energies , the time evolution of @xmath21 describes the current - induced local motion of sks . in particular ,
as discussed below , it also describes the generation or annihilation of sk - ask pairs . to reveal the sk - ask pair creation mechanism ,
we decompose the effective field according to @xmath22 by combining eqs .
( [ eq::llg ] ) , ( [ eq::qxyt ] ) and ( [ eq::basis ] ) , we readily obtain the sk equation of motion @xmath23 with the sk currents [ eq::jsk ] @xmath24\mathbf v_s\label{eq::jskd1}\\ & \qquad-[{\ensuremath { ( \hat{\mathbf v } \cdot\nabla){\ensuremath{\mathbf
n}}}}]^2\mathbf v_{\perp}\big\}\ , , \label{eq::jskd2}\end{aligned}\ ] ] with contributions parallel to the current flow ( @xmath25 ) and perpendicular to it ( @xmath26 ) .
the coefficients read [ eq::jsk_coeff ] @xmath27/(1+\alpha^2)\ , , \label{eq::jt}\\ j_2 = & [ -\alpha+\beta - ( { \ensuremath{b_{\perp 1}}}-\alpha { \ensuremath{b_{\perp 2}}})]/(1+\alpha^2)\ .\label{eq::jd}\end{aligned}\ ] ] the sk equation of motion ( [ eq::eom ] ) resembles a continuity equation which connects the sk `` charge '' density @xmath28 with the sk current density .
we note , however , that conservation of @xmath0 in eq .
( [ eq::q ] ) in the present case is not a consequence of noether s theorem , albeit conserved quantities may still exist for eq .
( [ eq::eom ] ) @xcite under continuous variation of @xmath29 @xcite .
the physical meaning of @xmath30 and @xmath31 becomes apparent when we consider sk in the steady state where @xmath32 and thus @xmath33 . for not too large current densities , no major structural changes of the magnetization
occur and @xmath6 remains parallel to @xmath29 .
then , the perpendicular components @xmath34 vanish and the coefficients @xmath35 and @xmath36 in eq .
( [ eq::jsk_coeff ] ) are constant .
a case of special importance occurs when @xmath37 , which implies that @xmath38 , @xmath39 .
then , @xmath40 , such that the undistorted sk density @xmath28 moves with the velocity @xmath41 , according to eq .
( [ eq::jskt ] ) .
this motivates to call @xmath30 a sk current density .
when @xmath42 ( but still assuming @xmath43 ) , @xmath36 becomes nonzero .
then , we may rewrite eqs .
( [ eq::jskd1],[eq::jskd2 ] ) in the form @xmath44 , with the coefficients @xmath45 and @xmath46 ^ 2/q$ ] .
we can simplify @xmath47 , where @xmath48 is the angle between @xmath49 and @xmath50 .
this term @xmath51 only adds to the contribution of @xmath30 ( though with a different dependence on @xmath8 , @xmath9 , as well as on the shape of the vector field @xmath29 ) to drive sk density and ask density along @xmath52 depending on the explicit angle @xmath48 .
+ crucial for the following is the term @xmath53 .
first , it points perpendicularly to the externally applied spin current and , second , it drives sk- and ask - densities in opposite directions , as it changes sign under the inversion @xmath54 .
we therefore identify the contribution ( [ eq::jskd2 ] ) as being responsible for separating the sk from the ask density resulting in a common sk - ask pair .
the separation takes place perpendicularly to the external current .
actually , this process can be expected to be a common scenario in real materials for sufficiently strong applied charge current densities .
the only further prerequisites are @xmath55 and small spatial fluctuations of the sk density @xmath21 , which also imply finite gradients @xmath49 and @xmath50 and thus a finite @xmath31 .
a finite gradient @xmath50 is , strictly speaking , not necessary for a non - vanishing current @xmath31 [ cf .
eq .
( [ eq::jskd2 ] ) ] . nevertheless , it is important for a finite divergence @xmath56 . only in this case , the skyrmion current can not be gauged away and is physically relevant .
having such a current means that regions of negative and positive sk density @xmath21 are separated .
in addition , regions of opposite signs appear quite naturally in the topologically trivial state @xmath57 , as regions of finite @xmath28 , which we have postulated , have to cancel each other to sum up to zero . ultimately , a sk - ask pair is formed out of these fluctuations when this is energetically favorable .
we note in passing that the detailed motion of asks is typically more complicated than that of sks , since commonly , an isolated ask is not a stationary solution and thus , already for @xmath58 , @xmath6 is clearly not parallel to @xmath29 , which implies that @xmath59 . in the following , we illustrate these general principles for a concrete model realized by the hamiltonian @xcite @xmath60\nonumber\\ & -\sum_{{\ensuremath{\mathbf r}}}\mathbf b_{\mathbf r}\cdot{\ensuremath{\mathbf n_{\mathbf r}}}\nonumber\end{aligned}\ ] ] defined on lattice sites @xmath61 ( unit lattice constant ) in two dimensions .
it supports diluted sks within certain ranges of the parameters .
@xmath62 is the exchange interaction and @xmath63 the dzyaloshinsky - moriya interaction ( dmi ) strength .
we use the values @xmath64 , @xmath65 reported for mnsi @xcite . here , we only discuss a bulk dmi which stabilizes bloch sks .
yet , we have also verified our findings for systems with an interfacial dmi which stabilizes nel sks @xcite .
no qualitative modifications occur and our findings thus apply to both kinds of sks . in the numerical simulations , we use a @xmath66 square lattice with periodic boundary conditions .
depending on the magnitude of the externally controlled zeeman - field @xmath67 , either a helical phase , a sk lattice or the ferromagnetic ( field polarized ) phase is the ground state @xcite .
a field @xmath68 is in fact strong enough to align all magnetic moments , @xmath69 .
then , @xmath21 remains zero everywhere and , according to eqs .
( [ eq::eom ] ) and ( [ eq::jsk ] ) , for all times , since @xmath70 , even at non - zero applied current densities . to realize at least a small initial non - zero sk density @xmath28 , we add a tiny modulation to the magnetic field pointing in the @xmath71-direction , i.e. , @xmath72 $ ] and @xmath73 . as a matter of fact , the precise form of the initial inhomogeneous magnetization configuration is of minor importance .
the time evolution of the system is calculated by solving the llg eq .
( [ eq::llg ] ) by standard advanced numerical methods .
starting from the fully field polarized state @xmath74 , we first let the system accommodate to the additional @xmath75 field , at zero external current .
after this initial equilibration , we switch on the current at @xmath76 and calculate @xmath21 at every time step .
a movie of this evolution is available in the sm @xcite while a selection of snapshots of @xmath28 is shown in fig .
[ fig::snapshots ] .
initially , the very small amplitude @xmath77 of @xmath75 generates a tiny seed sk density of both , positive and negative sign with an overall @xmath57 .
gradually , under the influence of the external current , sk - ask pairs begin to form with growing magnitudes of @xmath28 .
consistent with our theoretical prediction , the sk and ask centers separate in the @xmath71-direction , perpendicular to the external current flow . after its full development , since it is unstable , the ask disappears on a time scale @xmath78 .
thereby its diameter shrinks relatively quickly , eventually below the lattice constant . at this moment ,
@xmath79 abruptly changes by one .
( color online ) .
black solid line : time - dependence of the total sk number @xmath79 .
black dashed line : time - dependence of the total ask number defined as @xmath80 stemming from negative sk densities only .
note that @xmath81 does not need to be integer and that the restriction to lattice points imposes some small , unimportant ambiguity on the precise determination of @xmath21 .
red dashed line : time - dependence of the energy in reference to the initial energy , @xmath82 , per lattice site . before every @xmath0-jump
, @xmath81 gradually increases , accompanied by an increase of the energy which eventually is taken from the external current . ]
this scenario is demonstrated further in fig .
[ fig::q_vs_t ] , where we show the time - dependence of @xmath79 . over large time spans , the total sk number ( black line ) takes integer values , while occasionally @xmath79 jumps to the next integer within a short ( but on the graph resolvable ) transition time .
these transitions are accompanied by sudden rises of the total ask number @xmath80 , a quantity that we define by integrating over negative sk - density only . during the times when @xmath79 stays integer , @xmath83 may decrease gradually with time .
this indicates the gradual creation of sk - ask pairs , their growth and their spatial separation , before the finally isolated , but unstable ask annihilates during a time much shorter than the duration of its creation , as described above .
this initial gradual development of the first sk - ask pair due to a weak spatial inhomogeneity of the zeeman - field is clearly seen in fig .
[ fig::q_vs_t ] . on the other hand ,
as soon as a finite number of sks exist ( after 6300 ps in fig . [ fig::q_vs_t ] )
, their intrinsic inhomogeneous magnetization suffices to facilitate further creation of sk - ask pairs in their surroundings , then even at a homogeneous zeeman - field as we have convinced ourselves independently .
since the system starts very close to the ferromagnetic ground state , the sk creation costs energy .
this energy is pumped into the system by the charge current .
figure [ fig::q_vs_t ] confirms the connection between the increase of the energy and of negative sk - density .
the evolution of sk - ask pairs is overshadowed by the relatively short life time of the ask .
the details of this process are further illustrated by an additional movie @xcite where we set the dmi to zero .
then , neither the sk nor the ask is energetically preferred and the full sk - ask pair evolves in time . the duration for sk creation can be quantified by the time @xmath84 which we define as the time span from the onset of the current flow till the creation of the first sk .
since the ask annihilation is comparably fast , it is sufficient to define @xmath84 by the condition @xmath85 .
this creation time is a combination of the time @xmath86 needed to form a sufficiently large sk - ask pair and the annihilation time @xmath87 of the ask .
since both processes happen at least partially simultaneously , the resulting @xmath84 is not a direct sum of both .
still , @xmath88 such that we can safely take @xmath89 .
since we attribute the creation of sk - ask pairs to the existence of a finite @xmath31 , we expect sks to be created faster when the magnitude of @xmath31 is larger . from eqs .
( [ eq::jskd1],[eq::jskd2],[eq::jd ] ) we find @xmath90 in the limit of vanishing @xmath91 and @xmath92 . in fig .
[ fig::tau ] , this relation between @xmath84 and @xmath31 is confirmed by the numerical results .
indeed , @xmath84 depends on @xmath93 and @xmath94 .
in particular , no sks can be created when @xmath37 which implies that the dissipative current is essential for the charge current - induced sk creation . finally , we note that even though we have chosen a particular seed magnetic field @xmath95 to create sk density fluctuations , their precise origin is not important .
in fact , only an inhomogeneous @xmath96 , besides @xmath42 and @xmath97 , is necessary for @xmath31 to become non - vanishing .
thus , a multitude of ways are eligible to create such fluctuations , for example by local fields , material modification , or by temperature . on the other hand
, a change of @xmath0 will often be undesirable in distinct set - ups .
then , @xmath31-contributions to eqs .
( [ eq::jsk ] ) should be suppressed by a proper choice of the material with a small @xmath93 , or by avoiding magnetization fluctuations , apart from simply working in the low current regime . in this work ,
we have established the skyrmion equation of motion by combining the general definition of the skyrmion density and the landau - lifshitz - gilbert equation .
we here define `` skyrmion current densities '' that conserve the total skyrmion number of a sample . in the presence of in plane
spin current densities , we identify terms that give rise to simple movement of skyrmions against the externally applied charge flow . other contributions to skyrmion current densities that we identify
explicitly drive the separation of positive skyrmion density from negative antiskyrmion density perpendicularly to the charge current flow .
these latter contributions eventually cause the creation of skyrmion - antiskyrmion pairs , already out of very small magnetic inhomogeneities .
the theoretical predictions are corroborated by numerical simulations and applied to systems with bulk and interfacial dmi .
we acknowledge support from the dfg sfb 668 ( project b16 ) . + |
the energy spectrum of mesons produced in neutrino - nucleus interactions is modified by strong interactions with the residual nucleus .
recent high - statistics measurements of charged - current @xmath3production by miniboone @xcite and minerva @xcite have shown tension with available models @xcite .
a study of @xmath0production is complementary because of differences in the nuclear interaction due to strangeness conservation .
previous measurements of neutrino - induced charged - current @xmath0production have been carried out in bubble chambers with very limited statistics @xcite .
we report the first high - statistics measurement of this process based on a sample of 1755 selected event candidates , of which 885 are estimated to be charged - current @xmath0events with @xmath4 mev . at neutrino energies below 2 gev ,
cabibbo suppressed single kaon production @xmath5 is the dominant @xmath0production mechanism . at higher energies ,
@xmath0mesons arise via associated production accompanied by strangeness @xmath6 baryons ( @xmath7 , @xmath8 ) or mesons ( @xmath9 , @xmath10 ) such that there is no net change in strangeness ( @xmath11 ) .
this can occur through an intermediate resonance state or in deep inelastic scattering ( dis ) by hadronization , the production of mesons and baryons from the struck quark .
in particular , @xmath12 pairs created in hadronization lead to pairs of strange particles in the final state .
production of @xmath0by atmospheric neutrinos is a background in experimental searches for the proton decay @xmath13 , a channel favored by grand unification theories which incorporate supersymmetry .
the simplest minimal supersymmetric models @xcite give proton lifetimes that have been excluded by experiment . however , other models @xcite allow proton lifetimes greater than @xmath14 years , consistent with the current experimental lower bound of @xmath15 years from a 260 kiloton - year exposure by super - kamiokande @xcite .
the @xmath0from proton decay is below cherenkov threshold in water , but a liquid argon time projection chamber such as dune @xcite is able to reconstruct the @xmath0momentum precisely . the @xmath0momentum spectrum in @xmath13depends on the momentum distribution of the initial - state protons inside the nucleus .
a related issue is the extent to which @xmath0mesons born inside the nucleus experience final - state interactions ( fsi ) as they emerge into the detector medium .
kaons produced by neutrinos are subject to the same interactions . measuring @xmath0production by neutrinos on carbon is a first step toward understanding the spectrum for @xmath13 in the argon of the dunefar detector .
kaon - nucleus and pion - nucleus reactions differ because of strangeness conservation .
absorption is the dominant feature in the pion - nucleus inelastic cross section at pion kinetic energies in the few 100s of mev . in @xmath9-nucleus scattering ,
the @xmath9can be absorbed , converting a bound nucleon into a hyperon .
the analogous process for @xmath0-nucleus scattering is forbidden because there are no antibaryons in the nucleus .
a @xmath0produced inside the nucleus will exit unless it charge exchanges to a @xmath16 .
in addition , @xmath0can be produced in @xmath3-nucleus reactions by strong processes such as @xmath17 . in the giessen boltzmann - uehling - uhlenbeck model @xcite
, this kind of reaction gives an enhancement to the @xmath0production cross section at low @xmath0momentum . in genie @xcite , the event generator used by minervaand many other experiments , 13% of @xmath0produced in carbon reinteract before exiting the nucleus , distorting the spectrum toward lower kaon energies .
geniedoes not include @xmath0production either by pions or charge exchange in its fsi model . this paper reports a measurement at high statistics of inclusive charged - current @xmath0production by muon neutrinos , @xmath1 ch @xmath18 .
the differential cross section in @xmath0kinetic energy is measured and compared to predictions of current neutrino event generators with and without fsi treatments .
minervais a dedicated neutrino - nucleus cross section experiment in the numi beamline @xcite at fermilab .
the detector consists of a core of strips of solid plastic scintillator `` tracker '' surrounded by calorimeters on the sides and downstream end .
the electromagnetic and hadronic calorimeters intersperse scintillator with passive planes of lead and steel , respectively .
the upstream nuclear targets region is used only to veto front - entering events for this result .
the minos near detector is located 2 m downstream of minerva .
positive muons from antineutrino - induced charged - current reactions are rejected using curvature , but the muon momentum measurement is not used in this analysis .
the scintillator strips are arranged into planes stacked perpendicular to the horizontal axis , and are rotated @xmath19 and @xmath20 with respect to the vertical axis to enable unambiguous three - dimensional tracking of charged particles .
the cross section of the strips is triangular with a base edge of 3.4 cm and a height of 1.7 cm . in the center of each strip
is a wavelength - shifting optical fiber which is mirrored at one end and read out by a 64-channel multi - anode photomultiplier tube at the other .
a hit is defined as an energy deposit in a single scintillator strip .
the uncalibrated hit time is the time of the earliest charge recorded on a single channel , with an electronics resolution of 2.2 ns . when a charge threshold is exceeded , charge is integrated for 151 ns such that subsequent energy deposits in one strip due to the same neutrino interaction accumulate onto one hit .
in particular , the timing of a delayed @xmath0decay product is lost if the decay particle overlaps spatially with prompt energy due to other particles produced in the neutrino interaction . because of this effect , the reconstruction efficiency depends on the particle multiplicity .
the timing resolution is a function of the number of observed photoelectrons ( pe ) because it is based on the decay of the fluors in the scintillator and wavelength - shifting fiber .
for many - pe hits , the timestamp will come from light that resulted from very prompt decays of the scintillator and fiber ; at smaller numbers of pe , the recorded hit times are delayed relative to the true time of the energy deposition .
the timing resolution is 10 ns for 1 - 2 pe hits , 3 ns for 6 - 12 pe hits due to minimum ionizing particles , and approaches the 2.2 ns resolution of the electronics asymptotically at very high pulse heights .
timing information is first used to separate multiple neutrino interactions within a single 10 @xmath21s beam pulse .
hits are sorted by their time , and a scan is performed to find 80-ns windows where the total energy exceeds a threshold .
the window is moved forward in time until the threshold is no longer met .
this algorithm reliably separates neutrino interactions which occur 100 ns apart , and keeps a @xmath0and its decay products together .
the design , calibration and performance of the minervadetector , including the calibration of the timing response , is described in detail in ref .
the hit timing in the data acquisition system is described in ref .
the data for this measurement were collected between march 2010 and april 2012 , corresponding to @xmath22 protons on target ( pot ) .
the horn current was configured to focus positive pions , resulting in a @xmath1-enriched beam with 10% @xmath23contamination which is largely in the high - energy tail of the flux .
the neutrino beam is simulated by a geant4-based model @xcite that is tuned to agree with hadron production measurements on carbon @xcite by the procedure described in ref .
uncertainties on the neutrino flux arise from the statistical and systematic uncertainties in these hadron production experiments , as well as uncertainties in the beamline geometry and alignment @xcite .
the integrated neutrino flux is estimated to be @xmath24{cm^{-2}/pot}$ ] .
table [ tab : nu_flux ] lists the flux as a function of energy . | production of @xmath0mesons in charged - current @xmath1interactions on plastic scintillator ( ch ) is measured using minervaexposed to the low - energy numi beam at fermilab .
timing information is used to isolate a sample of 885 charged - current events containing a stopping @xmath0which decays at rest . the differential cross section in @xmath0kinetic energy , @xmath2 ,
is observed to be relatively flat between 0 and 500 mev .
its shape is in good agreement with the prediction by the genieneutrino event generator when final - state interactions are included , however the data rate is lower than the prediction by 15% . 0=1 0=1 0=0 |
the work of c.s.k . was supported by grant no . r02 - 2003 - 000 - 10050 - 0 from brp of the kosef .
y.d . is supported in part by nfsc under contract no.10305003 , henan provincial foundation for prominent young scientists under contract no.0312001700 and in part by the project sponsored by srf for rocs , sem .
this work is also supported by grant no .
f01 - 2004 - 000 - 10292 - 0 of kosef - nsfc international collaborative research grant . | the pure penguin process @xmath0 is one of the most important probes of physics beyond the standard model .
recently babar and belle have measured the unexpectedly large transverse polarization in the decays @xmath0 , which may single out new physics effects beyond the standard model .
we study the possibility that the phenomenon could serve as an important probe of anomalous tensor interactions . we find that a spin flipped tensor interaction with a small strength and a phase could give a possible solution to the polarization puzzle . + * pacs numbers 13.25.hw , 12.60.jv * ( 0,0 ) looking for signals of physics beyond the standard model is one of the most important missions of high energy physics .
it is well known that flavor - changing neutral currents induced in @xmath1 decays are one of the best probes of new physics beyond the standard model because they arise only through loop effects in the standard model ( sm ) . to this end , the decays @xmath0 are of particular interests , since they are pure penguin processes and have interesting polarization phenomena as well as relatively clear experiment signature . within the sm
, it is expected that both @xmath2 and @xmath3 are mainly longitudinally polarized , while its transverse polarization is suppressed by the power of @xmath4 . however , last year both babar and belle had observed rather small longitudinal polarizations in the decays @xmath5 due to @xmath6 , both groups have measured unexpectedly large transverse polarizations in the @xmath7 decays . this summer babar collaboration has again reported their full angular analysis of the the decay @xmath8
@xcite @xmath9 which has confirmed their previous measurements and called urgent theoretical explanations . the final states @xmath2 and @xmath10 are fast moving in the @xmath1 meson frame and any spin flip of fast flying quark will be suppressed by power of @xmath11 .
the charge interaction currents structure of the sm is left - handed , therefore , will result in the dominance of longitudinal polarization .
such situation has been known to us for many years @xcite .
so that , the recent measurements of large transverse polarizations in @xmath0 are referred as a puzzle within the high energy physics community @xcite . the analysis of the decays within the sm can be performed in terms of an effective low - energy theory with the hamiltonian @xcite @xmath12 the amplitude for the decay within the sm can be written as @xmath13~.\end{aligned}\ ] ] since @xmath1 meson is a pseudoscalar , the final two vector mesons must have the same helicity . in the helicity basis
, the amplitude can be decomposed into three helicity amplitudes , which are @xmath14~,\nonumber \\ h_{\pm\pm}&=&i\frac{g_f}{\sqrt{2}}v_{tb}v_{ts}^ { * } a(\phi k^ * ) m_{\phi}f_{\phi } \left [ ( m_{b}+m_{k^*})a_1 \mp \frac{2m_b p_c } { m_b + m_{k^*}}v \right]~.\end{aligned}\ ] ] in naive factorization @xcite , @xmath15 then the branching ratio is thus read as @xmath16 and the longitudinal and the transverse polarization rates are @xmath17 using the wilson coefficients @xmath18 evaluated at scale of @xmath19 @xcite , and the decay constants @xmath20 gev , @xmath21 gev and the form factors of light - cone qcd sum - rules @xcite , one can get @xmath22 it must be reminded that a theoretical estimation of the branching ratios depend very strongly on the form factors from different hadronic models and the theoretical frameworks of @xmath1 meson nonletponic decays , even though most frameworks and form factors predict dominance of the longitudinal polarizations . for example , recent calculation of @xmath23 by cheng and yang by using qcd factorization @xcite gives @xmath24 for lcsr and @xmath25 for bsw form - factors @xcite , respectively , while pqcd @xcite calculation gives @xmath26 where form - factors are not inputs . however , both studies present the dominance of longitudinal polarization .
after babar and belle measurements of the abnormal large transverse polarization , there have been some theoretical explanations ; namely , through the final state interactions ( fsi ) contributions @xcite , large annihilation contributions and new physics from right - hand current interactions @xcite and transverse @xmath2 from the emitted gluon of @xmath27 which might be enhanced by new physics @xcite . in this letter , we investigate the possibility that the abnormally large transverse polarization may arise from a new tensor interaction beyond the sm ( bsm ) , @xmath28 where @xmath29 is the relative interaction strength normalized to that of @xmath30 in the sm and @xmath31 is the new physics phase . in principle , such a tensor operator could be produced even in mssm @xcite .
interestingly , the recent study of radiative pion decay @xmath32 at pibeta @xcite has found deviations from the sm in the high-@xmath33 kinematic region , which may indicate the existence of a tensor quark - lepton interaction @xcite .
we also note that kagan mentioned the case of tensor operator for resolving the puzzle @xcite .
our starting point arises from the observation that the tensor interaction only contributes to transverse polarization but not to longitudinal one .
the matrix element reads @xcite @xmath34 which is scaled as @xmath35 since @xmath36 for fast flying @xmath2 .
however , if the @xmath2 meson is produced instead from a vector interaction vertex , we will have @xmath37 , and it is easy to understand that the longitudinal polarization dominate over the transverse one by a large factor @xmath38 because of @xmath39 . using the form factors defined in ref .
@xcite , we can write down the amplitude of the tensor operator in eq .
( [ tensor ] ) in naive factorization approximation , @xmath40 from this equation , we can get the new physics contributions , @xmath41~.\end{aligned}\ ] ] compared with eq.9 , the tensor interaction contributions to @xmath42 are enhanced by a factor of @xmath43 . [ cols="^,^ " , ] numerical results are presented in fig .
1 . from fig .
1(a ) , we can find that the transverse polarization in @xmath44 is very sensitive to the presence of new tensor interactions .
for @xmath45 , we can easily find solutions to the polarization puzzle depending on the phase of the tensor interaction .
for example , to account for @xmath46 within @xmath47 , we get intervals @xmath48 , @xmath49 , @xmath50 for @xmath51 , respectively . of course , the branching ratio measurements could also give constraints on such a tensor interaction operator , which are presented in fig .
1(b ) . here
we can see the windows are very narrow because the longitudinal contribution estimated within the sm already saturate the experimental branching ratio .
however , it is well known that theoretical calculations of the branching ratios of hadronic @xmath1 decays suffer from large uncertainties .
it is believed that polarization fractions could be predicted more accurately than the branching ratios , because some of hadronic uncertainties could be cancelled in the former ones . in the future , if theoretical frameworks for hadronic @xmath1 decays could achieve @xmath52 accuracy and their predictions of longitudinal branching ratio still saturate the experimental measurement , the tensor interaction scenario could be ruled out . in such a case , we need not only new physics contributions to transverse part but also new contributions destructive to longitudinal part
. however , it would be very hard to account for the large branching ratio of @xmath53 because the similarity between the amplitudes of @xmath53 and the longitudinal amplitude of @xmath54 in the heavy @xmath55 limit . in conclusion
, we have studied the large transverse polarization puzzle in @xmath54 decays , which is taken as an important probe of an anomalous tensor interactions .
we find that a relatively weak tensor interaction could resolve the puzzle .
if we take the coupling @xmath56 , such a solution might be a signal of new physics with tensor interaction at tev scale . with the running of @xmath1 factories babar and belle ,
we have witnessed many challenging phenomena .
theoretically , we need more accurate and complete framework to clarify whether the sm could explain those abnormal phenomena or not . + _ note added : when we finished our work , we note the paper@xcite where the same tensor operator is also studied . _ |
the author acknowledges the brazilian agencies funpe and finatec for partial support , and an anonymous referee for improvements .
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_ * 12 * 2927 de lorenci v a and svaiter n f 1999 _ found .
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d _ * 53 * 4382 sciama d w , candelas p and deutsch d 1981 _ adv .
phys . _ * 30 * 327 whittaker e t and watson g n 1963 _ a course of modern analysis _ , cambridge at the university press , p. 369 . stefani h 1993 _ general relativity : an introduction to the theory of the gravitational field _ , cambridge university press , p. 80 - 83 . | the circular noise is important in connection to mach s principle , and also as a possible probe of the unruh effect . in this letter
the power spectrum of the detector following the trocheries - takeno motion in the minkowski vacuum is analytically obtained in the form of an infinite series .
a mean distribution function and corresponding energy density are obtained for this particular detected noise .
the analogous of a non constant temperature distribution is obtained . and
in the end , a brief discussion about the equilibrium configuration is given .
key words : circular unruh effect the non inertial vacuum , and the noise associated to it , has been extensively studied .
it is called fulling - davies - unruh effect , after the discoverers @xcite .
the more simple situation of proper constant acceleration , is already very well understood .
for instance , a free scalar field can be quantized in rindler coordinates .
the vacuum obtained in these coordinates is unitary inequivalent to the minkowski vacuum .
the monopole type detector introduced by dewitt @xcite , can give a meaning to these vacua .
a detector at rest in rindler coordinates is equivalent to an accelerated one in minkowski space . as a consequence of poincar invariance , a detector in inertial motion in vacuum ,
does not get excited .
this can also be understood in the detailed balance context of @xcite .
the authors used the ddc @xcite formalism to obtain the einstein coefficients for spontaneous excitation and emition . for non inertial motion
the balance of the coefficients is upset , resulting in the unruh effect .
the thermal character of the noise in the kms sense , and the verification of other consistencies are reviewed in @xcite .
in @xcite it is shown the connection between the absorptions of particles and the noise to which the detector is submitted .
the rotational motion is different . besides its own importance connected to the concept of inertia ,
this motion is of experimental relevance , because it provides a possible verification of the unruh effect @xcite .
the ddc formalism was also used in the context of rotation to obtain the spontaneous excitation of the detector , the circular unruh effect @xcite . in the very interesting work @xcite ,
de lorenci and svaiter develop the quantization in trocheries - takeno @xcite coordinates , resulting in a non trivial vacuum .
davies _
et al _ also obtain a very interesting result @xcite concerning rotational motion . since now , the de lorenci - svaiter - trocheries - takeno vacuum is the only one available for rotation .
i do not attempt to enter into the vacuum question . in this letter , an analytical expression for the power spectrum in the form of an infinite series
is obtained , a result which has not yet appeared elsewhere . in @xcite the transition rate obtained here , is left over as an integral .
i suppose a detector in minkowski vacuum , constrained to a trocheries - takeno type motion . it should be stressed that by following the procedure outlined in this letter , inside the light cylinder of @xcite , results in a transition rate similar to equation ( [ eq3 ] ) below . it is assumed a monopole type coupling of the detector and field , @xmath0 where @xmath1 has energy levels .
we require both the detector and the field to obey schrdinger s unitary time evolution .
let us assume that in the very early past the detector is in the ground state with energy @xmath2 , @xmath3 and that the field is in the ( minkowski ) vacuum state @xmath4 .
as the detector moves , field and detector will undergo transitions to various states , in a trajectory dependent fashion @xcite .
since one does not care about the field s final state , the unknown final state of the field should be traced out from the transition probability for thetransitions in question .
this process yields , in first order perturbation theory the following expression for the transition rate @xmath5 where @xmath6 is the energy difference between the initial and final states of the detector and @xmath7 is the positive frequency wightman function .
@xmath8 depends on the internal constituency of the detector and a detailed discussion of it is given in @xcite and @xcite .
while the second term in ( [ eq1 ] ) corresponds to the noise this detector is submitted to , that s to say , on the way the field fluctuates as seen by the observer in his trajectory @xmath9 .
it is an easy exercise to show that a detector at rest in the trocheries - takeno coordinates @xmath10 @xmath11 according to ( [ eq1 ] ) , has a transition rate given by @xmath12 ^ 2 \sin[(s/2)\sinh(\omega r)r^{-1}]^2}ds,\ ] ] where @xmath13 is the proper time between two points in the trajectory of the detector . after a change in the integration variable the above transition rate ,
is written as @xmath14dx } { ( x)^2-v^2\sin(x)^2 } , \label{eq2}\ ] ] where @xmath15 the fact that @xmath16 , comes from the type of trajectory that the detector is following . in this sense , this trajectory is more physical , because the detector is not allowed to travel faster than the speed of light . in ( [ eq1 ] )
, the @xmath17 factor is associated to the adiabatic switching of the detector and the usual @xmath18 prescription is related to its size .
as @xmath16 , and the integral is over the real axis , the integrand in ( [ eq2 ] ) can be written as @xmath19}{(x - i\epsilon)^2 } \sum_{n=0}^{\infty}\left(\frac{v\sin(x - i\epsilon)}{x - i\epsilon}\right)^{2n}.\ ] ] after a binomial expansion , this last integral is evaluated using ordinary residue calculus @xmath20^{2n+2k-1 } \theta ( -e + k\omega\gamma ) } { ( -1)^{n-1}(2n+2k-1)(n-1)!(n+2k-1 ) ! } , \label{eq3}\ ] ] where @xmath21 is the heaviside step function , which indicates that the rotational motion is the thermal reservoir .
the time scales of the detector @xmath22 and the ( proper ) period of rotation of the detector @xmath23 are singled out in ( [ eq3 ] ) , a property also shown in @xcite and @xcite . as a spectrum , ( [ eq3 ] ) ,
can be divided by the energy @xmath24 and an _ effective _ distribution function for the scalar particles can be obtained @xmath25^{2n+2k-1 } \theta ( -e + k\omega\gamma ) } { ( -1)^{n-1}(2n+2k-1)(n-1)!(n+2k-1)!}. \label{dist}\ ] ] effective here is in a certain sense , that the distribution function is dependent on the measuring apparatus .
other consequences connected to the motion , should be perceived by other types of detectors .
only the detectable properties are taken into account .
this distribution function is understood as the mean number of particles per volume , with energy @xmath24 perceived by the detector . in the following
, density will be assumed to be per unit volume . in this spirit , the total energy density of the scalar particles is given by the following integral , which can be written in terms of the hypergeometric function @xmath26^{2n+2k-1 } } { ( -1)^{n-1}(2n+2k-1)(n-1)!(n+2k-1)!}\nonumber\\ & & e_t=\frac{\omega^2}{2 \pi v } \sum_{n=1}^{\infty}\sum_{k=1}^{\infty}\int_0^k dx \frac{\left[v\left(-x + k\right)\right]^{2n+2k-1 } } { ( -1)^{n-1}(2n+2k-1)(n-1)!(n+2k-1)!}\nonumber\\ & & e_t=\frac{1}{2 \pi r^2}\sum_{n=1}^{\infty}\sum_{k=1}^{\infty}\frac{(vk ) ^{2(n+k)}}{(-1)^{n-1}(2n+2k)(2n+2k-1)(n-1)!(n+2k-1)!}\label{limite}\\ & & e_t=\frac{1}{2\pi r^2}\sum_{k=1}^{\infty } \frac{(\tanh(\omega r)k)^{2k+2 } { } _ { 2}f_3(k+1/2,k+1;k+3/2,k+2,2k+1;-\tanh(\omega r)^2k^2)}{(k+1/2)(k+1)(2k)!}\label{energia},\end{aligned}\ ] ] where @xmath27 plays a role similar to the temperature , and there is an explicit dependence on the coordinate @xmath28 .
this corresponds to a non constant temperature distribution .
for instance , in the above expression ( [ energia ] ) , at the origin when @xmath29 , the energy density is @xmath30 , which makes sense , because the motion of detector when @xmath29 is inertial .
next , the convergence of the infinite summation ( [ limite ] ) , is discussed .
the second derivative with respect to @xmath31 of ( [ limite ] ) is of the type @xmath32 the last expression is valid asymptotically when @xmath33 and @xmath34 @xcite . in this asymptotic spirit , the summation ( [ converg ] ) can be replaced by the integral over @xmath35 , from @xmath36 to @xmath37 , which results in @xmath38 the original summation ( [ limite ] ) is obtained by integrating the last equation two times in @xmath31 @xmath39 which is plotted numerically in the following + + the above graphic indicates , in a indirect way , that the summation given in ( [ limite ] ) and ( [ energia ] ) converges , except when @xmath40 .
this divergence of the total energy density of the scalar particles perceived by the detector , is expected when the detector is moving ( almost ) with the velocity of light , @xmath40 . by summing the first few terms in ( [ energia ] ) , the following total energy density of scalar particles is obtained at a given @xmath28 , for @xmath41 and @xmath42 + showing that for a same distance @xmath28 from the origin , there is an increase in the energy for larger values of @xmath27 . it should be stressed that in spite that ( [ energia ] ) describes a non constant temperature distribution , it is an equilibrium configuration . this interesting equilibrium concept is well known and is expected if the space being considered is not homogeneous and isotropic as in trocheries - takeno case , see for example @xcite . the external condition that originates
this motion is responsible for this apparent non equilibrium .
the above construction avoids canonical quantization , and it could be usefull to a further understanding of external conditions . |
+ local - susceptibility measurements via the nmr shifts of @xmath0p and @xmath1v nuclei in the high - pressure phase of ( vo)@xmath2p@xmath2o@xmath3 confirmed the existence of a unique alternating antiferromagnetic chain with a zero - field spin gap of 34 k. the @xmath0p nuclear spin - lattice relaxation rate scales with the uniform spin susceptibility below about 15 k which shows that the temperature dependence of both the static and dynamical spin susceptibilities becomes identical at temperatures not far below the spin - gap energy .
magnetic excitations of a low - dimensional quantum antiferromagnet have been one of the current topics among the condensed matter physicists .
vanadyl pyrophosphate ( vo)@xmath2p@xmath2o@xmath3 had long been believed as a prototype of a spin-@xmath4 two - leg ladder which has a magnetic lattice intermediate between one and two spatial dimensions @xcite . the ladder model , however , has been rejected by an observation of a dominant magnetic interaction perpendicular to the supposed ladder axis via the inelastic neutron scattering ( ins ) measurements @xcite .
a dimerized ( alternating ) chain model has now been becoming accepted as an alternative starting point , although a mechanism of the major exchange interaction between distant pairs of v@xmath5 spins via po@xmath6 tetrahedra is still under study @xcite .
the ins experiments has also revealed the existence of the mode with a gap nearly twice the gap of the lowest excited triplet which can not be explained by a simple alternating - chain model .
this mode has first been assigned as a bound state of two magnons possibly formed via interchain couplings @xcite , but it was difficult to account for the intensity comparable to the fundamental mode .
recent nmr @xcite and high - field magnetization @xcite studies have suggested on this issue that the two structurally - distinguishable chains of v atoms , which were thought to be magnetically identical , have different spin - gap energies .
this gives a natural explanation for the existence of two distinct modes with almost equal spectral weight , and has been supported by the subsequent raman - scattering experiments @xcite and theoretical studies on relevant exchange interactions @xcite .
the above confusion concerning the modelling and interpretation of the experimental results of ( vo)@xmath2p@xmath2o@xmath3 comes not only from the unexpectedly strong v - v exchange via po@xmath6 tetrahedra , but also from the presence of structurally - inequivalent v chains @xcite .
more recently , azuma have found that ( vo)@xmath2p@xmath2o@xmath3 transforms into another phase with different symmetry under pressure @xcite .
all the v atoms occupies a unique crystallographic site in the high - pressure ( hp ) phase , so that the magnetic chains made of v@xmath5 spins are all equivalent .
therefore , hp-(vo)@xmath2p@xmath2o@xmath3 will be a better example of the alternating antiferromagnetic chain with quantum spin @xmath4 . in this letter
, we report microscopic characterization of the magnetic chains in the hp phase of ( vo)@xmath2p@xmath2o@xmath3 via nmr . a single spin component characterized by a zero - field gap of 34
k was found , presenting support for the double - chain scenario for the ambient - pressure ( ap ) phase .
single crystals of the hp phase of ( vo)@xmath2p@xmath2o@xmath3 were grown as described in @xcite . since the crystals were too small to observe an nmr signal , they were crushed into powders and the nmr measurements were made on these powders .
standard spin - echo pulse techniques were utilized for most of the experiments .
an example of the field - swept @xmath0p nmr spectrum in the hp phase of ( vo)@xmath2p@xmath2o@xmath3 is shown in figure [ fig:31pspectrum ] .
the spectrum in the ap phase @xcite is also shown for comparison .
the spectrum in the hp phase consists of a single line as expected from the unique crystallographic site of phosphor in the unit cell .
this is contrasted with the ap phase where the spectrum splits into two groups of lines owing to the presence of two kinds of v chains with different gap energies @xcite .
the line - shape analysis revealed that the symmetry of an nmr - shift tensor at the p site is almost uniaxial . assuming the exact uniaxial symmetry , we determined the two independent principal values @xmath7 and @xmath8 corresponding to the shift with the external field parallel and perpendicular to the local symmetry axis , respectively .
the results are shown in figure [ fig:31kvst ] as a function of temperature .
both @xmath7 and @xmath8 scale the bulk magnetic susceptibility @xmath9 which is corrected by subtracting the contribution of paramagnetic impurities .
following the standard @xmath10@xmath9 analysis , the tensor components of the hyperfine coupling at the p site were determined as @xmath11 t/@xmath12 and @xmath13 t/@xmath12 .
these values yield the isotropic and uniaxial components , @xmath14 t/@xmath12 and @xmath15 t/@xmath12 , respectively .
@xmath16 is larger than and different in sign from that due to the classical dipolar field of v@xmath5 spins @xmath17 t/@xmath12 , indicating that the v@xmath5 spins are transferred not only to the p-@xmath18 orbitals but also to the p-@xmath19 orbital .
the susceptibility of a one - dimensional ( 1d ) gapped spin system at temperatures well below the gap @xmath20 is proportional to @xmath21 @xcite . in order to determine @xmath20
, we fitted the @xmath22 dependence of the isotropic component of the nmr shift @xmath23 below 10 k to the form @xmath24 , where the reduction of @xmath20 by fields is explicitly written .
the result is shown in the inset of figure [ fig:31kvst ] .
the obtained parameters are @xmath25 % , @xmath26 k@xmath27 , and @xmath28 = 31 k which gives @xmath29 = 34 k with the use of the measured @xmath30 factor @xcite .
@xmath31 is in good agreement with that evaluated from the bulk @xmath9 but is larger than the values determined from the critical field of the magnetization process ( @xmath3223 k ) @xcite and the ins on polycrystals ( @xmath3225 k ) @xcite for unknown reasons .
a free - induction - decay ( fid ) signal of @xmath1v has also been observed below about 50 k. the spectrum was obtained by integrating the fid signal while sweeping the external field .
the @xmath22 dependence of the @xmath1v nmr shift @xmath33 determined from the peak position of the spectrum is shown in figure [ fig:51kvst ] .
also shown in the inset is a plot of @xmath23 versus @xmath33 with @xmath22 the implicit parameter .
a linear relation found between @xmath23 and @xmath33 demonstrates that the @xmath22 dependence of the local spin susceptibility is identical for both the sites .
this is a clear sign of hp-(vo)@xmath2p@xmath2o@xmath3 having only one independent spin component .
the @xmath22 dependence of @xmath33 was analyzed in the same way as that of @xmath23 using @xmath20 determined above .
the @xmath22-independent orbital ( van - vleck ) shift was then obtained to be 0.182 % .
the hyperfine coupling constant at the v site determined from the slope of the @xmath34 plot is @xmath35 t/@xmath12 , which is in a reasonable range as a core - polarization field of a @xmath36 transition - metal ion @xcite .
figure [ fig:31wvst ] shows the @xmath22 dependence of the @xmath0p nuclear spin - lattice relaxation rate @xmath37 .
@xmath38 above 8 k was determined as the time constant of the exponential recovery of @xmath0p magnetization @xmath39 . below 8 k where non - exponential recovery appears ,
we analyzed @xmath39 by fitting to the form @xmath40 which incorporates the relaxation rate @xmath41 due to paramagnetic impurities @xcite .
as shown in the inset of figure [ fig:31wvst ] , @xmath37 exhibits activated behavior below about 20 k. the exponential decrease of @xmath37 is , however , masked below @xmath328 k synchronizing the appearance of non - exponential recovery .
the asymptotic value of @xmath37 at low @xmath22 is suppressed by applying fields as expected for the impurity - limited relaxation rate .
@xmath37 depends on @xmath42 at higher temperatures as well where the recovery is exponential , but the @xmath42 dependence roughly follows the 1d diffusive form @xmath43 as observed in ap-(vo)@xmath2p@xmath2o@xmath3 @xcite .
details of the @xmath42 dependence of @xmath37 will be presented in a separated paper .
the activation energy was estimated as @xmath44 k by fitting the data between 8 and 20 k to the form @xmath45 .
as the interbranch ( @xmath46 ) transitions within the lowest excited triplet @xcite are expected to dominate the nuclear - spin relaxation due to the predominantly - isotropic hyperfine fields , the obtained @xmath47 would give an estimate of the zero - field gap .
@xmath47 indeed agrees well with @xmath29 evaluated from the nmr shift .
figure [ fig : t1tkvst ] shows the @xmath22 dependence of @xmath48 divided by @xmath49 .
one of the remarkable features of the result is that the ratio @xmath50 becomes @xmath22 independent below about 15 k. ( an upturn below @xmath327 k is due to the impurity contribution to @xmath37 and is extrinsic . )
it is well known that , while the nmr shift is proportional to the uniform static susceptibility @xmath51 , @xmath37 samples the dissipative part of the dynamical susceptibility @xmath52 at the nuclear larmor frequency @xmath53 @xcite ; @xmath54 here @xmath55 is the fourier transform of the hyperfine coupling . since @xmath55 has a maximum at @xmath56 = 0 , @xmath37 at the p site is most sensitive to @xmath57 which is dominant at low @xmath22 in a gapped 1d spin system @xcite .
the @xmath22-independent behavior of @xmath50 therefore indicates that the @xmath22 dependence of @xmath58 and @xmath51 at low @xmath22 is identical and should be described by a common energy gap .
such a characteristic of the magnetic excitations in a gapped 1d spin system has been predicted theoretically based on a picture of free magnons @xcite , but has rarely been observed experimentally @xcite . to our knowledge , this is the first experimental verification of @xmath48 and @xmath10 having identical @xmath22 dependence at low @xmath22 , not relying on any model - dependent form of these quantities . from the experimental viewpoint , it is worth noting that the scaling between @xmath48 and @xmath10 holds below @xmath59 .
this suggests nearly free propagation of magnons being realized at temperatures not far below @xmath20 .
it is therefore practical to use experimental data in the region @xmath60 for a reliable estimate of @xmath20 , although the activated behavior of physical quantities such as @xmath9 and @xmath37 is theoretically justified only for @xmath61 @xcite . above about 20 k , the scaling breaks down and @xmath62 increases gradually with @xmath22
this means that @xmath63 grows more rapidly than @xmath51 .
as the temperature is now comparable with or higher than @xmath20 , interactions between magnons and/or the @xmath64 component of spin fluctuations will become increasingly important and would enhance @xmath65 over @xmath51 . in conclusion ,
we have measured @xmath0p and @xmath1v nmr in the high - pressure phase of ( vo)@xmath2p@xmath2o@xmath3 .
it was found that the temperature dependence of the local static spin susceptibility at the p site is identical with that at the v site .
the dynamical spin susceptibility @xmath65 near @xmath66 also scales with the static susceptibility at low temperatures below about a half of the spin - gap energy which was estimated to be 34 k at zero field .
all of these observations provides microscopic evidence for a unique kind of magnetic chain existing in the high - pressure phase of ( vo)@xmath2p@xmath2o@xmath3 , as well as for coexistence of magnetically - inequivalent chains in its ambient - pressure phase . |
|
estimates for the ambient neutrino flux are an important input parameter to experiments analyzing underground neutrino interactions and upward going muons to understand the time evolution of a neutrino beam .
different directions provide neutrino fluxes with varying source distance so observation of the angular distribution is an essential tool in the study of neutrino oscillations .
since the overall flux normalization is uncertain , experiments frequently place a greater emphasis on the shape of the distribution than the absolute event rate .
this note points out _ depth dependent _ effects that can also provide a directional modulation .
these effects are modest , but predominantly effect the higher end of the neutrino spectrum .
upward going muons @xcite are usually attributed to muon neutrino interactions in the rock surrounding the detector . in order to be detected as an upward going muon , the lepton produced in a neutrino interaction must propagate through the rock to be recorded in the detector .
if we approximate the muon energy loss as muon energy independent then the range increases linearly with the muon energy .
so the target rock surrounding the detector has a larger effective mass for neutrino interactions at high energy , scaling roughly as @xmath0 . over a substantial range of neutrino energies
the cross section rises linearly . so that a constant mass detector will have more high energy neutrino interactions than low energy neutrino interactions at the same flux .
these two factors suggest that the neutrino induced muon flux is sensitive to the third power of the neutrino energy .
small neutrino flux differences at high energies are substantially amplified by this @xmath1 factor .
we present a one dimensional model to show that the atmospheric decay path length is a function of the detector depth .
detectors which are above sea level will see neutrinos with a higher decay path length than detectors below sea level . to first order
the high energy part of the neutrino flux is proportional to the decay path length .
figure [ geom ] illustrates the geometry . this figure is not to scale .
we take @xmath2 to be the radius of the earth , 6380 km and @xmath3 to be the radius at which neutrino source particles are produced .
@xmath4 will be one interaction length below @xmath3 .
most decays will occur between @xmath3 and @xmath4 .
@xmath5 represents the detector depth .
if the detector is above sea level @xmath5 will be negative .
we take as the decay length the difference in length for ray originating at @xmath5 and ending at a point along the ray at radius @xmath3 or @xmath2
. it should be clear from figure [ geom ] , with its disproportionate scale that the decay length will depend on detector depth .
for muons we take @xmath6 , the surface of the earth .
a particle initiating in the upper atmosphere will travel a distance s before being absorbed .
@xmath7 very near the horizon , the particle path may not intersect @xmath4 , if the detector is above sea level ( @xmath8 ) . in that case
we approximate the decay length by the distance from the upper atmosphere to the detector .
@xmath10 is the zenith angle .
note for upward going neutrinos @xmath11 . in figure [ maxrel ]
we illustrate this effect for muons , where we take @xmath6 and @xmath12 km .
the figure shows the maximum decay length for muons below the horizon . in most cases
this maximum is obtained at the horizon .
but when the detector is above sea level , @xmath13 , the maximum decay path length is achieved near the horizon . notice that the decay path length increases with the detector height
. common detector depths , @xmath5 are in the range of -1 km @xmath14 2 km .
detectors located in the mountains tend to be deep underground but well above sea level .
in figure [ murel ] we explore the relative flux , as a function of neutrino parent particle energy , for 4 different detector depths .
this figure plots the contribution to the neutrino flux of a detector at @xmath15 - 2 , -1 , 1 or 2 km .
relative to the contribution to the neutrino flux for a detector located at sea level ( @xmath16 ) .
the flux is averaged over the solid angle region of @xmath17 , the angular bin just below the horizon .
variations are about 5% to 10% . in figure [ murel ]
one sees that the enhancement is not present at low energies , where all particles will decay .
there is a transition region at moderate energies where the decay length is comparable to the absorption length . at the highest energies the decay probability scales linearly with the available decay length
so the flux differences directly reflect the path length differences due to detector depth .
the shape differences for muons , pions and kaons are due to the differences in masses , lifetimes and absorption lengths .
figure [ murel2 ] is similar to figure [ murel ] except that now the solid angle region @xmath18 is considered .
variations are now of the order of 0.6% to 1.2% .
the much lower flux modification away from the horizon indicates that standard neutrino flux calculations , that do not include the detector depth , will not correctly represent the angular distribution .
figure [ mpkprob ] plots the muon , pion and kaon decay probability as a function of decay particle energy .
the contribution at high energies is dominated by the particle with the shortest lifetime .
figure [ shower ] illustrates the depth effect in hadronic shower evolution .
the multiple curves are for hadrons initiating at greater depth into the atmosphere .
each curve is 2 absorption lengths deeper in than the one to its right .
the depth modulation is maintained at approximately the same amplitude , but as showers go deeper into the atmosphere the curves move to lower energies since the absorption length drops .
higher energy hadrons are more likely to be absorbed than to decay when the are formed lower in the atmosphere .
this paper has made no attempt to quantitatively sum the various contributions to the atmospheric neutrino flux .
muons , pions and kaons all contribute but their relative contributions depend on their initial fractions and the fate of the other contributions . at very high energies `` prompt '' sources of neutrinos such as
charm decay become important . at the highest energies muons produced via decays of the form @xmath19 and
@xmath20 , or drell - yan processes constitute a significant source of neutrino flux .
our analysis suggests that there is a modest location dependent contribution to the high energy atmospheric neutrino flux .
detectors above sea level ( but still underground ) will see enhancements of the high energy flux in the vicinity of the horizon .
this would be manifest as an angular distortion and an increased rate .
detectors below sea level would expect to see the opposite effect , with fewer high energy events and fewer events near the horizon . while these effects are of the order of 5% to 10% they contribute a systematic distortion when comparing data taken at different locations or when comparing observations from a deep detector to a flux estimate for a sea level location .
todor stanev has recently reached similar conclusions about the influence of detector depth .
i would like to thank o. ryazhskaya for pointing out the significance of muon production via hadronic resonance decay ( @xmath19 ) as a major source of neutrinos at high energies .
this work was supported in part by the us department of energy under grant de - fg02 - 00er41145 .
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thesis , institute for cosmic ray research , university of tokyo ( 1989 ) . | we note that detector depth can influence the decay path length available for the primary and secondary particles that are the source of atmospheric neutrinos . as a consequence
there is a location dependent modulation to the neutrino flux , which could be as large as 5 - 10% in some directions . |
the variability of grbs provided the main evidence for the internal - external shocks scenario .
external shocks can not produce efficiently such variability @xcite .
internal shocks can produce such temporal structure provided that there are two time scale within the inner engine " - a short time scale that produces the variability and a long time scale that determines the duration of the burst .
so far variability was shown only for long bursts .
it is an open question whether short bursts arise in internal shocks as well . using a new algorithm @xcite we study their variability .
we also present some new results on the temporal structure of long bursts .
our results provide further support for the internal shocks scenario and show that three different time scales operate within the inner engine " .
we analyze the distribution of @xmath4 ( where @xmath5 is the duration of the shortest pulse in a burst , and @xmath6 is the total duration of the burst ) in a sample of the brightest 33 short bursts ( peak flux in 64ms@xmath74.37@xmath8 ) with a good tte data coverage ( for batse data types review @xcite ) .
the tte data is binned into 2msec time bins .
we compare the results to a sample of 34 long bursts with the same peak flux , using the 64ms concatenate data to which we have added a poisson noise so that the signal to noise ratio of both samples would be similar .
we call this later sample the _ noisy long _ set .
fig [ dt / t in shorts ] depicts @xmath4 in both data sets : _
short _ and _
noisy long_. in the _ short _ set the median of @xmath4 is 0.25 .
35% of bursts have @xmath9 and 35% of the bursts show a smooth structure ( @xmath10 ) .
this result could mislead us to the conclusion that a significant fraction of the short bursts have a smooth time profile . but a comparison with the _
noisy long _ results show that also in this group more than 20% of the bursts are single pulsed , while there were no such bursts in the original ( without the added noise ) _
long _ set .
we conclude that short bursts are variable and hence are most likely produced in internal shocks .
while the observed variability is not as large as seen in long bursts one has to remember that when studying variability of short bursts we are approaching the instrumental limitations both in terms of the time scales and of the signal to noise ratio .
it is possible that 10%-20% of the short bursts are produced by external shocks .
according to the internal shocks model @xcite the source ejects relativistic shells with different velocities and shocks arise when faster shells catch slower ones .
we show in @xcite that both the pulses width @xmath11 and the intervals between pulses @xmath12 are proportional to the same parameter - the separation between two following shells , namely the variability time scale of the inner engine " . therefore both distributions should be similar .
moreover , any interval should be correlated to the width of its neighboring pulses .
we have applied our algorithm to a sample of the 68 brightest long bursts in batse 4b catalog ( peak flux in 64ms@xmath710.19@xmath8 ) .
this resulted in 1330 pulses ( 1262 intervals ) .
our null hypothesis was that both @xmath13 and @xmath14 , have lognormal distributions .
the @xmath15 test gives a probability of @xmath16 that the pulses width were taken from a lognormal distribution with @xmath17 ( @xmath18 ) and @xmath19 ( @xmath20 corresponds to @xmath21 between 0.5 and 2.3sec ) .
the @xmath12 distribution shows , however , an excess of long intervals relative to a lognormal distribution .
the @xmath15 probability for a lognormal distribution is * @xmath22*. mcbreen@xcite and li & fenimore@xcite suggest that this deviation is due to the limited resolution ( 64ms ) . however , fitting the intervals above the median with a half gaussian fails .
the inconsistency is not due to the resolution .
many of the long intervals are dominated by a quiescent time : periods within the burst with no observable counts above the background noise . when excluding _ all _ the intervals that contained a quiescent time the @xmath15 probability that the data is lognormal is * @xmath23 * , with @xmath24 ( @xmath25 ) and @xmath26 ( @xmath20 corresponds to @xmath27 between 0.53 and 3.1sec ) .
the similarity between the parameters of both distributions is remarkable .
moreover , we find , as predicted by the internal shocks model , a linear correlation , @xmath28 , between intervals and the following pulses .
the average @xmath28 is 0.48 , showing a strong correlation .
for most short bursts @xmath2 .
this suggests that these bursts are produced by internal shocks .
if , later , the ejecta encounters a surrounding ism then we expect it to produce an external shock and emit an afterglow . for some ( 30% of our sample ) short bursts @xmath29 . however , a comparison with the _
noisy long _ set , shows that this feature could very well be due to the noise .
we can not rule out the possibility that 10%-20% of the short bursts are produced by external shocks or by a single internal collision .
the distribution of interval between pulses shows an excess of long intervals relative to a lognormal distribution . after removing intervals that include quiescent times
the distribution is consistent with a lognormal distribution with comparable parameters to the pulse width distribution .
this result suggests that the @xmath12 distribution is made from the sum of two different distributions : a lognormal distribution that is also compatible with the @xmath11 distribution and the quiescent times distribution . as @xmath30 reflects the central engine behavior
, this suggests that there are two different mechanisms operating within the source .
a short time scale mechanism , with a lognormal distribution and a longer time scale mechanism that turns the central engine on and off and is responsible for the quiescent times .
results that support this suggestion were obtained by ramirez & merloni @xcite .
the correlation between the interval and the following pulse confirms this suggestion and is in an excellent agreement with the internal shocks model .
1 sari , r. & piran , t. , 1997 , apj 485 , 270 nakar , e. & piran , t. , 2001a in preparation scargle , j. d. 1998 , apj v.504 , p.405 rees . m. j. & meszaros , p.,1994 , apj , 430 , l93 nakar , e. & piran , t. , 2001b in preparation mcbreen b. personal communication mcbreen , b. , et .
1994 , mnras , 271 , 662 li , hui ; fenimore , e. 1996 , apj 469 , l115 ramirez - ruiz , e. , merloni , a. , 2001 , mnras 320 l25 | we analyze the temporal structure of long ( @xmath0 ) and short ( @xmath1 ) batse bursts .
we find that : ( i ) in many short bursts @xmath2 ( where @xmath3 is the shortest pulse ) .
this indicates that short bursts arise , like long ones , in internal shocks .
( ii ) in long bursts there is an excess of long intervals between pulses ( relative to a lognormal distribution ) .
this excess can be explained by the existence of _ quiescent times _ , long periods with no signal above the background that arise , most likely , from periods with no source activity .
the lognormal distribution of the intervals ( excluding the _ quiescent times _ ) is similar and correlated with the distribution of the pulses width , in agreement with the predictions of the internal shock model . |
we thank r. liotta for stimulating discussions and his reading of the manuscript .
this work was supported by the swedish research council ( vr ) under grant nos .
621 - 2012 - 3805 , and 621 - 2013 - 4323 .
the calculations were performed on resources provided by the swedish national infrastructure for computing ( snic ) at nsc in linkping and pdc at kth , stockholm .
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phys . a 929 ( 2014 ) 191 . | the empirical pairing gaps derived from four different odd - even mass staggering formulas are compared . by performing single-@xmath0 shell and multi - shell seniority model calculations as well as by using the standard hfb approach with skyrme force we show that the simplest three - point formula @xmath1 $ ] can provide a good measure of the neutron pairing gap in even-@xmath2 nuclei .
it removes to a large extent the contribution from the nuclear mean field as well as contributions from shell structure details .
it is also less contaminated by the wigner effect for nuclei around @xmath3 .
we also show that the strength of @xmath4 can serve as a good indication of the two - particle spatial correlation in the nucleus of concern and that the weakening of @xmath4 in some neutron - rich nuclei indicates that the di - neutron correlation itself is weak in these nuclei .
the occurrence of a systematic odd - even staggering ( oes ) of the nuclear binding energy has long been identified in nuclear physics , which is associated with the pairing correlation @xcite .
it plays an important role in many nuclear phenomena and is the dominant many - body correlation beyond the nuclear mean field . yet , in spite of the many efforts performed in the study of pairing correlations , there are still features which may be induced by the pairing interaction that are not well understood @xcite .
in particular , this is the case in neutron - rich nuclei , where the study of effects induced by pairing may shed light on the understanding of various exotic phenomena ( see , e.g. , refs .
@xcite ) .
the simplest expression one can use to extract the empirical pairing gap from the oes of the binding energy is the three - point formula @xcite , which for systems with even neutrons acquires the form @xcite @xmath5\\ = -\frac{1}{2}[s_n(n+1,z)-s_n(n , z)]\end{gathered}\ ] ] where @xmath6 is the ( positive ) binding energy and @xmath7 is the one - neutron separation energy . the proton pairing gap can be defined in a similar way .
the above formula indicates that @xmath8 measures the additional binding gain by the last neutron in the even-@xmath2 system relative to the odd system with one more neutron .
however , besides pairing , a number of other mechanisms may contribute to the oes @xcite .
this includes effects induced by the mean field in deformed nuclei ( or the kramers degeneracy ) and the contribution from the diagonal interaction matrix elements of the two - body force . as discussed in detail in refs .
@xcite by satula and co - workers , the contribution from the quickly varying single - particle structure of the mean field to the empirical pairing gap is minimized in odd - mass systems . in even systems where the last neutrons occupy different orbitals
the single - particle energy contributes substantially to @xmath8@xcite .
alternatively , there is another version of the three - point formula written as @xmath9\\ = \frac{1}{2}\left[b(n , z)+b(n-2,z)-2b(n-1,z)\right ] \\ = \frac{1}{2}[s_{2n}(n , z)-2s_n(n-1,z)],\end{gathered}\ ] ] which actually corresponds to @xmath10 for the case of odd nuclei @xcite .
@xmath11 is smaller than @xmath8 in most cases .
it is often stated that @xmath11 measures the pairing effect in the odd nuclei , as illustrated in ref .
@xcite , whereas @xmath8 is impacted by single particle states ( see e.g. , recent discussion in ref . @xcite and references therein ) .
the challenging problems thus arise include : one lacks a measure of the pairing gap in the even system , which is mixed with the deformation effect , and the empirical pairing gap for the odd system is related to pairing only in an indirect manner ( i.e. , the energy loss due to the absence of pairing ) .
the physics becomes even more obscure when abrupt changes occur , e.g. , around shell closures . in practice , as a compromise , the value of @xmath11 has often been compared to the theoretical pairing gap calculated for the even systems @xcite and to the oes derived from theoretical binding energies @xcite . the direct comparison between the theoretical pairing gap and empirical oes is convenient from a computational point of view since only one single calculation is required , which avoids the complicated handling of the blocking effect in the odd nuclei . it is known that the theoretical pairing gap , e.g. , that from the bcs theory , is not an observable and can not be compared with the empirical oes in a straightforward way .
however , they can be quantitatively quite close to each other in most cases and both of them are still important quantities that deserves further attention .
in particular , within the bcs approach , the corresponding pairing gap is given by @xmath12 where @xmath13 is the pairing strength , and @xmath14 , @xmath15 are the standard occupation numbers .
this implies that the pairing gaps can serve as a signature of the change in two - particle spatial correlation / clusterization , since they are also proportional to @xmath16 .
this feature is also responsible for the clustering of the four nucleons that eventually constitute the @xmath17-particle at the nuclear surface of heavy nuclei @xcite . in this paper
we would like to argue that , among the expressions for the oes studied here , the simple three - point formula @xmath18 removes to a large extent the contribution from the varying part of the nuclear mean field as well as contributions from other shell structure details and can serve as a reliable indication for the pairing effect in even-@xmath2 systems .
in other words , @xmath18 can be compared to the theoretical pairing gap in a semi - quantitive manner and thus contains fruitful information on the pairing effects . in particular
, the abrupt changes in @xmath18 do have physical meaning .
moreover , by using @xmath18 one can make it more convenient to extract the neutron - proton interaction from binding energy differences @xcite .
we will also show that @xmath18 is free from the wigner effect for nuclei around @xmath3 and that its weakening in some neutron - rich nuclei may indicate that the di - neutron spatial correlation itself is weak in those nuclei .
there are other formulas available for the pairing gap including the so - called four - point and the five - point formulas .
the four - point formula is defined as @xcite @xmath19\\ = \frac{1}{2}[\delta^{(3)}(n)+\delta^{(3)}_c(n)].\end{gathered}\ ] ] that is , it measures the average value of @xmath10 in adjacent even and odd systems .
the five - point formula is given by @xcite @xmath20\\ = \frac{1}{4}[\delta^{(3)}_c(n+2)+2\delta^{(3)}(n)+\delta^{(3)}_c(n)].\end{gathered}\ ] ] the five - point formula is also used in refs .
@xcite . in refs . @xcite
, the experimental pairing gap is taken as the average of adjacent ones deduced through the three - point formula as @xmath21 , \end{aligned}\end{aligned}\ ] ] which is actually also a five - point formula involving the same group of nuclei as @xmath22 but with different weights for each nucleus .
our calculations show that there is no significant difference between the results derived from @xmath23 and @xmath18 for open - shell nuclei where the pairing gap is a smooth function of @xmath2 . for the same reason , @xmath24 and @xmath25
show quite a similar behavior for most nuclei .
noticeable differences between @xmath26 and @xmath18 may be seen where abrupt changes in pairing correlations are expected to happen , e.g. , around shell closures , which is smoothed out in the former case .
[ htdp ] empirical neutron pairing gaps ( in mev ) from different oes formulas for all even - even nuclei as a function of neutron number @xmath2 . results which errors larger than @xmath27 kev are marked in red color .
the dashed curves are determined by fitting to the data .
the solid horizontal lines show the average value of @xmath28 ( 1.08@xmath290.40 mev ) and the corresponding @xmath30 uncertainty ) . , scaledwidth=45.0% ] [ cols="^,^,^,^,^",options="header " , ] the empirical pairing gaps obtained by various oes formulas are shown in fig .
[ fig:4gaps_errors ] for which the nuclear binding energies are extracted from refs .
@xcite .
the results are fitted by the expression @xmath31 where @xmath32 and @xmath17 are parameters to be determined .
our calculations show that this expression performs equally well as the usual @xmath33-dependence fit , as can be seen in table [ tab : fitt ] where the results of fitting a power function to the different mass formulas as a function of neutron number , @xmath2 , and mass numbers , @xmath33 , are given .
it is also seen that the dependence of the gap upon the neutron or mass number is weakest for @xmath4 .
this is consistent with the conclusions of refs .
@xcite that the pairing gap should not show significant mass dependence . only in nine cases
one has @xmath4 larger than 2 mev .
they correspond to @xmath34be ( 4.11 ) , @xmath35be ( 2.57 ) , @xmath35c ( 3.53 ) , @xmath36c ( 2.8 ) , @xmath37o ( 3.15 ) , @xmath38ne ( 2.6 ) , @xmath39 mg ( 2.3 ) , @xmath40si ( 2.02 ) and @xmath41ti ( 2.0 ) ( within parenthesis are the corresponding pairing gaps in mev ) .
the mean values of the pairing gaps corresponding to the different expressions given above are ( in mev ) @xmath8 = 1.46 , @xmath4 = 1.08 , @xmath42 = 1.26 and @xmath22 = 1.26 .
we also evaluated the empirical pairing gaps for the proton for which one obtains @xmath43 mev , which contains a smooth contribution from the coulomb field .
in table [ tab : fitt ] we also included calculations for the even-@xmath2 odd-@xmath44 nuclei .
however , it should be mentioned that the empirical oes @xmath4 thus extracted contains a sizable negative contribution from the residual neutron - proton interaction between the odd particles in the intermediate odd - odd nuclei . as indicated in eqs .
( 1 ) , ( 3 ) and ( 4 ) , all these oes formulas contain constantly a contribution from the mean field which peaks at the shell closure and persists in open - shell nuclei @xcite .
for the same reason , the oes formula eq .
( 2 ) may not be applicable to evaluate the pairing gaps in odd-@xmath2 nuclei .
differences between the neutron gaps derived from different gap formulas in fig .
1 with respect to @xmath18 . the right bottom figure shows the neutron gaps for @xmath45 nuclei in comparison with their corresponding fitted curves from fig . 1 . , scaledwidth=45.0% ] same as fig .
[ fig : diff_gaps_subplot3 ] but for the difference between @xmath46 and @xmath18 in selected isotopic chains .
, scaledwidth=45.0% ] the differences between the various gap formulas and @xmath47 are plotted in figs . [
fig : diff_gaps_subplot3 ] and [ fig : diff_gaps_subplot4 ] .
the dispersal of the data below @xmath48 ( @xmath49 ) as well as around shell closures can be an indication of the significant mean - field contribution to the gaps in above regions , which is expected to show a @xmath50 dependence @xcite . in this context it is worthwhile to point out that the differences between @xmath8 and @xmath28 was found to be a consequence of the gap between the single - particle energies of the corresponding neighboring orbitals @xcite .
as can be seen in fig .
[ fig : diff_gaps_subplot4 ] , the differences between @xmath47 and @xmath51 show quite small values for nuclei that can be reasonably described within a single-@xmath0 shell or nearly - degenerate systems , e.g. , for nuclei with @xmath2 between 20 and 28 ( @xmath52 ) as well as @xmath2 below ( @xmath53 ) and above ( @xmath54 ) @xmath55 . for these systems , as we will show below , the difference between @xmath47 and @xmath51 is mainly induced by the pauli and particle blocking effects .
@xmath56 show quite large values around @xmath3 nuclei with @xmath57 and 22 .
one may suspect that @xmath56 is still contaminated by the wigner effect , which refers to the additional binding gained in @xmath3 nuclei .
this is indeed the case for all the other three oes formulas where , as seen in the lower right panel of fig .
2 , the calculated gap values for @xmath3 nuclei are systematically much larger than the average values . on the other hand ,
the calculated @xmath58 values for @xmath3 nuclei follow nicely the average behavior , as it was also shown in ref .
@xcite , even though relatively large fluctuations are present .
these fluctuation may be due to dramatic changes in the mean field when going from the daughter ( @xmath59 ) system to the mother nucleus .
for instance , they may be due to quite different deformation properties .
an illustration of this is provided by the nucleus @xmath34be , which shows a deformed two-@xmath17-particle cluster structure while @xmath60be ( as well as the mirror nucleus @xmath60he ) is spherical .
this is also the case for the nuclei @xmath38ne and @xmath41ti which are expected to gain additional binding due to the strong neutron - proton quadrupole correlation .
to illustrate the origin of the oes and the difference between different formulas , we start with the simple seniority model . for a system with @xmath61 identical particles in a single @xmath0-shell
, the binding energy can be solved analytically in the seniority scheme .
the hamiltonian for such a model can be written as @xcite , @xmath62 where @xmath63 represents the quasi - spin operator , and @xmath64 and @xmath65 are creation and annihilation operators .
@xmath13 is the strength of the pairing interaction .
the energy of the state with seniority @xmath66 can be written as @xmath67 if one assumes @xmath68 for the ground state of even - even system and @xmath69 for that of the odd system , the expression above can be simplified as @xmath70(j+1)g,\\ & = & \left[\frac{n}{2}\right]\left(\left[\frac{n}{2}\right]-1\right)g + \delta_{v,1}\left[\frac{n}{2}\right ] g+\left[\frac{n}{2}\right]e_2\nonumber\end{aligned}\ ] ] where @xmath71 $ ] denotes the largest integer not exceeding n/2 and corresponds to the total number of @xmath68 pairs .
the nonlinear term in the equation above , which is proportional to @xmath72 or more exactly @xmath73\left(\left[\frac{n}{2}\right]-1\right)$ ] , is related to the energy loss due to the pauli effect .
the @xmath74 term in above equation indicates the energy loss in the @xmath69 odd system due to the the particle ( pauli ) blocking effect : the unpaired particle blocks the scattering of other pairs to its own level . in practice
, the odd system corresponds to a even system with one less particle and with a lower degeneracy . a schematic plot for the competition between the pauli blocking effect and pairing blocking effect of the unpaired odd particle .
, scaledwidth=45.0% ] @xmath75 is the energy of one pair .
this term is the one that contributes to the theoretical oes and for systems with even @xmath61
we have @xmath76 it should be emphasized that a striking feature one thus finds is that the two blocking terms cancel each other in @xmath77 and they do not contribute to the pairing gap . a schematic picture is given in fig . [ sch ] to illustrate this point .
however , as implied from the figure , this is not the case for @xmath78 for which one has , @xmath79 where the term @xmath80 is due to the superfluous contribution from the blocking effects .
this unwanted term is the main origin of the differences between @xmath81 and @xmath10 , as shown in fig .
[ fig : diff_gaps_subplot4 ] , in nuclei that can be well described within a single @xmath0 shell . for non - degenerate systems the pairing collectivity manifests itself through the correlated contribution from many configurations , which is induced by the non - diagonal matrix elements of the pairing interaction in a shell - model context . for two particles in a non - degenerate system with a constant pairing
, the energy can be evaluated through the well known relation , @xmath82 the corresponding wave function amplitudes are given by @xmath83 where @xmath84 is the normalization constant .
all amplitudes @xmath85 contribute to the two - particle clustering with the same phase due to the strongly attractive nature of the pairing interaction .
the correlation energy induced by the monopole pairing corresponds to the difference @xmath86 where @xmath87 denotes the lowest orbital . as the gap @xmath88 increases the amplitude @xmath85
becomes more dispersed , resulting in stronger two - particle spatial correlation .
this difference , or more exactly @xmath89 with the self energy removed , is an important measure of the two - particle spatial correlation at the surface , reflected in a corresponding clustering of the two nucleons forming the pair ( see , e.g. , ref .
@xcite ) .
this clustering induces an increase in the strength of the corresponding pair - transfer reaction . as an example , in fig .
[ fig3 ] we consider a simple model with a set of equally spaced levels with double degeneracy .
we consider 16 levels and the single - particle energy is taken as @xmath90 .
the total energy is obtained by diagonalizing the corresponding hamiltonian matrix .
it is found that the total energy for such a system follows closely a relation similar to eq .
( [ eqs ] ) @xmath91\left(\left[\frac{n}{2}\right]-1\right)\mathcal{g } + \delta_{v,1}(\varepsilon_b+\delta)\nonumber\\ & & + \left[\frac{n}{2}\right]e_2,\end{aligned}\ ] ] where @xmath92 is the single - particle energy of the unpaired orbital for a odd system , @xmath87 is the energy loss due to the related blocking effect .
it contributes significantly to the oes and determines its evolutions as a function of pair number .
@xmath93 is a parameter that is related to the pairing strength and level density .
one has @xmath94 and 1.06 for @xmath95 and 0.5 , respectively . within the simple bcs context
, the separation energy is approximately given by @xmath96 and @xmath97 , where @xmath98 is the fermi energy .
one thus gets @xmath99 but one should bear in mind , as the exact solution of the pairing hamiltonian in fig .
[ fig3 ] indicates , that there is still a sizable difference between the blocking effect and the oes especially for small systems with only few particles .
pairing gaps @xmath100 for a equally spaced douby degenerate system with 16 levels and @xmath95 ( solid circle ) and 0.5 ( open circle ) .
the triangles denote the contribution from the particle blocking effect , @xmath87.,scaledwidth=40.0% ] from a macroscopic point of view , there may be a residual contribution to @xmath47 from the symmetry energy ( expected to be negative ) and other non - linear terms of the binding energy @xcite .
our calculations with the liquid drop model show that the average residual contributions are around -60 kev and -200 kev for neutron and proton pairing gaps , respectively .
the later case is dominated by a smooth contribution from the coulomb field .
the main argument for the usage of @xmath101 instead is that the smooth non - linear terms in the binding energy can be canceled up to the fourth order @xcite .
that is , it removes the liquid - drop contribution to the oes to the largest extent .
however , as mentioned in ref .
@xcite , the disadvantage is that the odd - even effects may be diminished as a result of the averaging over nuclei further apart .
it should also be mentioned that there is an additional contribution to the binding energy from the diagonal matrix element with @xmath102 ( the so - called self - energy ) which is equal to @xmath103g$ ] . in the ideal case
, one should have this contribution removed and the pairing gap for a single-@xmath0 system will be of the form @xmath104 for heavy nuclei the bcs coupling constant roughly takes @xmath105 which gives a contribution to @xmath100 that is comparable but opposite to that of the smooth contribution from the nonlinear terms mentioned above . in the other words , one may expect that these two unwanted contributions largely cancel each other . as a result ,
if one assume that both contributions to the binding energy have been taken into account by the hf configuration , for the neutron pairing gap one is expected to have @xcite @xmath106 all the variety of oes formulas studied above have their advantages and disadvantages ( see , earlier discussions in refs .
@xcite ) . we will focus on the simple @xmath47 particular for two reasons : it is the one that may be least contaminated by the nuclear shell effect and it involves only three nuclei .
these are important for our study of unstable nuclei where the experimental data are scarce wheras the unknown shell evolution can play a decisive role . for open shell nuclei ,
the uncertainty as related to the different definiation of the oes is much smaller as compared to the uncertainty induced by our limitted understanding of the density functional and the shell structure of dripline nuclei .
our aims are to understand the pairing properties of neutron dripline nuclei and to extract reliable information from binding energies based on the gap @xmath107 .
we hope that this may shed light on our understanding of the stability mechanisms as well as probing the importance of di - neutron spatial correlations in these nuclei .
it is theoretically suggested that di - neutron correlations may be enhanced in some situations such as in a low density region of nuclear matter and in the surface of finite neutron - rich nuclei @xcite . to explore this point further
we have done systematic calculations in semi - magic neutron - rich ( dripline ) nuclei by using the hartree - fock - bogoliubov ( hfb ) formalism , which is expected to be more reliable than the simple bcs approach . in the standard hfb formalism
, the hamiltonian is reduced to the mean field in the particle - hole channel and the pairing field in the particle - particle channel .
the hfb equations are , @xmath108 where @xmath109 and @xmath110 are the two components of the single quasi - particle wave functions .
we evaluated the coordinate - space solutions by using the hfb solver hfbrad in a spherical box @xcite . in the particle - hole channel we used the skyrme functional with the sly4 parameter set @xcite . in the particle - particle channel we used the zero - range @xmath87 interaction given by @xcite @xmath111 here
@xmath112 is the pairing strength , @xmath113 is the isoscalar nucleonic density and @xmath114 .
@xmath115 and 1 correspond to the volume and surface pairings , respectively .
we have done calculations by using different pairing interactions but for simplicity only results corresponding to the mixed pairing with @xmath116 are shown .
the pairing strength is fitted to give a mean neutron gap of @xmath117mev in @xmath118sn and no @xmath33 or isospin dependence is considered .
calculations are done in a box with the size @xmath119 fm .
only quasiparticle states with energy lower than 60 mev are taken into account .
calculated @xmath120 and @xmath121 for ca ( upper ) and sn ( lower ) together with the experimental @xmath47 and calculated @xmath47 by using the hfrabd and hfbtho codes .
( explained in the text).,title="fig:",scaledwidth=40.0% ] calculated @xmath120 and @xmath121 for ca ( upper ) and sn ( lower ) together with the experimental @xmath47 and calculated @xmath47 by using the hfrabd and hfbtho codes .
( explained in the text).,title="fig:",scaledwidth=38.0% ] besides oes from calculated binding energies , two different theoretical gaps will be compared with the experimental pairing gap @xmath122 : the canonical gap @xmath120 , which consists of the diagonal elements of the pairing - field matrix for the lowest canonical state ( lcs ) , and the average gap @xmath121 , that is the average value of the pairing fields @xcite . as typical examples , in fig .
[ fig : tincalcium ] we plotted @xmath120 and @xmath121 calculated for calcium and tin isotopes , which have been intensively studied quite recently from different perspectives .
the results are compared with experimental @xmath47 and calculated @xmath47 which is the pairing gap calculated from the hfb binding energies by using eq .
( 2 ) . in the latter case
, the binding energies are calculated using the code hfbrad ( in the coordinate representation within the spherical symmetry ) @xcite and compared with those from the code hfbtho ( in the axial deformed harmonic oscillator basis ) @xcite as a cross - check for our calculations .
the two calculations should give very similar results if the influence of both the continuum and deformation is negligible .
indeed , as can be seen from the figure , the results from the two codes are very close to each other in most cases and come even closer if spherical symmetry constraint is applied in the latter case . in both codes calculations for odd-@xmath2 isotopes
are done within the blocking approximation using the equal filling approximation @xcite . in practice ,
we have done calculations by blocking all possible quasiparticle orbitals around the fermi surface and the one that gives the highest binding energy is chosen .
a self - consistent treatment of the blocking for the one - quasiparticle hfb state is done in ref .
@xcite by taking into account beyond mean field effects using the generator coordinate method . in general the values of calculated @xmath47
are closer to the experimental @xmath47 than the two theoretical hfb pairing gaps , which vanish at closed shell .
the results for @xmath120 and @xmath121 are practically the same in most cases in fig .
[ fig : tincalcium ] .
but it should be mentioned that both definitions of the theoretical pairing gap have their advantages and disadvantages .
the use of @xmath120 as a measure of the pairing gap is questioned in ref .
@xcite and in refs .
@xcite for dripline nuclei . in the relativistic hartree - bogoliubov calculations for selected isotopic and isotonic chains with a finite - range pairing force as presented in ref .
@xcite , it is seen that @xmath121 are systematically smaller than @xmath120 and come closer to the @xmath10 and @xmath123 indicators . in ref .
@xcite , it is also shown that the neutron @xmath120 vanishes at the drip line for nearly all semi - magic isotopic chains studied whereas the gap @xmath121 can persist in some cases .
on the other hand , @xmath121 and @xmath120 can give quite similar prediction for bound nuclei .
calculations in ref .
@xcite show that @xmath120 can be closer to the experimental average gap eq .
( [ eq : averr ] ) than @xmath121 . in the relativistic mean field calculations
@xcite , the calculated mean gaps and oes agree pretty well with each other . in ref .
@xcite , the mean gap and oes from calculated binding energies are compared with the empirical oes for even - even hafnium isotopes , where it is found that quantatively the mean gap reproduces better the trend in experimental data .
the level spacing is crucial for pairing correlation which strongly depends on the shell structure @xcite and on the deformation @xcite .
a general calculations including the deformation effects are done recently in ref .
@xcite with a separable pairing interaction of finite range .
it is shown that the differences in the underlying single - particle structure represent the major source of uncertainty in the prediction of drip line and the pairing properties in neutron rich nuclei depend substantially on the different covariant energy density functionals .
in particular , the emergence of deformation driving intruder orbitals can lower the chemical potential and make the system bound whereas extruder orbitals with high @xmath124 values can make the system unbound . a systematic calculation on the possible effect of the density dependence of the zero - range pairing force on the pairing correlation of dripline nuclei
is also shown in ref .
@xcite . calculated
@xmath120 and @xmath121 for ca ( upper ) and sn ( lower ) isotopes upto the neutron dripline with three different skyrme parameter sets in comparison with the corresponding calculated oes @xmath18.,title="fig:",scaledwidth=40.0% ] calculated @xmath120 and @xmath121 for ca ( upper ) and sn ( lower ) isotopes upto the neutron dripline with three different skyrme parameter sets in comparison with the corresponding calculated oes @xmath18.,title="fig:",scaledwidth=40.0% ] to explore the dependence of our calculations on the functionals , in fig .
[ fig : tincalcium2 ] we extended our calculations for ca and sn isotopes shown in fig .
[ fig : tincalcium ] to the neutron dripline .
calculations are done with the siii @xcite , sly4 @xcite as well as the recently proposed sv - bas @xcite skyrme functionals .
the two - neutron dripline occurs around @xmath125 and @xmath126 for those two isotopic chains .
it is thus found that the calculated oes agrees well with the two pairing gaps for known nuclei but noticable differences are seen as the neutorn number increases . in particular , big differences among different calculations
are seen for ca isotopes around @xmath127 in relation to the different predictions of the emergence of the @xmath127 , 34 and 40 subshells .
significant deviations between @xmath121 and @xmath120 are seen in sv - bas calculations for nuclei beyond the dripline .
in fact , ref .
@xcite has shown that there is a distinct difference between the mean gap and the lowest canonical gap beyond drip - line for calculations with surface - peaked pairing interaction .
a similar deviation may happen in calculations with the mixed pairing interaction , as in the case shown in fig .
[ fig : tincalcium2 ] . however , this is usually not the case for volume interactions .
it should be mentioned that the time - odd field is not considered in the hfbtho and hfbrad calculations shown in the figure , which may affect the binding energy of the odd-@xmath33 nucleus and the corresponding oes .
the time - odd field can contribute to the ground state mean fields of odd-@xmath33 and odd - odd nuclei ( breaking the kramer s degeneracy ) as well as in nuclear rotation and other dynamic processes @xcite .
the time - odd field , which is still relatively poorly understood and functional dependent , is neglected in most relativistic and non - relativistic mean field calculations .
the possible influence of the time - odd field in light @xmath128 nuclei is discussed in ref .
@xcite .
systematic skyrme hartree - fock plus bcs calculations with the time - odd field for odd-@xmath33 nuclei between@xmath129 are presented recently in ref .
@xcite .
it was shown that the influence of the time - odd field is generally small and decrease rapidly with increasing mass number .
in particular , there is no indication that the deviation between experimental and theoretical oes can be improved by the inclusion of the time - odd field @xcite , from which the fluctuation induced is much smaller than that from the different functional .
skyrme hfb calculations with the time - odd field are also done for the whole mass table in ref .
@xcite and for rare earth nuclei with @xmath130 and @xmath131 in ref .
@xcite .
it is found that the average energy shift as induced by the time - odd field is only 50 kev but with a large deviation of 42 kev and hence the equal filling approximation is precise for most practical calculations .
a similar conclusion may be draw from gogny hfb calculations where full calculations with the time - odd field give very similar results to those from the filling approximation and the inclusion of the time - odd field hardly improves the gap description @xcite .
recent systemtic calculations on the effect of the time - odd field in the relativistic mean field approach can be found in refs . @xcite and references therein .
ref .
@xcite found that the time - odd field in the relativisitic mean field approach always induces an additional binding but weakly affects the relative energies of different quasiparticle states in medium and heavy mass nuclei .
the influence of that attractive contribution from the time - odd mean field to the odd nuclei into oes can be of up to 10% in light nuclei and of around 5 - 6% in heavy nuclei .
however , even in that case , the required modification of the strength of pairing force is modest @xcite , which is significantly smaller than earlier expectations . in ref .
@xcite , it is suggested that the @xmath18 can be a measure of the sole pairing gap if the contribution from the time - odd reversal symmetry breaking field cancels out the contribution from the smooth part of the total energy .
upper : the two - neutron spatial correlation plots for @xmath132ca ( left ) and @xmath133ca ( right ) .
lower : same as upper but for @xmath134sn ( left , 4 holes ) and @xmath135sn ( right , 4 particles ) .
calculations are done with the sly4 force .
notice that the scale is different.,scaledwidth=45.0% ] in ref .
@xcite it is mentioned that for spherical nuclei where the drip line occurs around neutron closed shells the pairing gap is expected to be reduced .
our calculations show that this is indeed the case for neutron - rich ca and sn isotopes .
our understanding of the shell structure in ca isotopes have been significantly extended recently ( see , e.g. , refs .
@xcite ) . @xmath127 and 34 have been shown to be new magic numbers in ca isotopes , a conclusion which is supported by hfb calculations @xcite .
the @xmath18 values for @xmath136ca are much smaller than those for nuclei in the @xmath137 shell . the pairing gap for @xmath133ca is expected to be even smaller . in the upper panel of fig . [ fig : twopar_subplot ] , following the same procedure as in ref .
@xcite , we evaluated in the canonical basis the two - neutron spatial correlations in @xmath133ca and compared it with that in @xmath132ca .
the results are plotted as a function of the angle @xmath138 between the two neutrons and the radius @xmath139 where @xmath140 is the radius of the single - particle wave function .
for strongly correlated wave functions , the two - neutron spatial correlation is expected to peak at @xmath141 at the surface . as can be seen from the figure ,
the peak in @xmath132ca is much stronger than that in @xmath142ca .
the pairing tensor as a function of radius @xmath140 for neutron - rich nuclei @xmath143ca ( solid line ) and @xmath144sn ( dashed line ) as calculated from different skyrme parameterizations.,scaledwidth=45.0% ] the spatial correlation of the neutron pair can also be inferred from the pairing / abnormal density @xmath145 . in fig .
[ fignnn ] , we plotted the calculated pairing tensor which is defined as @xmath146 and is related to the pair transfer form factor , for two nuclei @xmath143ca ( solid line ) and @xmath144sn .
@xmath143ca is at the neutron dripline for which the calculated pairing tensors and pairing gaps from difference functionals can be quite different .
the nucleus @xmath144sn is within the dripline .
the pairing tensors calculated from the three functional are quite close to each other . but as can be seen from fig .
[ fig : tincalcium2 ] , there is a significant difference between the theoretial mean gap @xmath121 and the oes from the theoretical binding energies .
a similar deviation is also seen in ref .
@xcite .
the origin for such a large deviation is not exactly known yet .
it may be related to the fact that , for sn isotopes in this region , the chemical potential @xmath98 is pretty close to zero and the quasiparticle orbitals involved in the blocking calculations are all unbound . for such cases ,
the theoretical oes and gaps have to be carefully interpreted .
there is a noticeable kink at @xmath147 for tin isotopes which may be related to the occupancy of the low degeneracy orbital @xmath148 .
a sudden drop occurs in the experimental pairing gaps in the sn isotopes when going from @xmath149 to @xmath150 .
this can be reproduced by the hfb calculations with the volume and mixed pairing interactions @xcite .
that drop is related to the reduced level density above n=82 .
that is , there is a noticeable gap between the @xmath151 orbital and the higher- lying ones . which may result in a @xmath152 sub shell closure @xcite .
the reduced pairing collectivity in these nuclei can be clearly seen in the two - neutron spatial correlation plots given in the lower part of fig .
[ fig : twopar_subplot ] , where we compared @xmath134sn , which have four holes in the core @xmath153sn , and @xmath135sn , with four particles above the core .
as can be seen from the figure , the peak in @xmath134sn is around one order of magnitude stronger than that in @xmath135sn .
hfb describes very well the pairing gap as well as the two - particle spatial correlation in open - shell nuclei .
a known problem is that both the bcs and the hfb condensates collapse at closed shell , since in this case all orbitals are fully occupied ( c.f . , eq .
( 13 ) ) .
in fact , as the systematic calculations in ref .
@xcite shows , roughly 20 - 30% of the known nuclei contain collapsed bcs or hfb condensates .
it is therefore fair to affirm that the failure of these two approaches to reproduce the oes does not necessary mean that there is no pairing correlation in these nuclei .
two typical examples are @xmath154ca and @xmath153sn shown in fig .
[ fig : twopar_subplot ] .
these two nuclei show @xmath47 values similar to neighboring nuclei below the closed shell .
indeed our calculations with the seniority model @xcite show that the two - neutron spatial correlations in these two nuclei are as strong as those in neighboring ones .
again , @xmath47 is a good indication of the two - neutron correlation in these cases . anyway , as mentioned above , comparisons between the theoretical gaps from even - even nuclei can only be compared with the empirical pairing gap in a semi - quantitative manner . in summary
, in this paper we compared the pairing gaps derived from four different oes formulas .
we showed that @xmath100 gauge very well the nuclear pairing correlation since it removes to a large extent the contribution from the single - particle structure of the nuclear mean field and the shell effect .
it can serve as a reliable filter if one is primarily interested in evaluating the pairing effect in structure model calculations .
this is particularly interesting for the study of dripline nuclei since experimental data on those nuclei are usually scarce and show large fluctuations of shell structure .
in addition , @xmath100 is expected to be less contaminated by the wigner effect for nuclei around @xmath3 .
we have also shown that the strength of @xmath100 can be a good semi - quantative indication for the two - particle spatial correlation .
this is supported by our calculations with the hfb model with skyrme force as well as with the multi - shell seniority model .
moreover , we found that the weakening of @xmath4 in some neutron - rich nuclei indicates that the di - neutron correlation is weak in those nuclei .
as examples , the pairing gaps and di - neutron spatial correlations in neutron - rich calcium and tin isotopes are evaluated in detail .
calculations for the different pairing gaps and oes with different functional quantatively agree well with each other as well as with experimental data
. however , these results need to be carefully examined when one approaches the dripline , where large deviations between different functionals and different definations of the pairing gaps may be seen . |
we are grateful to dr .
d. divincenzo for some helpful comments on the manuscript .
financial support for this research has been provided by the national science foundation through grant phy-9220726 .
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symposium on the foundations of modern physics 1994 _ , edited by k. v. laurikainen , c. montonen and k. sunnarborg ( editions frontires , gif - sur - yvette , france , 1994 ) p. 85 | shor s algorithms for factorization and discrete logarithms on a quantum computer employ fourier transforms preceding a final measurement .
it is shown that such a fourier transform can be carried out in a semi - classical way in which a `` classical '' ( macroscopic ) signal resulting from the measurement of one bit ( embodied in a two - state quantum system ) is employed to determine the type of measurement carried out on the next bit , and so forth . in this way the two - bit gates in the fourier transform
can all be replaced by a smaller number of one - bit gates controlled by classical signals .
success in simplifying the fourier transform suggests that it may be worthwhile looking for other ways of using semi - classical methods in quantum computing .
0 cm 0 cm -2.0 cm 23.5 cm 16.5 cm recently shor @xcite has shown that a quantum computer @xcite , if it could be built , would be capable of solving certain problems , such as factoring long numbers , much more rapidly than is possible using currently available algorithms on a conventional computer .
this has stimulated a lot of interest in the subject @xcite , and various proposals have been made for actually constructing such a computer @xcite .
the basic idea is that bits representing numbers can be embodied in two - state quantum systems , for example , in the spin degree of freedom of a spin half particle , and the computation proceeds by manipulating these bits using appropriate gates .
it turns out that quantum computations can be carried out using circuits employing one - bit gates , which produce a unitary transformation on the two - dimensional hilbert space representing a single bit , together with two - bit gates producing appropriate unitary transformations on a four - dimensional hilbert space @xcite .
one - bit gates should be much easier to construct than two - bit gates , since , for example , an arbitrary unitary transformation on the spin degree of freedom of a spin half particle can be produced by subjecting it to a suitable time - dependent macroscopic magnetic field .
on the other hand , a two - bit gate requires that one of the bits influence the other in a non - trivial way , and this without leaving any record in the environment , since the computer utilizes coherent quantum states . in this letter
we shall show how the quantum fourier transforms which in shor s algorithms immediately precede a final measurement can be carried out in a semi - classical fashion which requires no two - bit gates .
the trick is to measure a particular bit and then use the result to produce a classical signal which controls a one - bit transformation carried out on the next bit just before it is measured , and so forth .
it is of interest for at least three reasons .
first , it represents a completely new ( so far as we know ) technique for quantum computation , in which the results of certain measurements , converted into `` classical '' signals ( imagine a pulse of several volts traveling down a coaxial cable ) , can be used to influence a later step in the computation @xcite .
second , computing the fourier transform is considerably simplified in the sense that it requires no two - bit gates .
third , a simple way of seeing why the semi - classical method actually works is to adopt a point of view in technical terms , a particular family of consistent histories in which the results of a measurement are used to infer the state of a quantum system before the measurement was carried out .
this perspective may prove useful in thinking about other issues in quantum computing , quantum optics , and quantum effects in atomic physics .
since shor has described his algorithms in considerable detail in his publications @xcite , we shall not discuss them here .
it will be sufficient to note that after a certain number of steps of the quantum computation have been carried out , the relevant quantum state @xmath0 is a coherent superposition @xcite of different states @xmath1 labeled by an integer @xmath2 between 0 and @xmath3 , where @xmath4 .
the state @xmath0 is then subjected to a unitary transformation @xmath5 , a sort of discrete fourier transform , which carries each basis state @xmath1 of the @xmath6-dimensional hilbert space into @xmath7 this is followed by a measurement of the integer @xmath8 , that is , a measurement of each of its @xmath9 bits .
a set of gates which carries out this fourier transform @xcite is shown in fig . 1 for @xmath10 .
the bits to be transformed enter from the left .
one can imagine that they are spin 1/2 particles , with the results of the preceding computation embodied ( as a coherent superposition ) in their collective spin degrees of freedom .
these particles then move through a series of gates , indicated by circles , and eventually arrive at measuring devices , shown as squares , where a particular component of spin , say @xmath11 , is measured by a stern - gerlach device , with @xmath12 in units of @xmath13 interpreted as the bit @xmath14 , and @xmath15 as the bit @xmath16 . if the binary representation of the number @xmath2 is @xmath17 with each @xmath18 zero or one , the state @xmath1 can be conveniently written as a tensor product @xmath19 using the same notation for @xmath20 , we can rewrite ( [ e.1 ] ) in the form @xmath21 where the state @xmath22 will be said to have a _ phase _
@xmath23 between 0 and 1 .
the phases @xmath24 in ( [ e.4 ] ) take the values : @xmath25 in terms of our picture of a spin half particle , @xmath26 represents a spin component of @xmath27 in a direction in the @xmath28 plane determined by @xmath23 . the one - bit gates in the top row of fig . 1
transform the bit entering on the left to one leaving on the right through : @xmath29 ( in a spin picture , the spin is rotated by @xmath30 about the @xmath31 axis . )
the two bit gate labeled with an integer @xmath32 converts the bits entering on the left into those leaving on the right according to the scheme : @xmath33|11\rg .
\end{array } \label{e.8}\ ] ] here we use the convention that the left element in each ket @xmath34 in ( [ e.8 ] ) is the bit which in fig .
1 enters the two - bit gate at a point marked by a black dot and also leaves at a black dot , while the right element in each ket denotes the bit which enters and leaves the gate at a point labeled by a circle .
it is helpful to think of ( [ e.8 ] ) as a transformation in which one bit acts as a `` control '' which enters and leaves the gate as a zero or one , while the other `` target '' bit enters as @xmath26 and undergoes a phase shift , so that it leaves as @xmath35 , where @xmath36 . from this perspective
it is easy to see how the network in fig .
1 produces the desired result .
suppose that the bit @xmath37 enters the left - most one - bit gate in fig . 1 in the state @xmath16 .
it emerges at the point @xmath38 in the state @xmath39 .
as it passes downwards through the successive two bit gates its phase is shifted by the bits @xmath40 , @xmath41 , and @xmath42 , acting as control bits , by an amount @xmath43 if , on the other hand , @xmath37 arrives as @xmath14 , the one - bit gate converts it to @xmath44 , so that the bit which emerges as @xmath45 has a phase @xmath46 , in agreement with ( [ e.6 ] ) .
the same sort of analysis can be applied to the rest of the circuit .
however , one can equally well regard the bits entering and leaving the gates through the black dots in fig . 1 as the control bits , and it is this point of view which is useful for constructing the semiclassical fourier transform .
suppose that the final measurement reveals that the bit @xmath45 is 1 , corresponding to @xmath14 .
then , since a control bit enters and leaves the two - bit gates unchanged , we conclude that this bit was also in the state @xmath14 at point @xmath38 , just after emerging from the first one - bit gate . similarly ,
if the measurement yields @xmath47 , we conclude that the bit was in the state @xmath16 at the point @xmath38 .
hence the circuit would work equally well if the measurement on this bit were actually carried out at the point @xmath38 in fig . 1
, were it not for the fact that this bit is also needed in order to influence @xmath40 , @xmath41 , and @xmath42 , now regarded as target bits , as they pass through the two - bit gates controlled by @xmath45 . however , if @xmath45 is measured at @xmath38 and the result is converted to a classical signal , this signal can be used to determine the action of a corresponding set of one - bit gates acting upon @xmath40 , @xmath41 , and @xmath42 . applying this type of analysis to the other parts of fig . 1 ,
one is led to the arrangement shown in fig
. 2 , where all the two bit gates in fig . 1 have been eliminated , and their work taken over by one - bit gates controlled by classical signals ( double lines ) and followed by measurements .
each of the boxes in fig .
2 performs the following operations .
the incoming bit is first subjected to a unitary transformation , equivalent to a phase shift followed by ( [ e.7 ] ) : @xmath48 where @xmath23 is the phase transmitted as a classical signal from the previous box .
the bit is then measured to yield the result @xmath49 or @xmath50 . the outputs are two classical signals represented by double lines : one is the result of the measurement , and the other represents a phase @xmath51 which is sent to the next box .
the very first box uses @xmath52 in ( [ e.10 ] ) .
readers unfamiliar with the rules which allow one to use the results of a measurement to infer the state of a quantum system prior to the measurement are referred to the relevant literature @xcite .
the basic idea is that one can add to a quantum history , consisting of an initial state and the result of a measurement , a projector , for example @xmath53 representing property of the quantum system at a time just prior to the measurement .
the conditional probability of @xmath54 is one , given that the measurement yields @xmath55 .
but in the situation shown in fig . 1 , @xmath54 commutes with the unitary transformations corresponding to the three 2-bit gates which precede the measurement of @xmath45 , and therefore one can `` push '' the corresponding property backwards in time to the point @xmath38 in fig . 1 , and again conclude that it occurred with probability one .
anyone who feels uncomfortable with this method of reasoning can , of course , use traditional techniques to verify that the arrangement in fig .
2 will yield the same probability to observe a number @xmath8 as that in fig . 1 .
( note that it is necessary to check this for an initial state @xmath0 which is an arbitrary linear combination of the different @xmath1 states . )
the scheme in fig . 2 should be quite a bit simpler to realize than that in fig . 1 , because it only requires one - bit operations controlled by classical signals rather than the more difficult and more numerous two - bit operations indicated in fig . 1
however , the need to carry out a measurement on one bit before beginning to measure another could be a disadvantage if the physical elements representing the bits are short lived or decohere rapidly on the time scale required to carry out a measurement and convert it into a classical signal . if this turns out to be a problem , a possible remedy might be to arrange the earlier part of the quantum computation in such a way that the more significant bits of @xmath2 are produced earlier than the less significant bits .
an important question is whether other parts of shor s algorithms ( or other applications of quantum computing ) can make use of similar semi - classical operations .
we have no specific proposals , but we think the idea is worth further study .
there are bits other than those entering the final fourier transform which are produced elsewhere in the computation , and it is conceivable that measuring some of these could be used in modify later steps in the calculation , or perhaps for the non - trivial task of correcting errors . in connection with the latter ,
see @xcite .
finally , we note that adopting alternative perspectives or points of view about what is going on in a quantum computation can yield useful insights .
the traditional perspective , represented in almost all work on quantum computing up till now , in which the `` wave function of the computer '' develops unitarily in time until a measurement is made , has demonstrated its value through the work of various people who have brought quantum computation to its current state of development . in this letter
we have shown that an alternative point of view , in which the results of measurements are traced backwards in time , can also be valuable .
the general principles of quantum mechanics allow for a variety of viewpoints or , to use the technical term , consistent families , and recent developments in the foundations of quantum theory @xcite permit one to make effective use of these without becoming entangled in paradoxes , mysterious long - range influences , and the like . |
surface plasmon polaritons ( spps ) are collective oscillations of electrons occuring at the interface of materials .
more than hundred years after their discovery @xcite , spps have promoted new applications in many fields such as microelectronics @xcite , photovoltaics @xcite , near - field sensing @xcite , laser techonology @xcite , photonics @xcite , meta - materials design @xcite , high order harmonics generation @xcite , or charged particles acceleration @xcite .
most of these applications are based on expensive noble metals such as gold , silver or platinum , as these materials greatly support the plasmonic phenomena , exhibit very small ( plasmonic ) losses and the experimental results match well with the associated theory @xcite .
although there were numerous studies addressing spps in lossy materials @xcite , some specific aspects remain to be investigated . in this paper , a mathematical condition for spp excitation at flat interfaces is provided .
this approach includes the widely accepted theory but reveals a wider ( material dependent ) domain of spp excitation than predicted by the existing literature .
the importance of the terms originating from losses is underlined and complemented by formula of the spp near - field period and lifetime .
at a planar interface between two different materials , the electric field components ( @xmath0 ) and magnetic field components ( @xmath1 ) can be calculated by solving the helmholtz equation for transverse magnetic ( tm ) and transverse electric ( te ) boundary conditions @xcite . for the geometry provided in fig .
[ fig : scheme ] , the mathematical solutions crucially depend on two complex - valued properties : the dielectric permittivities @xmath2 ( linked to the optical refractive indices @xmath3 of medium @xmath4 by @xmath5 ) , and the complex - valued wavenumbers @xmath6 ( associated with electromagnetic field modes in the medium @xmath4 ) . at the interface between two media ( 1 and 2 ) , the conservation of light momentum results in the condition @xcite
@xmath7where @xmath8 is the spp wavenumber along the interface , @xmath9 is the wavenumber of the incident light ( @xmath10 : light angular frequency , @xmath11 : light velocity in vacuum ) .
scheme of a planar interface between medium 1 and 2 at which surface plasmon polaritons are considered .
the wavevector components along the surface normal axis are indicated as @xmath12 and @xmath13 are the complex dielectric permittivities of both media .
@xmath14 is the complex wavenumber of the spps propagating along the surface plane .
, title="fig:",width=302 ] [ fig : fig1 ] in tm geometry , the continuity conditions for the electromagnetic fields results in the relation @xcite @xmath15equation ( [ eq : mainsppcondition ] ) represents the _ dispersion relation of surface plasmon polaritons _ at the interface between two semi - infinite media .
the signs of @xmath16 and @xmath17 were taken positive here , accounting for the exponential decay of the electromagnetic field amplitude in the direction perpendicular to ( away from ) the interface .
the combination of eqs .
( [ eq : definitionofsppwavenumber ] ) and ( [ eq : mainsppcondition ] ) provides the solutions of the spp wavenumber @xmath14 : @xmath18 it must noted that in a generalized view , the characterization of lossy waves can be treated by calculating an observable response function @xmath19 which allows to construct a dispersion relation by locating its complex zeros / poles @xcite . as already noted by ritchie et al .
@xcite , when damping is relevant , the dispersion relation @xmath20 for @xmath21 may have complex solutions ( @xmath22 ) .
conversely , if @xmath23 is real - valued , @xmath14 may be complex - valued . although straightforward in a theoretical framework , there is some ambiguity about the significance of complex values of @xmath23 or @xmath14 in the interpretation of experiments @xcite . in experiments it may be difficult to observe temporal or spatial decay of a resonance due to its rapidity or smallness .
the properties of such excitations are usually extracted from the transfer of energy and momentum to the system , involving both real @xmath23 and real @xmath24 . as an example
, dispersion relations have been determined by attenuated total reflection ( atr ) in otto configuration @xcite . in this approach , a beam is totally reflected at the basis plane of an optical prism .
excitation of spp in a neighbored metal surface may be realized via coupling through a gap of a dielectric medium ( air ) .
spp manifest as drops in the totally reflected signal , when momentum matching between light and spp occurs .
experimentally , as underlined by kovener et al .
@xcite , this can be realized either for a variation of frequency @xmath23 at a fixed angle of incidence @xmath25 , or via a variation of @xmath25 at a fixed @xmath23 .
the first procedure produces dispersion curves with a specific `` bend back '' feature , while the second procedure results in curves without that feature @xcite .
spps can be excited only if the dispersion relation [ eq .
( [ eq : mainsppcondition ] ) ] is fulfilled . in order to extract the spp excitation conditions from the dispersion relation ,
a sign analysis can be performed on the real and imaginary parts of eq .
( [ eq : mainsppcondition ] ) , which can be mathematically developed to : @xmath26 by assuming @xmath27 this equation can be used to deduce a constraint on the sign of real part of the dielectric permittivities @xmath13 , resulting in @xmath28 equation ( [ eq : conditionsymmetricspp ] ) defines the first necessary condition for excitation of surface plasmon polaritons , which is equivalent to @xmath29 the physical meaning of eq .
( [ eq : conditionsspp1 ] ) , named _ condition 1 _ for spp excitation , is the following : in presence of a perfect dielectric medium ( e.g. for @xmath30 or @xmath31 ) , eq .
( [ eq : conditionsspp1 ] ) implies that spps can only be excited at a dielectric - metal interface .
this is usually fulfilled when @xmath32 .
( [ eq : conditionsspp1 ] ) reduces to the widely accepted expression @xcite @xmath33 however , in presence of _ two absorbing media _ ( having then @xmath34 and @xmath35 ) , the physical meaning is less intuitive . the condition given by eq .
( [ eq : conditionsspp1 ] ) is more complex due to non - vanishing contributions of the imaginary parts of the dielectric permittivities .
consequences of this additional term , important for lossy materials , will be discussed in section [ sec : exploration ] .
assuming purely real - valued dielectric permittivities , eq .
( [ eq : betadefinition ] ) is typically used to derive another condition for spp excitation .
this approach is called _ perfect medium approximation _ ( pma ) and will be outlined in the following . for simplicity , we adopt the following notations : @xmath36 and @xmath37 . if @xmath38 and @xmath39 , then @xmath14 is real - valued ( @xmath40 ) , and eq .
( [ eq : betadefinition ] ) becomes and widely used in literature @xcite .
in particular , when medium 1 is air ( @xmath45 ) , the joint application of eqs .
( [ eq : condition1-re ] ) and ( [ eq : realcondition ] ) leads to the well admitted condition @xmath46 however , beyond the perfect medium approximation , it must be noted that eq .
( [ eq : betadefinition ] ) can be treated using fully complex permittivity values since @xmath14 is defined in @xmath47 for _ any _ value of the dielectric permittivities @xmath48 . as a consequence , in presence of one ( or more ) `` lossy '' materials , e.g. , when @xmath34 or @xmath35 , _ there is no other restriction for spp excitation than the condition 1 _ given by eq .
( [ eq : conditionsspp1 ] ) . in other words , performing an _ ad - hoc _ restriction of the dielectric permittivity to its real part(s ) may lead to an oversimplified spp excitation condition .
[ [ exploration - of - plasmon - active - material - combinations - secexploration ] ] exploration of plasmon - active material combinations [ sec : exploration ] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ in this section , the plasmon activity of a wide set of material combinations is explored by comparing predictions of the pma [ real - valued eqs .
( [ eq : condition1-re ] ) and ( [ eq : realcasescondition2 ] ) ] with the more general case [ complex - valued eq .
( [ eq : conditionsspp1 ] ) ] . for that , if not stated differently , data of the optical constants were taken from ref .
values are listed in [ sec : appendixoptical ] . in a first step ,
a selection of different metals exposed to air are analyzed .
the results for the spp - activity for 12 different noble and transition metals are provided in tab .
[ tab : spp - active - interfaces - air ] .
here we restrict the study to two wavelengths frequently used in laser processing : 800 nm and 400 nm .
however , these calculations can be generalized to other material combinations and wavelengths .
the spp - activity of the metal - air interfaces is indicated by a green tick ( ) , whereas the interfaces which do not support spps are marked by a red cross ( ) . at both wavelengths the generalized model [ eq .
( [ eq : conditionsspp1 ] ) ] predicts similar results as the pma .
interestingly , and opposed to the pma , niobium ( nb ) is predicted to support spps when interfaced with air , upon 400 nm irradiation .
.[tab : spp - active - interfaces - air]analysis of spp - activity of several metal ( @xmath49 ) surfaces irradiated in air ( @xmath50 ) at @xmath51 nm and @xmath52 nm wavelengths .
meaning of the symbols : @xmath53 spp are excited , @xmath54 : spp are not excited at the interface .
bold font indicates interfaces where the prediction deviates from accepted theories . [ cols="^,^,^,^,^ " , ] | the possibility to excite surface plasmon polaritons ( spps ) at the interface between two media depends on the optical properties of both media and geometrical aspects .
specific conditions allowing the coupling of light with a plasmon - active interface must be satisfied .
plasmonic effects are well described in noble metals where the imaginary part of the dielectric permittivity is often neglected ( perfect medium approximation ) .
however , some systems exist for which such approximation can not be applied , hence requiring a refinement of the common spp theory . in this context
, several properties of spps such as excitation conditions , period of the electromagnetic field modulation and spp lifetime then may strongly deviate from that of the perfect medium approximation . in this paper ,
calculations taking into account the imaginary part of the dielectric permittivities are presented .
the model identifies analytical terms which should not be neglected in the mathematical description of spps on lossy materials .
these calculations are applied to numerous material combinations resulting in a prediction of the corresponding spp features . a list of plasmon - active interfaces is provided along with a quantification of the above mentioned spp properties in the regime where the perfect medium approximation is not applicable .
may 21st , 2016 _ keywords _ : surface plasmon polaritons , lossy materials , plasmon lifetime |
one of the challenges in rl is the trade - off between exploration and exploitation . the agent must choose between taking an action known to give positive reward or to explore other possibilities hoping to receive a greater reward in the future . in this context ,
a common strategy in unknown environments is to assume that unseen states are more promising than those states already seen .
one such approach is optimistic initialization of values ( * ? ? ?
* section 2.7 ) .
several rl algorithms rely on estimates of expected values of states or expected values of actions in a given state @xcite .
optimistic initialization consists in initializing such estimates with higher values than are likely to be the true value . to do so , we depend on prior knowledge of the expected scale of rewards .
this paper circumvents such limitations presenting a different way to optimistically initialize value functions without additional domain knowledge or assumptions . in the next section
we formalize the problem setting as well as the rl framework .
we then present our optimistic initialization approach .
also , we present some experimental analysis of our method using the arcade learning environment @xcite as the testbed .
consider a markov decision process , at time step @xmath0 the agent is in a state @xmath1 and it needs to take an action @xmath2 .
once the action is taken , the agent observes a new state @xmath3 and a reward @xmath4 from a transition probability function @xmath5 .
the agent s goal is to obtain a policy @xmath6 that maximizes the expected discounted return @xmath7 $ ] , where @xmath8 $ ] is the discount factor and @xmath9 is the action - value function for policy @xmath10 . sometimes it is not feasible to compute @xmath9 , we then approximate such values with linear function approximation : @xmath11 , where @xmath12 is a learned set of weights and @xmath13 is the feature vector .
function approximation adds further difficulties for optimistic initialization , as one only indirectly specifies the value of state - action pairs through the choice of @xmath12 .
an approach to circumvent the requirement of knowing the reward scale is to normalize all rewards ( @xmath14 ) by the first non - zero reward seen ( @xmath15 ) , _ i.e. _ : @xmath16 .
then we can optimistically initialize @xmath17 as @xmath18 , representing the expectation that a reward the size of the first reward will be achieved on the next timestep to @xmath19 . for sparse reward domains , which is common in the arcade learning environment ,
the mild form is often sufficient . ] . with function approximation
, this means initializing the weights @xmath12 to ensure @xmath20 , _
e.g. _ : @xmath21
. however , this requires @xmath22 to be constant among all states and actions . if the feature vector is binary - valued then one approach for guaranteeing @xmath23 has a constant norm is to stack @xmath24 and @xmath25 , where @xmath26 is applied to each coordinate .
while this achieves the goal , it has the cost of doubling the number of features .
besides , it removes sparsity in the feature vector , which can often be exploited for more efficient algorithms .
our approach is to shift the value function so that a zero function is in fact optimistic .
we normalize by the first reward as described above .
in addition , we shift the rewards downward by @xmath27 , so @xmath28 .
thus , we have : @xmath29\\ & = & \underbrace{\mathbb{e}_\pi\bigg[\sum_{k = 0}^\infty \gamma^k \frac{r_{t+k+1}}{|r_{1\mbox{\tiny{st}}}| } \bigg]}_{\frac{q_\pi(s_t , a_t)}{|r_{1\mbox{\tiny{st}}}| } } + \underbrace{\sum_{k = 0}^\infty \gamma^k ( \gamma - 1)}_{-1}\end{aligned}\ ] ] notice that since @xmath30 , initializing @xmath31 is the same as initializing @xmath32 .
this shift alleviates us from knowing @xmath33 , since we do not have the requirement @xmath34 anymore .
also , even though @xmath35 is defined in terms of @xmath15 , we only need to know @xmath15 once a non - zero reward is observed . in episodic tasks this shift will encourage agents to terminate episodes as fast as possible to avoid negative rewards . to avoid this
we provide a termination reward @xmath36 , where @xmath37 is the number of steps in the episode and @xmath38 is the maximum number of steps .
this is equivalent to receiving a reward of @xmath39 for additional @xmath40 steps , and forces the agent to look for something better .
we evaluated our approach in two different domains , with different reward scales and different number of active features .
these domains were obtained from the arcade learning environment @xcite , a framework with dozens of atari 2600 games where the agent has access , at each time step , to the game screen or the ram data , besides an additional reward signal .
we compare the learning curves of regular sarsa(@xmath41 ) @xcite and sarsa(@xmath41 ) with its q - values optimistically initialized .
basic _ features with the same sarsa(@xmath41 ) parameters reported by @xcite .
basic _ features divide the screen in to @xmath42 tiles and check , for each tile , if each of the 128 possible colours are active , totalling 28,672 features .
the results are presented in figure 1 .
we report results using two different learning rates @xmath43 , a low value ( @xmath44 ) and a high value ( @xmath45 ) , each point corresponds to the average after 30 runs .
the game freeway consists in controlling a chicken that needs to cross a street , avoiding cars , to score a point ( @xmath46 reward ) .
the episode lasts for 8195 steps and the agent s goal is to cross the street as many times as possible .
this game poses an interesting exploration challenge for ramdom exploration because it requires the agent to cross the street acting randomly ( @xmath47 ) for dozens of time steps .
this means frequently selecting the action `` go up '' while avoiding cars .
looking at the results in figure 1 we can see that , as expected , optimistic initialization does help since it favours exploration , speeding up the process of learning that a positive reward is available in the game .
we see this improvement over sarsa(@xmath41 ) for both learning rates , with best performance when @xmath44 .
the game private eye is a very different domain . in this game the agent
is supposed to move right for several screens ( much more than when crossing the street in the game freeway ) and it should avoid enemies to avoid negative rewards . along the path the agent can collect intermediate rewards ( @xmath48 ) but its ultimate goal is to get to the end and reach the goal , obtaining a much larger reward .
we can see that the optimistic initialization is much more reckless in the sense that it takes much more time to realize a specific state is not good ( one of the main drawbacks of this approach ) , while sarsa(@xmath41 ) is more conservative .
interestingly , we observe that exploration may have a huge benefit in this game as a larger learning rate guides the agent to see rewards in a scale that was not seen by sarsa(@xmath41 ) .
0.47 0.47 0.47 0.47 thus , besides our formal analysis , we have shown here that our approach behaves as one would expect optimistically initialized algorithms to behave .
it increased agents exploration with the trade off that sometimes the agent `` exploited '' a negative reward hoping to obtain a higher return .
rl algorithms can be implemented without needing rigorous domain knowledge , but as far as we know , until this work , it was unfeasible to perform optimistic initialization in the same transparent way .
besides not requiring adaptations for specific domains , our approach does not hinder algorithm performance .
the authors would like to thak erik talvitie for his helpful input throughout this research .
this research was supported by alberta innovates technology futures and the alberta innovates centre for machine learning and computing resources provided by compute canada through westgrid . | in reinforcement learning ( rl ) , it is common to use optimistic initialization of value functions to encourage exploration .
however , such an approach generally depends on the domain , viz . , the scale of the rewards must be known , and the feature representation must have a constant norm .
we present a simple approach that performs optimistic initialization with less dependence on the domain . |
the gauge sector of electroweak interactions has been checked to coincide with the standard model ( sm ) prediction to the per - mil level , at lep and slc . on the contrary , there is no direct experimental evidence for the higgs mechanism , supposed to be responsible for electroweak symmetry breaking and the generation of masses .
direct search of the higgs boson at lep yields the lower limit @xcite : @xmath2 gev / c@xmath1 at @xmath3 cl .
precision measurements on the other hand give @xcite : @xmath4 gev / c@xmath1 at @xmath5 cl . once a higgs particle is found , if ever , all its properties should be measured precisely to completely characterise the higgs mechanism . among those ,
the coupling of the higgs boson to fermions ( the yukawa coupling ) , which is supposed to scale with the fermion mass : @xmath6 where @xmath7 is the yukawa coupling of a fermion f of mass @xmath8 and @xmath9 is the vacuum expectation value of the higgs field , @xmath10 gev .
the top quark is the heaviest fermion , thus the top - higgs yukawa coupling should be the easiest to measure . if @xmath11 , this parameter can be measured through the branching ratio of the higgs boson decay into a pair of top quarks .
otherwise , i.e. for lower values of the higgs boson mass , the process @xmath0 allows in principle a direct measurement of this coupling .
feasibility studies of the measurement of the top - higgs yukawa coupling via the process @xmath0 at a linear collider have already been performed @xcite @xcite for a higgs boson mass of 120 - 130 gev / c@xmath1 .
this is the most favourable case ( taking into account the lower mass bound ) as the cross - section of this process decreases with increasing higgs boson mass and as a higgs boson of such a mass decays predominantly to a pair of b quarks , allowing a very effective signal and background separation using b - tagging algorithms .
one of the studies ( @xcite ) showed that a neural network analysis was essential to get a precise result .
we repeated this work and extended it up to @xmath12 150 gev / c@xmath1 .
when @xmath13 135 gev / c@xmath1 , the @xmath14 decay mode dominates .
this channel was also studied , for masses up to 200 gev / c@xmath1 .
the lowest order feynman diagrams contributing to the @xmath0 process are shown in figure [ diagrammetth ] . the amplitude of the diagram where the higgs boson is radiated from the z boson is not expressing the top - higgs yukawa coupling .
however , since it modifies only slightly the cross - section of the process , it can safely be neglected . the cross - section and
the top - higgs yukawa coupling thus verify to a good approximation : @xmath15 . for this work ,
the following assumptions were made : @xmath16 gev / c@xmath1 and @xmath17 .
the higgs branching ratios were calculated with the hdecay @xcite program .
the values obtained for the @xmath18 and @xmath14 modes , which are the main decays within the higgs mass range considered in this paper , are shown in table [ brhiggs ] and figure [ crosssectiontth ] . .__higgs branching ratios for the @xmath18 and @xmath14 modes ( as given by hdecay ) and cross - section at lowest order of the process @xmath0 ( as given by comphep ) , for various higgs mass values and for @xmath19 800 gev . in the calculation of the cross - section ,
initial state radiation and beamstrahlung were taken into account . _ _ [ cols="^,^,^,^ " , ]
i thank marc winter and iouri gornouchkine for valuable discussions .
s. dittmaier , m. kramer , y. liao , m. spira and p. zerwas , phys . lett .
* b441 * ( 1998 ) 383 .
+ s. dawson and l. reina , phys
* d59 * ( 1999 ) 054012 .
+ g. blanger _
et al . _ , hep - ph/0307029 .
+ c. farrell , a. hoang , phys . rev .
* d72 * ( 2005 ) 014007 . via the process @xmath0 for various channels and their combination , for various higgs boson masses and for two values of the relative uncertainty on the residual background normalisation.__,width=566,height=793 ] | understanding the mechanism of electroweak symmetry breaking and the origin of boson and fermion masses is among the most pressing questions raised in contemporary particle physics .
if these issues involve one ( several ) higgs boson(s ) , a precise measurement of all its ( their ) properties will be of prime importance . among those , the higgs coupling to matter fermions ( the yukawa coupling ) . at a linear collider ,
the process @xmath0 will allow in principle a direct measurement of the top - higgs yukawa coupling .
we present a realistic feasibility study of the measurement in the context of the tesla collider .
four channels are studied and the analysis is repeated for several higgs mass values within the range 120 gev / c@xmath1 - 200 gev / c@xmath1 .
addtoresetequationsection = 20 cm = 15 cm |
the first mathematical descriptions of the effects of gravity , made by galileo in his study of the free fall of bodies and by kepler in his study of planetary motions , were purely empirical . though newton offered a coherent explanation of what was behind the laws governing gravitational effects , it was only with einstein s general relativity that we had an apparently complete theory of gravity . however , at the end of the 20@xmath3 century , a new enigma concerning the motion of ` celestial bodies ' emerged , in particular , in studying rotation curves of spiral galaxies .
while newton s law of gravity predicts that the velocity of rotation in the interior of a galaxy should fall with increasing distance from the galactic center if the observed light traces mass , what is observed is the maintenance of a constant velocity with increasing radius , generating flat rotation curves @xcite .
two simple ways of dealing with this problem have been suggested : 1 . assuming that there is more mass ( _ i.e. _ , dark matter ) in galaxies than is observed ; 2 . modifying the law of gravity .
while much work has been done in the search for possible particle candidates for dark matter @xcite , very little has been done to explore the possibilities of modified gravity laws . until now
, the most popular suggestion for a modified gravitational law has been modified newtonian dynamics , or , mond @xcite . in mond the acceleration @xmath4 of a body in an external gravitational field
is not exactly equal to the acceleration @xmath5 obtained from the newtonian gravitational force .
mathematically , one can write @xmath6 , where @xmath7 is a dimensionless function of the ratio @xmath8 of the acceleration @xmath4 to an empirically determined constant @xmath9 . only in the limit
@xmath10 is newtonian gravity restored .
the strongest objection to mond is that it does not have a relativistic theory supporting it . for recent articles criticizing mond ,
see scott _
( 2001 ) @xcite and aguirre _ et al . _
( 2001 ) @xcite .
for a recent positive review of mond , see sanders ( 2001 ) @xcite .
the objective of this letter is to expand the original mond proposal by presenting mathematical alternatives for the modified gravitational law .
specifically , we present several alternative mathematical alternative formulations for the dimensionless function @xmath11 , thus following closer the structure of the pioneering work of mond by milgrom @xcite . in the next section we present the basics of mond .
simulated rotation curves for several possible mondian - like functions are given in section [ sec : formulas ] .
the final section presents some brief conclusions and perspectives for future work .
as discussed in the introduction , the original mond proposal uses the relation @xmath12 where @xmath5 is the usual newtonian acceleration and @xmath13 is a function which obeys @xmath14 therefore , in the limit of large accelerations , @xmath15 , the usual newtonian gravity law is obtained . in the other extreme , @xmath16 , however , we have @xmath17 thus , using @xmath18 , where @xmath19 is the rotation velocity of the galaxy , @xmath20 which is a constant , as is observed for large galactic radii .
it is common in the literature ( _ e.g. _ @xcite , @xcite ) to use the expression @xmath21 this formula , proposed by milgrom @xcite , has the advantage of being invertible . with it one
can solve eq .
( [ mond ] ) analytically for the acceleration @xmath4 and , consequently , for the rotation velocity @xmath19 as a function of the radius @xmath22 .
however , other functions are also possible , and are discussed in the next section .
in his work on the implications of mond for galaxies @xcite , milgrom used as a model for a spiral galaxy of total mass @xmath23 , a disc of mass @xmath24 and a central spheroidal bulge of mass @xmath25 .
the fractional masses for the disc and the spherical bulge are @xmath26 and @xmath27 , respectively , so that the total fractional mass @xmath28 inside a radius @xmath29 is @xmath30 where @xcite @xmath31 \;,\ ] ] @xmath32 and @xmath33 is the incomplete gamma function . @xmath34 and @xmath35 are numerical constants .
the dimensionless variable @xmath36 is the ratio of the radius @xmath22 to the characteristic length @xmath1 .
the ratio of @xmath37 to @xmath1 , @xmath38 , is less than unity .
the radii @xmath1 and @xmath37 are obtained , in practice , by adjusting the luminosity profiles of the spheroidal and disc components , using the empirical law of de vaucoulers for the spherical bulge and an exponential function for the disc . following the mond proposal ,
we define @xmath39 where @xmath40 is a dimensionless function with a dimensionless argument @xmath41 , similar to the @xmath11 of milgrom @xcite in eq .
( [ mu ] ) .
this new function @xmath42 is such that @xmath43 we investigate the following functions @xmath44 which obey the constraints of eq .
( [ constraints ] ) : @xmath45 the behaviour of each of these functions as a function of @xmath46 can be seen in the expansions @xcite@xmath47 ^{-1 } & \\ & \simeq 1 + 27y^2/45-\left ( 27y/45\right ) ^4+\left ( 27y/45\right ) ^6 + ... & \left ( y\ll 1\right ) \end{array } \end{array } \right.\;\;.\ ] ] the functions are plotted in figure [ galmond4 ] . using these functions , together with equations ( [ gamma ] ) ,
( [ gammad ] ) and ( [ gamas ] ) , we obtain curves for the dimensionless rotation velocity @xmath48 as a function of @xmath49 for different values of @xmath23 , @xmath50 , and @xmath38 .
the curves are shown in figures [ galmond6 ] and [ galmond7 ] .
inspection of figures [ galmond6 ] and [ galmond7 ] shows clearly that all the functions @xmath42 produce flat rotation curves .
this is true not only for the particular values of @xmath23 , @xmath51 , and @xmath52 of the figures , but for the entire range of physically reasonable values for these parameters .
figure [ galmond7 ] shows that a comparison between the curves obtained , using the different @xmath53 functions presented , together with the original milgrom proposal ( eq .
( [ mu ] ) ) , may be useful to distinguish between them , since each curve has a peculiar feature in the region @xmath2
. it would be interesting to test the formulas presented here against observational data , noting that @xmath54 and @xmath52 are not free parameters , but are given by the luminosity profiles of the galaxies .
the mass @xmath23 and the constant @xmath9 are the only free parameters to be adjusted .
the study of different galaxies gives a single value for @xmath9 , the mass @xmath23 and the mass - luminosity ratio , @xmath55 , of each galaxy .
@xmath11 and @xmath56 can lead to different relativistic extensions of mond , important for future studies .
for instance , using the expression for the gravitational potential @xmath57 , valid for purely radial forces , one can naively ascribe a @xmath58 to the modified gravitational laws obtained with @xmath59 , @xmath60 and @xmath61 , for example , @xmath62 @xmath63 and @xmath64 + \varphi_0 \;\;,\ ] ] where @xmath65 is a constant of integration .
therefore , in the search for a complete theory for mond , it is important to study alternative mondian functions .
the mondian functions given in this letter can be seen as a step in this direction .
ssc thanks the brazilian agency fapesp for financial support under grant 00/13762 - 6 .
both ssc and ro thank fapesp for partial support under grant 00/06770 - 2 and the brazilian project pronex / finep ( 41.96.0908.00 ) for partial support . | we present new mathematical alternatives for explaining rotation curves of spiral galaxies in the mond context . for given total masses , it is shown that various mathematical alternatives to mond , while predicting flat rotation curves for large radii ( @xmath0 , where @xmath1 is the characteristic radius of the galactic disc ) , predict curves with different peculiar features for smaller radii ( @xmath2 ) .
they are thus testable against observational data . , gravitation : phenomenology , galaxies : internal motions 04.90.+e , 95.30.sf , 98.62.dm |
the oh / ir source irc+10420 = iras19244 + 1115 identified with the peculiar high luminosity star v1302aql is a unique object , which has been carefully and comprehensively studied over the last decades but still remains a puzzle .
of the two hypotheses about its nature neither seems to be convincingly preponderant as yet . according to fix and cobb ( 1987 ) , hrivnak et al . , ( 1989 ) and others this is a degenerate core giant evolving through the proto - planetary nebula stage with a luminosity no higher than @xmath3 . according to jones et al . , ( 1993 ) , humphreys and davidson ( 1994 ) and oudmaijer et al .
( 1996 ) this is a core - burning hypergiant of @xmath4 .
the difficulty of choice is due to : * the uncertainty of fundamental observational parameters , such as spectral class and distance ; * the fact that with the difference in mass , age , even type of stellar population the evolutionary processes and their observational evidence are similar : in both alternatives the effective temperature of the star increases , there is a gaseous - dust envelope inherited from the red giant or supergiant phase , which interacts with the stellar wind ; * the presence of several competing models : thin chromosphere in the expanding gaseous - dust envelope such optically thick that we see the light of the star being multiple scaterring by circumstellar dust ( fix and cobb , 1987 ) ; a gaseous - dust disk in a clumpy envelope ( jones et al . ,
1993 ) ; jets with a small angle of opening ( oudmaijer et al . , 1994 ) ; and at last infall of circumstellar material onto photosphere ( oudmaijer , 1995 ) .
outer regions of the source of radius 2 - 3 arcsec are mainly described and mapped by radio astronomy techniques from emission of molecules ( paper by nedoluha and bowers ( 1992 ) and references therein ) .
the gas envelope has been imaged by the methods of infrared speckle interferometry and coronagraphy ( ridgway et al .
, 1986oc ; kastner and weintraub , 1995 ) .
the image of the dust envelope also extends to several seconds of arc , but the radiation is sharply enhanced in the region of about 0.1arcsec in radius . however space or ground - based speckle images in the optical range , which could refine the structure of the central region , unknown to us . here
the high resolution optical spectrum of irc+10420 , which contains the emission and absorption lines of the envelope and absorption ones of the photosphere or of the pseudophotosphere of the central star , is described .
.observation log of irc+10420 [ cols="^,^,^ " , ]
so , the optical spectrum of irc+10420 of the years from 1992 through 1996 * points to the increase in the temperature : spectral class a5 instead of f8 in 1973 ; * contains absorptions ( mainly of ions ) formed in the photosphere , apparently stationary with respect to the star center of mass ; * contains emission details too , which are formed in the expanding envelope and perhaps in its compressing layers ; * rezembles the spectra of late - type b[e ] stars ; the metallicity , which is close to solar , and the altered [ n / c]-value allow us to consider irc+10420 as a massive object at the evolution stage of at least after the first dredge - up and not to reject the hypothesis of jones et al .
( 1993 ) who suggested that irc+10420 is a true hypergiant with a mass of about @xmath5 , evolving from the red supergiant phase to the wolf - rayet stage .
the nature of irc+10420 is still open question .
new observations are necessary to obtain full chemical abundance pattern and to coordinate luminosity , distance and radial velocity of this object . besides that we need more careful indentification of extremely plentiful and variable features of the optical spectra of irc+10420 .
for example , what are the enigmatic narrow strong absorption details @xmath6 ? for the present one can say only that these are not telluric lines . it should be noted that in the frames of the study of supergiants with infrared excess ( klochkova , 1995 ; zas et al . , 1995 ) we have obtained also the spectra of the supergiant hd179821 = iras19114 + 0002 , which has been considered analogous to irc+10420 ( kastner , weintraub , 1995 ) . based on these spectra results
have recently been obtained ( zas et al . , 1996 ) for hd179821 , using the model atmosphere method : @xmath7 , logg=1.3 , iron peak elements are slightly underabundant , sc and ti are slightly overabundant . but for this object zas et al .
( 1996 ) revealed the overabundance of sodium , s - process ( y , zr ) and r - process ( eu ) elements .
the overabundance of s - process points to the post - agb stage of evolution of hd179821 .
however for more general conclusions about the nature of hd179821 and its likeness to irc+10420 , abundances of cno - triad are needed . _
_ we thank prof .
yu.n.efremov for helpful discussion on localization of irc+10420 in the galaxy and dr .
r.oudmaijer for a part of his ph.d.thesis kindly made available to us .
we are also indebted to the referee for detailed and fruitful discussion and suggestions .
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mnras , 282 , 1171 zickgraf f .- j . , stahl o. , wolf b. 1992 , a&a , 260 , 205 | to understand the evolutionary stage of the peculiar supergiant irc+10420 , we have been taking spectra for several years at the 6 m telescope .
the optical spectrum of irc+10420 of the years from 1992 through 1996 points to the increase in the temperature : spectral class a5 instead of the former f8 , as was pointed out by humpreys et al . ,
( 1973 ) .
now it resembles the spectra of late - type b[e ] stars .
the spectrum contains absorptions ( mainly of ions ) formed in the photosphere , apparently stationary with respect to the star center of mass , and emissions too , which can be formed in the fossil expanding envelope as well as partly in its compressing region .
using our spectra and spectral data obtained by oudmaijer ( 1995 ) we estimated the atmospheric parameters @xmath0 , logg=1.0 , @xmath1 and concluded that metallicity of irc+10420 is solar : the average value @xmath2_{\odot } = -0.03}$ ] .
combination of results allows us to consider irc+10420 as a massive supergiant evolving to the wr - stage .
= -3 cm = -2 cm _ special astrophysical observatory , nizhnij arkhyz , 357147 russia _
* keywords : * stars : evolution stars : hypergiants stars : individual : irc+10420 |
inclusive unpolarized and polarized deeply inelastic diffractive scattering at high energies and momentum transfer is one of the important processes in lepton
nucleon scattering . as found by experiment , cf .
@xcite , there are interesting relations between the cross sections of these processes and those of inclusive deeply inelastic scattering : _ i ) _ the scaling violations of both processes are quite similar and _ ii ) _ the ratio of the differential cross sections in @xmath2 and @xmath3 are widely constant in the whole kinematic domain and are of @xmath4 . whereas the latter aspect can not be understood with perturbative methods the former calls for a rigorous analysis in perturbative qcd . in recent analyses @xcite
this aspect has been investigated both for the unpolarized and the polarized case on the basis of the light cone expansion . by this method
the semi - exclusive processes of diffractive scattering could be related to forward scattering processes at short distances , for which similar evolution equations as in the deep inelastic case apply .
moreover a callan gross and wandzura - wilczek relation between the twist2 contributions of the diffractive structure functions were derived . in this note
we give a summary of these papers .
the process of deep inelastic diffractive scattering is @xmath5 , with a significant rapidity gap between @xmath6 and the remaining hadrons .
the differential scattering cross section for single
photon exchange is given by @xmath7 with @xmath8 and @xmath9 the leptonic and hadronic tensors .
using current conservation , p and t invariance and the hermiticity relation for the hadronic tensor one finds a representation of the hadronic tensor in terms of four unpolarized and eight polarized structure functions @xcite .
we will henceforth consider the case of small values of @xmath10 . in this limit
the outgoing and incoming proton momenta are related by @xmath11 and the cross section depends on two unpolarized and two polarized structure functions only @xmath12 with @xmath13 and @xmath14 for @xmath15 .
( [ eqhadr ] ) is considered in the generalized bjorken limit : @xmath16 and @xmath17 = fixed .
the non - forward variable @xmath18 is related to another variable often used , @xmath19 , by @xmath20 . in the limit
@xmath21 the above structure functions depend on the three variables @xmath22 and @xmath3 . since for diffractive processes the outgoing proton
is well separated in rapidity from the diffractively produced hadrons ( rapidity gap ) , one may apply a. mueller s generalized optical theorem @xcite to calculate the scattering cross section .
this is done moving the outgoing proton into an incoming anti - proton and considering the absorptive part of deep inelastic forward scattering off the state @xmath23 summing over all final - state spins . note that under this interchange @xmath24 is kept space like . due to this operation
we may now evaluate the compton
operator @xmath25 \\ & = & -e^2 \frac{\tilde x^\lambda}{2 \pi^2 ( x^2-i\epsilon)^2 } rt \left [ \overline{\psi } \left(\frac{\tilde
x}{2}\right ) \gamma^\mu \gamma^\lambda \gamma^\nu \psi \left(-\frac{\tilde x}{2}\right ) - \overline{\psi } \left(-\frac{\tilde x}{2}\right ) \gamma^\mu \gamma^\lambda \gamma^\nu \psi \left(\frac{\tilde x}{2}\right ) \right ] s \nonumber\end{aligned}\ ] ] between the above states for forward scattering .
we represent this operator in terms of a vector and an axial - vector operator , which are in turn related to the associated scalar and pseudo - scalar operators , through which we introduce the respective operator expectation values , see @xcite defining non forward parton densities @xmath26 , @xmath27 with @xmath28 and @xmath29 . here
we neglect sub - leading components @xmath30 . after passing a series of steps , see @xcite , we may express the hadronic tensor in this approximation by one unpolarized and one polarized distribution function , @xmath31 and @xmath32 , respectively . for quarks and anti - quarks these distribution functions , which are the diffractive parton distributions , read @xmath33
the upper sign refers to quarks , the lower to anti - quarks , and @xmath34 in the unpolarized case , @xmath35 in the polarized case , where @xmath36 .
the diffractive structure functions @xmath37 and @xmath38 obey the representation @xmath39\nonumber\\ g_1^d(\beta,\eta , q^2 ) & = & \sum_{q=1}^{n_f } e_q^2 \left [ f_{q5}^d(\beta , x_{{{\mathbb{p}}}},q^2)+\overline{f}^d_{q5 } ( \beta , x_{{{\mathbb{p}}}},q^2)\right]~.\end{aligned}\ ] ] after some calculation one finds for the twist2 contributions to the hadronic tensor the relations @xmath40 the callan gross relation between the structure functions depending on @xmath41 is modified due to the emergence of @xmath2 , while the wandzura wilczek relation holds in the new variable @xmath42 $ ] .
the emergence of the integral term in one of the above relations is due to a basic connection between a vector valued non forward distribution function and the associated scalar one @xcite .
the corresponding term exceptionally cancels in the callan gross relation but is present in most relations of this type , see also @xcite .
the evolution equations of the diffractive parton densities can be formulated starting with the evolution equations for the scalar quark and gluon operators in the flavor non singlet and singlet case , see e.g. @xcite . @xmath43 with @xmath44 the factorization scale .
forming expectation values as in the foregoing section one notices that the evolution does not depend on the value of the light - cone mark @xmath45 , which can be set to 0 .
moreover the all - order rescaling relation @xmath46 where @xmath47 , is applied .
after some calculation one finds the following evolution equations @xmath48 these equations apply both to the unpolarized and polarized diffractive parton densities of twist2 to all orders in the coupling constant . in the calculation
the absorptive part of the distribution was taken , which identifies the original momentum fraction , cf .
@xcite , @xmath49 with @xmath50 and results in evolution equations with a support [ 0,1 ] , unlike those in @xmath51 . if compared to the case of deep - inelastic scattering the evolution is here not in @xmath2 but in the new variable @xmath41 .
otherwise the same evolution equations are obtained .
this holds also for higher twist operators , for which the argument is exactly the same as given in this section , see @xcite .
we derived the twist2 evolution equations for the unpolarized and polarized twist2 diffractive parton distributions considering these processes in the light
cone expansion at short distances .
we also derived relations between the diffractive structure functions in the unpolarized and polarized case .
the observed similarity of the scaling violations between deep - inelastic diffractive and deep
inelastic structure functions was shown in the present approach being due to the same structure of evolution equations which act in the former case on the variable @xmath41 and in the latter on @xmath2 . polarized deep
inelastic scattering was not yet observed nor studied in detail in a larger kinematic domain .
it would be interesting to know if the pattern of relations as observed for unpolarized scattering repeats and the predictions of the present paper can be verified .
the compass experiment and polarized experiments at future high - energy facilities @xcite could clarify this .
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m. anselmino et al . , tesla - n study group : electron scattering with polarized targets at tesla desy 00160 , trp0020 , hep - ph/0011299 . | polarized inclusive deep - inelastic scattering is formulated in the light cone expansion .
the qcd evolution of the leading twist distribution functions is derived .
it is shown that the twist2 contribution to the structure functions @xmath0 is obtained via @xmath1 by a wandzura wilczek relation . |
we use shells made of vinylpolysiloxane ( a silicone - based elastomer ) with elastic moduli of @xmath0 , @xmath1 and @xmath2 mpa , as well as shells made of latex .
the shells range from @xmath3@xmath4 mm in diameter , @xmath3@xmath5 mm in length and approximately @xmath6@xmath0 mm in thickness .
we clamp one end of these shells onto a rigid nozzle and pass air through them at flow rates ranging from @xmath0@xmath7 liters per second .
when the flow rate of air in the shells exceeds a certain critical value , dependent on the dimensions and material properties of each shell , the shell becomes unstable and begins to vibrate .
the mode of vibration corresponds to one of the circumferential normal modes of vibration of cantilevered cylindrical shells .
which mode is observed depends on the dimensions and material properties of the shell .
we observed the first three modes . in the first mode , commonly known as the garden hose mode , " the shells oscillate side - to - side with the frequency of approximately @xmath8 hz . in the second mode , the surface of the shell bends inwards , obstructing the fluid flow and causing a large jump in the pressure drop across the nozzle . in this mode , the shell can vibrate with frequencies from @xmath9@xmath10 hz , depending on the volumetric flow rate of air .
we observed that the frequency of oscillation is directly proportional to air flow rate .
additionally , when the shell vibrates in the second mode with average frequencies ranging from approximately @xmath11@xmath12 hz , the vibration is unstable and the oscillation frequency varies widely between periods .
the second mode is the most robust and can be observed in the largest range of parameters in our shells . in the third mode of vibration , the circumference of the free end of the shell
is divided into three
flaps " oscillating inwards and outwards . in this mode ,
the shells vibrate with frequency of approximately @xmath13@xmath14 hz .
the images were captured with a phantom v5.2 high speed color camera .
the images of the second and third mode were captured using a stroboscopic technique and the final video is a concatenation of frames taken from different oscillation periods . each frame is slightly offset in phase , yielding a slow - motion effect .
we would like to express our gratitude to felice frankel for her help with cinematography , and to prof .
john bush who kindly lent us the high speed camera .
we would also like to thank prof .
pedro reis and dr .
arnaud lazarus for sharing with us their data on elastic properties of vinylpolysiloxane elastomers . | in this fluid dynamics video , we demonstrate the first three circumferential modes of fast , large amplitude vibrations of compliant cylindrical shells carrying a fluid . |
rotating magnetospheres are widely believed to be responsible for the relativistic jet phenomenon in active galactic nuclei ( agn ) @xcite .
here we adress the question whether centrifugal acceleration of charged test particles at the base of such a jet magnetosphere may possibly produce a seed population of relativistic electrons which is required for efficient particle acceleration . for , in order to explain the origin of the nonthermal emission extending up to tev energies in some blazars ,
several acceleration processes have been proposed among which fermi - type particle acceleration mechanisms ( i.e. diffusive shock acceleration @xcite ) are quite promising .
however such kind of mechanisms require a pre - accelerated seed population of electrons with lorentz factors of the order of @xmath5 @xcite .
it seems therefore quite interesting whether in the case of agn centrifugal acceleration by rotating jet magnetosphere may potentially fill this gap by providing pre - accelerated seed particles . for an analytical treatment ,
we consider the following simplified model : motivated by mhd - scenarios for the origin of jets via rotating jet magnetospheres @xcite ( see fig . [ jet ] ) a projected two - dimensional model topology is applied where the magnetic field is supposed to rotate rigidly with a fraction of the rotational velocity of the black hole @xcite .
test particles with rest mass @xmath6 and charge @xmath7 are assumed to be injected at time @xmath8 and position @xmath9 with velocity @xmath10 parallel to the rotating field line .
consider the forces acting on a particle in a rotating frame of reference @xcite : particles , which are injected at ( @xmath8,@xmath9 ) with velocity @xmath10 along the magnetic field line @xmath11 experience a centrifugal force in the radial direction given by @xmath12 where @xmath13 denotes the lorentz factor and @xmath14 the angular velocity of the field .
additionally , there is also a relativistic coriolis term in the noninertial frame governed by the equation @xmath15 which acts as a deviation - force in the azimuthal direction . in the inertial rest frame
the particle sees the field line bending off from its initial injection position , therefore it experiences a lorentz force ( @xmath16 ) @xmath17 where @xmath18 is the relative velocity between the particle and the magnetic field line . due to the lorentz force
a particle tries to gyrate around the field line .
initially , the direction of the lorentz force is perpendicular to the direction of the coriolis force , but as a particle gyrates , it changes the direction and eventually becomes antiparallel to the coriolis force .
hence , the bead - on - the - wire approximation is valid if the lorentz force is not balanced by the coriolis force @xcite . in this case , the accelerated motion of the particle s guiding center due to the centrifugal force may be written as @xmath19 where @xmath20 .
the constrained motion is then given by the azimuthal components of forces @xmath21 generally , the bead - on - the - wire approximation is supposed to break down if @xmath22 exceeds @xmath23
( i.e. when @xmath24 in eq .
[ constraint ] becomes @xmath25 ) .
using the argument that the hamiltonian for a bead on a relativistically moving wire @xmath26 is a constant of motion , the equation for the radial accelerated motion could be reduced to a simple form which has been solved analytically yielding @xcite @xmath27 where @xmath28 , ( @xmath29 ) is the jacobian elliptic cosine ( sine , respectively ) , and @xmath30 is an elliptic integral of the first kind , i.e. @xmath31 with @xmath32 .
the lorentz factor may then be written as @xmath33^{2}}\,,\ ] ] or , if expressed as a function of the radial co - ordinate , as @xmath34 apart from radiation losses ( e.g. inverse - compton losses in the radiation field of the accretion disk , see @xcite ) , the maximum attainable lorentz factor @xmath1 is in particular limited by the breakdown of the bead - on - the - wire approximation ( i.e. when the particle leaves the field line and thus , acceleration becomes ineffective ) in the vicinity of the light cylinder @xmath0 . using the definition of the hamiltonian @xmath35 and eq .
[ gamma_r ] and setting @xmath36 , one may derive an upper limit for the maximum lorentz factor @xmath1 from eq .
[ constraint ] @xmath37 where @xmath38 denotes the magnetic field strength at the light cylinder and where for clarification @xmath39 has now been inserted . for typical bl lac conditions , i.e. a light cylinder radius @xmath40 m , and a field strength @xmath41 t , eq .
[ gmax ] results in an upper limit on the maximum lorentz factor @xmath42 .
the results derived in the simple toy - model presented here support flares on accretion disks as providing a seed population of relativistic electrons with lorentz factors up to @xmath43 in bl lac type objects .
such pre - accelerated particles are required for models involving diffusive shock acceleration of @xmath44 in relativistic jets , cf .
@xcite , @xcite .
particle acceleration by rotating jet magnetospheres may thus possibly represent an interesting explanation for the required pre - acceleration .
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rieger , f.m . , and mannheim , k. , _ a&a _ * 353 * , 473 ( 2000 ) . | centrifugal acceleration of charged test particles at the base of a rotating jet magnetosphere is considered .
based on an analysis of forces we derive the equation for the radial accelerated motion and present an analytical solution . it is shown that for particles moving outwards along rotating magnetic field lines , the energy gain is in particular limited by the breakdown of the bead - on - the - wire approximation which occurs in the vicinity of the light cylinder @xmath0 .
the corresponding upper limit for the maximum lorentz factor @xmath1 for electrons scales @xmath2 , with @xmath3 the magnetic field strength at @xmath0 , and is at most of the order of a @xmath4 for the conditions regarded to be typical for bl lac objects .
such values suggest that this mechanism may provide pre - accelerated seed particles which are required for efficient fermi - type particle acceleration at larger scales in radio jets . |
the dimension of the multiwire chambers deployed in modern high energy physics experiments is usually large conforming to the scale of experimental setup .
the electrostatic instability in such chambers may be crucial when the amplitude of the oscillation caused by the action of electrostatic force alone or combined with the gravity becomes comparable to the electrode spacings .
the study of the wire deflection in such a geometry is usually a complex affair since an interplay between several physical forces determines the wire stability .
the approximation of constant or linear dependence of the force on the wire deflection is not adequate to solve for the differential equation governing the wire dynamics because all the wires in the chamber move in a collective way influencing each other giving rise to a nonlinear effect .
since the exact solutions for the differential equation involving the nonlinear force are no longer known , it has to be solved numerically . of various methods of estimating the electrostatic sag from the differential equation ,
only the linear and iterative methods have been attempted in several geometries @xcite . in these works ,
the electrostatic force has been estimated from the 2d field calculation @xcite which differs significantly from 3d solutions .
owing to the 2d nature of the problem , the sag is normally overestimated due to the fact that the whole length of the wire is considered to be at maximum sag . in this work ,
an accurate 3d computation of electrostatic field has been carried out through the use of a nearly exact boundary element method ( nebem ) @xcite which has yielded precise force estimation . in order to reduce complexity ,
only the normal component of the field has been considered in the calculation .
the deflection of each segment has been assumed to be very small in comparison to its length .
the calculation has been carried out for a geometry similar to that of rich detector in alice @xcite .
the anode plane consists of gold - tungsten wires with @xmath0 m diameter with pitch @xmath1 mm .
the upper cathode plane is made of copper - berrylium wires with diameter @xmath2 m and pitch @xmath3 mm while the lower one is a uniform conducting plate .
the separation of upper and lower cathodes from the anode are respectively @xmath4 mm and @xmath5 mm and length of the detector in z - direction is @xmath6 cm .
the anode plane is supplied with high voltage w.r.t . the cathode planes .
the second order differential equation in an equilibrium state of the wire can be written as @xmath7 where @xmath8 , @xmath9 are the electrostatic and gravitational forces per unit length while @xmath10 the stringing tension of the wire . using three point finite difference formula , it can be rewritten as @xmath11.(\delta z)^2\ ] ] where @xmath12 , @xmath13 and @xmath14 represent the deflections of respective segments . the electrostatic force on the @xmath15-th segment has been computed using nebem solver for the given 3d geometry .
the required sag due to the action of either of the electrostatic and gravitational forces or combined may be obtained from this equation .
thus the set of equations for the segments on a wire can be represented as @xmath16 where @xmath17 is the tridiagonal coefficient matrix whose inverse has been calculated following standard numerical receipe . in the present work ,
five anode wires have been considered with discretization of @xmath18 linear segments while that of the cathode plate has been @xmath19 .
it should be noted that no plates on the sides of the chamber have been taken into account .
the calculation procedure has been validated by calculating wire sag due to gravitational force and comparing with the analytic solution for gravitational force only as @xmath20 where @xmath21 and @xmath22 , @xmath23 , @xmath24 are the length , radius and density of the wire respectively .
the results has been illustrtaed in fig.[fig : gravsagandcath ] which has demonstrated the validity of the method . gravitational sag of central anode and cathode wires , scaledwidth=45.0% ]
the normal electric field components acting on the anode and cathode wire segments for anode voltage of @xmath25v have been plotted in fig.[fig : normalef ] .
the field component on each segment has been calculated from the vectorial addition of field components at four radial locations on the segment periphery .
the wire sag at the centre due to electrostatic force following the solution of tridiagonal matrix equation [ eqn.[eqn : mateq ] ] has been shown as a function of anode voltage in fig.[fig : wiresag ] for anode and cathode wires separately .
it is evident from the result that the sag in the anode wire changes more rapidly than the cathode wires .
r0.5 the central wire in the anode plane has been found to undergo more deflection in comparison to the edge wires .
the calculation of @xcite for wire sags in this chamber has reported less deflection in comparison to our result . in @xcite ,
an additional restoring electrostatic force has been considered to be operational when the wire gets deflected which in turn has helped to reduce the wire sag . in our calculation , no such dynamic consideration of the electrostatic force with the wire deflection has been incorporated . to reproduce the actual wire sags ,
an iterative process can be carried out each time calculating the electrostatic force due to new position of the deflected wire .
using the nebem solver , the electrostatic field could be accurately calculated for the three dimensional geometry of multiwire rich chamber .
an fdm approach to compute the wire sag has been developed and validated for the case of gravitational sag calculation . in the present calculation ,
no restoring effect of electrostatic force has been considered unlike the earlier work which has led to larger sag estimates .
the restoring force aspect will be implemented in future by iterative technique to estimate a realistic wire sag in this chamber . | a numerical method of determining the wire sag in a multiwire proportional chamber used in rich @xcite by solving the second order differential equation which governs the wire stability has been presented .
the three point finite difference method ( fdm ) has generated a tridiagonal matrix equation relating the deflection of wire segments to the force acting on it .
the precise estimates of electrostatic force has been obtained from accurate field computation using a nearly exact boundary element method ( nebem ) solver @xcite . |
a decade ago , deep h@xmath0 observations indicated that some disk galaxies can support limited star formation at their extreme outer edge ( e.g. ferguson et al .
galex imaging then surprisingly revealed that m 83 ( thilker et al . 2005 ) and ngc 4625 ( gil de paz et al .
2005 ) have extended uv disks ( xuv - disks ) unapparent in the distribution of hii regions .
we have since demonstrated that outer disk sf activity is commonplace , with @xmath1 1/3 of nearby s0-sm galaxies having discernible xuv - disk structure ( thilker et al .
2007 ) . for detailed information , see the review by gil de paz ( this volume ) or thilker et al .
( 2007 ) .
the relative lack of hii regions compared to uv clumps in the low sfr outer disk has been largely explained as a stochastic effect , tied to the very limited hii region lifetime compared to the time - scale for uv production ( boissier et al .
2007 ) . however , alternative contributing factors ( top - light imf , low density ism ) have yet to be ruled out and motivate our hst analysis .
hst acs uv
visible imaging of eight xuv - disk fields was obtained for m83 .
single locations in each of ngc 5055 ( fig . 1 ) and ngc 2090 are also being studied .
we observed in four band - passes ( f150lp , f435w , f606w , and f814w ) using the wfc and sbc .
optical observations of ngc 2090 were obtained using wfpc2 ( after the failure of acs / wfc ) .
hst resolves the xuv - disk sources into loosely clustered complexes of individual stars .
these complexes , likely evolved ob associations , are low mass ( @xmath2 m@xmath3 ) , intermediate age structures .
only very few hst detections are consistent with being zero - age upper - ms stars having mass @xmath4 15 m@xmath3 ( fig .
h@xmath0 emission is detected from complexes in which they are found .
observed association sizes vary from 100 pc to @xmath1 500 pc with significant internal sub - clustering .
the largest groupings may be blended associations .
cmds ( fig .
1 ) suggest multiple generations within larger complexes ( up to age of @xmath1 200 myr ) .
boissier , s. , et al .
2007 , apjs , 173 , 524 ferguson , a. , et al .
1998 , apj , 506 , l19 gil de paz , a. , et al .
2005 , apj , 627 , l29 thilker , d. a. , et al . 2005 , apj , 619 , l79 thilker , d. a. , et al .
2007 , apjs , 173 , 538 | we describe hst imaging of recent star formation complexes located in the extended uv disk ( xuv - disk ) component of ngc 5236 ( m 83 ) , ngc 5055 ( m 63 ) , and ngc 2090 .
photometry in four fuv
visible bands permits us to constrain the type of resolved stars and effective age of clusters , in addition to extinction .
the preliminary results given herein focus on cmd analysis and clustering properties in this unique star - forming environment . |
the quasiclassical technique is one of the most powerful methods to tackle transport problems .
its main virtue relies in the fact that starting from a microscopic quantum formulation of the problem at hand it aims at deriving a simpler kinetic equation resembling the semiclassical boltzmann one . in deriving such an equation
some of the information at microscopic level is suitably incorporated in a set of parameters characterizing the physical system at macroscopic level .
since the first application to superconductivity , this equation is known as the eilenberger equation ( for a review see for instance @xcite ) .
we have recently derived@xcite such an equation for a two - dimensional electron gas in the presence of spin orbit coupling with hamiltonian @xmath1 where @xmath2 is a momentum dependent internal magnetic field . in the case of rashba spin - orbit coupling @xmath3 . in ref .
@xcite we adopted the standard @xmath0-integration procedure to arrive at the eilenberger equation , and , though this leads to correct results , we feel the need for a deeper understanding , which we provide in the present paper . in
so doing we follow an analysis carried out by shelankov@xcite .
finally , we use the eilenberger equation to study the response to an external electric field in the presence of magnetic impurities .
in deriving the eilenberger equation a key observation is that , by subtracting from the dyson equation its hermitian conjugate , one eliminates the singularity for equal space - time arguments and gets a simpler equation for the @xmath0-integrated green function @xmath4 here @xmath5 is the green function in wigner space , i.e. the fourier transform of @xmath6 with respect to the relative coordinate @xmath7 .
the `` check '' indicates that the green function is a @xmath8 by @xmath8 matrix in the keldysh space @xcite . to shed some light on the meaning of the @xmath0-integration ,
let us consider first the space dependence of the two - point retarded green function for free electrons in the absence of spin - orbit coupling @xmath9 at large distances , the integral is dominated by the extrema of the exponential under the condition of constant energy .
this forces the velocity to be parallel or antiparallel to the line connecting the two space arguments , @xmath10 .
it is then useful to consider the momentum components parallel ( @xmath11 ) and perpendicular ( @xmath12 ) to @xmath13 . given the presence of the pole , one can expand the energy in powers of the two momentum components @xmath14 . in the case of the retarded green function ,
the important region is that with velocity parallel to @xmath13 .
we then get @xmath15 one sees how the green function is factorized in a rapidly varying term @xmath16 , and a slow one , @xmath17 .
this suggests to write quite generally @xmath18 where @xmath19 is slowly varying and @xmath20 indicates the free green function .
explicitly , in the present equilibrium case @xmath21 for the advanced green function one can go through the same steps with the difference that the integral is dominated by the extremum corresponding to a velocity antiparallel to @xmath22 , so that one has the ingoing wave replacing the outgoing one . in the non - equilibrium case shelankov
has shown that @xmath23 and furthermore that the quasiclassical green function corresponds to the symmetrized expression @xmath24 when sending to zero the relative coordinate @xmath22 .
when the spin - orbit coupling is present the green function becomes a matrix in spin space and the fermi surface splits into two branches @xmath25 .
we always assume this splitting to be small compared to the fermi energy , i.e. @xmath26 . in the case of the rashba interaction
we write @xmath27 where @xmath28 is the projector relative to the @xmath29 energy branch and the curly brackets denote the anticommutator .
this ansatz allows us to proceed in wigner space as before , while retaining the information on the coupling and coherence of the two bands .
eq.([6bis ] ) is the equivalent in real space of the ansatz for the green function @xmath30 used in ref.@xcite .
with such an ansatz , eq.([6bis ] ) , we obtain from eq.([5special ] ) @xmath31 what we have explicitly shown for the retarded component of the green function can be extended to the advanced and keldysh components too .
notice that @xmath32 and @xmath33 coincide in the absence of spin - orbit coupling , since in that case @xmath34 .
the derivation of the eilenberger equation can now be done following the steps detailed in ref.@xcite .
we do not repeat them here and give just the final result @xmath35\big ) \nonumber \\ & = & - { \rm i } \left [ \check \sigma , \check g \right ] , \label{11}\end{aligned}\ ] ] where @xmath36 , @xmath37 and both the momentum @xmath38 and the internal field @xmath39 are evaluated at the @xmath40-branch of the fermi surface .
finally , @xmath41 is the self - energy .
it is often convenient to expand @xmath42 in terms of pauli matrices , @xmath43 , to explicitly separate charge and spin components .
physical quantities like charge and spin densities and currents are related to the keldysh component of @xmath42 .
for example the spin current for @xmath44 , @xmath45 is @xmath46 where @xmath47 and @xmath48 is the angle average over the directions of @xmath49 .
focusing on the rashba interaction , we study the effects of magnetic impurities on spin currents . in @xcite and @xcite
the problem has been recently tackled via diagrammatic techniques .
we show how analogous results can be obtained in a simple and rather elegant way relying on eq.([11 ] ) .
as it is well known , spin currents arising from the spin hall effect in such a system are completely suppressed by the presence of non - magnetic scatterers . by taking the angular average of eq.([11 ] ) , one obtains a set of continuity equations for the various spin components which let one easily understand the origin of this cancellation .
explicitly , by assuming @xmath50-wave and non - magnetic impurities randomly distributed in the system @xmath51 the self - energy in the born approximation turns out to be @xmath41 @xmath52 , @xmath53 being the momentum scattering rate .
the continuity equations for the @xmath45 spin components then read @xmath54 a rather important peculiarity of the rashba hamiltonian is that it lets one write the vector product appearing above in terms of the various spin currents , so that , by choosing for example @xmath55 , we are left with @xmath56 under stationary and homogeneous conditions this implies the vanishing of the @xmath57 spin current .
as soon as magnetic impurities are introduced in the system , their presence changes the self - energy and leads to the appearance of additional terms in eq.([12 ] ) .
we assume the magnetic scatterers to be also isotropic and randomly distributed @xmath58 and , proceeding again in the born approximation , we obtain the self - energy @xmath59 here @xmath60 is the spin - flip rate
. with this , and by considering again stationary and homogeneous conditions , eq.([12 ] ) becomes @xmath61 which in terms of the real spin current and polarization means @xmath62 by assuming a low concentration of magnetic impurities , we can use in eq.([fine1 ] ) the value of the @xmath63-spin polarization valid in their absence , @xmath64@xcite , @xmath65 being the external , homogeneous electric field .
we then get the spin hall conductivity to first order in @xmath66 @xmath67 a results that differs from those on refs.@xcite .
this is not surprising for ref.@xcite , which neglects normal impurity scattering and then considers the opposite limit .
the reason why our result does not agree with the low magnetic impurity - concentration limit of eq.(20 ) of ref.@xcite is not clear to us and deserves further investigation .
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matter * 5 * , 2603 ( 1993 ) . | we discuss the quasiclassical green function method for a two - dimensional electron gas in the presence of spin - orbit coupling , with emphasis on the meaning of the @xmath0-integration procedure . as an application of our approach ,
we demonstrate how the spin - hall conductivity , in the presence of spin - flip scattering , can be easily obtained from the spin - density continuity equation .
ep2ds-17 , manuscript , latex-2e , style files 72.25.ba , 72.25.dc |
the european space agency s gaia mission , approved for launch in 201012 , aims at surveying the galaxy to 20th visual magnitude , using a combination of astrometric measurements ( for trigonometric parallaxes and proper motions ) , multiband photometry ( for basic stellar parameters like temperature and metallicity ) , and radial - velocity measurements .
targeted accuracies versus magnitude allow direct distances and motions to be obtained for large samples of intrinsically bright stars across the galaxy and in some nearby local group galaxies .
expected typical accuracies are shown in table 1 . in total more than 1 billion stars will be observed , of which 50100 million will obtain individual parallax distances to better than 5 per cent .
a primary science goal is to study formation , evolution and structure of the galaxy , for which large - scale mappings of star formation histories are essential . for a full description of the very broad range of science goals
see perryman et al .
( 2001 ) . in its present design gaia
comprises two astrometric instruments , with @xmath4 m@xmath5 apertures and a combined 0.5 deg@xmath5 field of view , and a separate photometric / spectroscopic instrument with a @xmath6 m@xmath5 aperture .
the latter performs photometry in @xmath711 bands for astrophysical classification , and @xmath8 spectroscopy in the 849874 nm wavelength range , mainly for radial velocities . during its lifetime of at least 5 years
, the satellite will scan the entire sky repeatedly , so that each object is observed at multiple epochs .
the above numbers and accuracy predictions refer to the recently ( may 2002 ) completed revised design , aiming at a substantially reduced mission cost compared with the previous baseline ( perryman et al .
2001 ) , while preserving all science goals intact .
cccccccc @xmath9 & @xmath10 & @xmath11 & @xmath12 & @xmath13 & @xmath14 & @xmath15)$ ] & @xmath16 + mag & @xmath17as & @xmath17as yr@xmath18 & km s@xmath18 & & & & kpc + 15 & 13 & 8 & 1.1 & 0.007 & 0.20 & 0.24 & 25 + 17 & 32 & 18 & 6.3 & 0.01 & 0.27 & 0.32 & 60 + 19 & 90 & 50 & & 0.04 & 0.60 & 0.63 & 150 + 20 & 160 & 90 & & 0.13 & 1.1 & 1.3 & 250 +
the availability of precise photometry is essential for age derivations using isochrone fitting to the main sequence turn - off ( msto ) point .
simulations of gaia photometry demonstrate that this method may be successfully exploited with gaia even in such distant stellar systems as the magellanic clouds ( kuinskas et al .
2002 ) , but only for populations younger than @xmath19 gyr . in this paper
we argue that gaia observations of agb stars can be used to determine star formation histories to even greater distances and for much older populations .
gaia will provide a wealth of astrometric and spectrophotometric data on galactic and extragalactic agb stars .
their uses are at least twofold : ( a ) as kinematic tracers , using distances and space motions obtained from the astrometric and radial - velocity data ; ( b ) for age determinations , using basic stellar - atmosphere parameters ( @xmath0 , @xmath1 and @xmath20 $ ] ) derived from the spectrophotometric data , combined with distances and theoretical isochrones . from the astrometric and radial - velocity accuracies in table 1
it is obvious that gaia will yield accurate distances ( @xmath21% ) and full space velocities ( @xmath22 km s@xmath18 ) for individual agb stars up to distances of @xmath23@xmath24 kpc , if no interstellar extinction is present .
extensive simulations by the vilnius gaia group ( vanseviius et al . 2002 ; kuinskas et al .
2002 ) show that gaia will also provide precise metallicities ( @xmath15 ) \leq 0.3 $ ] ) and gravities ( @xmath25 ) for agb stars brighter than @xmath26 ( table 1 ) .
precise effective temperatures ( @xmath27 ) are derived down to @xmath28 .
this holds within a broad range of metallicities ( @xmath20>-2 $ ] ) and ages ( 0.0515 gyr ) .
metallicity estimates of intermediate age and old stellar populations can also be obtained from the slope of the red giant branch ( e.g. ferraro et al .
our simulations show that the method could provide an independent estimate of @xmath29 $ ] with gaia , effective up to distances of @xmath30 kpc , if no interstellar extinction is present ( kuinskas et al .
2002 ) .
we have recently shown ( kuinskas et al .
2000 ) that reliable ages can be derived using isochrone fits to the agb sequences on the observed hr diagram .
it is essential for this procedure to have precise effective temperatures of the agb stars , which can be derived by fitting synthetic spectral energy distributions to observed photometric fluxes ( e.g. , _ bvrijhk _ ) .
the method was successfully tested and compared with the msto method on a sample of populous star clusters in the magellanic clouds spanning a wide range of ages ( table 2 and fig . 1 ) .
for galactic agb stars , it is clear that the distance information needed to construct the observational hr diagrams will be available through gaia .
it thus appears that precise age estimates ( @xmath31 ) can be obtained for a wide range of ages ( 0.0510 gyr ) and metallicities ( @xmath20>-2 $ ] ) .
gaia will provide unique astrometric and photometric data for studying individual and collective properties of stars in the galaxy and its surroundings .
agb stars , being intrinsically bright , will provide precise individual distances , kinematics , @xmath0 , @xmath1 and @xmath20 $ ] up to distances of @xmath2315 kpc .
using isochrone fitting to the agb stars will give reliable ages ( @xmath32 ) for a wide range of ages and metallicities .
if distances are known by other means ( e.g. in distant clusters ) , the method can be used up to @xmath33 kpc .
thus , agb stars will allow the formation histories and kinematics of stellar populations to be probed in a diversity of astrophysical environments both in the milky way and in neighbouring galaxies .
the work was supported by a grant ( nb00-no30 ) of the nordic council of ministers and by a grant of the wenner - gren foundations .
ak thanks the workshop organisers for financial support to attend the event .
bertelli , g. , bressan , a. , chiosi , c. , fagotto , f. , nasi , e. : 1994 , _
a&as _ , * 106 * , 275 .
ferraro , f.r .
, montegriffo , p. , origlia , l. , fusi pecci , f. : 2000 , _ aj _ , * 119 * , 1282 .
katz , d. , munari , u. : 2002 , _ gaia rvs status report , rvs - coco-004 _ + ( ` http://wwwhip.obspm.fr/gaia/rvs/bibliography/rvs-coco-004.txt ` ) .
kuinskas , a. , vanseviius , v. , sauvage , m. , tanab , t. : 2000 , in : mid- and far - infrared astronomy and future space missions , eds .
t , matsumoto & h. shibai , _ isas report sp _
14 * , 51 .
kuinskas , a. , bridius , a. , vanseviius , v. : 2002 , _ ap&ss _ , * 280 * , 159 .
perryman , m. a. c. , de boer , k. s. , gilmore , g. , hog , e. , lattanzi , m. g. , lindegren , l. , luri , x. , mignard , f. , pace , o. , de zeeuw , p. t. , 2001 , _ a&a _ , * 369 * , 339 .
vanseviius , v. , bridius , a. , drazdys , r. : 2002 , _ ap&ss _ , * 280 * , 31 . | we discuss the tracing of star formation histories with esa s space astrometry mission gaia , emphasizing the advantages of agb stars for this purpose .
gaia s microarcsecond - level astrometry , multi - band photometry and spectroscopy will provide individual distances , motions , @xmath0 , @xmath1 and @xmath2 $ ] for vast numbers of agb stars in the galaxy and beyond .
reliable ages of agb stars can be determined to distances of @xmath3200 kpc in a wide range of ages and metallicities , allowing star formation histories to be studied in a diversity of astrophysical environments . -20pt
-20pt -20pt -10pt |
recently , a lot of interest has grown around the possibility of applying string inspired techniques to the non - perturbative regime of qcd .
the starting point is the ads / cft correspondence @xcite , a conjectured duality between a maximally supersymmetric strongly coupled conformal field theory and the supergravity limit of type iib string theory , which involves theories different from qcd .
further developments @xcite have tried to apply the correspondence to qcd , induced by the evidence of the existence of a window of energy in which qcd shows an approximate conformal behaviour @xcite .
these developments have taken different directions .
the framework through which i move here is the so - called soft wall model of ads / qcd @xcite , a phenomenological model originally built to holographically describe chiral symmetry breaking and then adapted to several strong interaction processes . for a list of other approaches the reader can refer to @xcite . in the following ,
i discuss the scalar glueball sector and how the spectrum and the two - point correlation function are represented in the soft wall model .
then , i comment on the results , comparing them with current phenomenology and lattice data .
the considered model is defined in a @xmath0 curved space ( the bulk ) with metric : @xmath1 with @xmath2 ; @xmath3 is the ads curvature radius , and the coordinate @xmath4 runs in the range @xmath5 .
qcd is supposed to live on the boundary @xmath6 , where the element @xmath7 describes a flat minkowski space .
in addition to the ads metric , the model is characterized by the presence of a background dilaton field : @xmath8 exponentially coupled to the fields , whose functional form is chosen in such a way to have linear regge trajectories for light vector mesons @xcite ; @xmath9 is a dimensionful parameter setting the scale of qcd quantities and it is of @xmath10 .
it is the responsible of the breaking of conformal symmetry and it is fixed by the experimental slope of the rho mesons trajectory .
@xmath11 glueballs can be described in qcd by the dimension four operator @xmath12 $ ] . in the five dimensional theory its dual field is a massless scalar @xmath13 @xcite , whose action is given by : @xmath14 where @xmath15 is a parameter introduced to give the correct dimension to the action .
the ads / cft dictionary states that this action is equivalent to the qcd partition function , in which the source of @xmath16 is the boundary value @xmath17 of the field @xmath13 .
the following relation can be written : @xmath18 where the function @xmath19 is called bulk - to - boundary propagator , since it links the fields in the bulk with the sources on the boundary .
it is possible to obtain qcd correlation functions functionally deriving the action ( [ action ] ) with respect to @xmath17 .
the two - point function obtained in this way is , in the limit @xmath20 @xcite : @xmath21+\non\\ & & + q^2\left[-\fr{\n^2}{2}+\fr{c^2}{4}\left(1 - 4\g_e+2\ln4 - 2\ln(q^2/\n^2)\right)\right]+\\ & & -\fr{5c^4}{6}+\fr{2c^6}{3q^2}+{\cal o}\left(\fr{1}{q^4}\right)\biggr\}\;\;,\non\end{aligned}\ ] ] to be compared with the qcd result @xcite : @xmath22 matching ( [ piads ] ) with ( [ piqcd ] ) ( @xmath23 ) one gets the fully analytic form of the correlator . by casting it in the form : @xmath24 it is possible to find the poles @xmath25 and the related residues @xmath26 , corresponding to the mass spectrum and the decay constants of the scalar glueballs . the results for the lowest lying state are : another point is that in the large @xmath31 expansion there is a dimension two condensate , absent in qcd since there are no ways to construct scalar local gauge invariant quantities with that dimension @xcite .
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[ 1999/12/01 v1.4c il nuovo cimento ] |
there are three distinct types of solar wind identified by @xcite .
first , there is relatively high coronal electron temperature wind originating from loops in the streamer stalk region @xcite .
second , there is solar wind from the outside of this region .
this wind includes coronal hole wind that has relatively low coronal electron temperatures and high wind speeds , as well as slower solar wind with lower coronal electron temperatures than the stream stalk region .
the third type of solar wind is the transient interplanetary coronal mass ejections ( icmes ) which are caused by the coronal mass ejections ( cmes ) @xcite .
the streamer stalk region is the narrow region in the middle of the streamer belt , which has the highest density fluctuations and the lowest solar wind speeds @xcite .
@xcite provide observational evidence that the streamer stalks can be the coronal sources of the slow solar wind .
@xcite suggests that slow solar wind originates from regions of rapidly expanding flux - tubes located above small coronal holes and at the boundaries of the large polar holes .
based on a comparison of solar remote and in - situ observations , @xcite suggests that low - speed wind with higher @xmath2 ratios may originate from open fields in or near active regions .
fisk and collaborators ( e.g. * ? ? ?
* ; * ? ? ?
* ) suggest that reconnection between open and closed field lines releases material to form the solar wind .
this model provides a reasonable explanation for the differences between fast and slow solar wind .
the distribution of the three types of wind varies with the solar cycle . at solar minimum ,
the coronal holes concentrate at both poles and high latitude coronal hole wind is observed @xcite .
the heliospheric current sheet is flat and lies near the equatorial plane , and the streamer belt stalk wind occurs in a band around the current sheet @xcite .
the icme rate is roughly proportional to the solar activity levels and therefore is very low at solar minimum @xcite . at solar maximum ,
the current sheet tilts to high latitudes , and the streamer - stalk wind , which still occurs in a band around the current sheet , now can reach high latitudes .
the polar coronal holes shrink , resulting in less coronal hole wind in the heliosphere .
the increasing rate of icmes can temporarily enhance the open magnetic flux of the sun .
subsequently , interchange reconnection between the large icmes loops and the open field of the sun eliminates the increased magnetic flux @xcite .
further , there is no compelling observational evidence to suggest that disconnection of open magnetic flux occurs at the heliospheric current sheet @xcite .
hence , the expectation was , prior to this solar minimum , the open magnetic flux would return to a constant background level , as it had in previous minima @xcite .
in the current solar minimum , both the open magnetic flux and the mass flux of the solar wind are reduced compared to any previous solar minimum for which there are good space observations . in this paper , we offer a possible explanation for the decrease in open magnetic flux in the current minimum .
we point out that the streamer - belt - stalk - associated wind originates from a narrower region in the current solar minimum compared to the previous one , and thus the region outside the streamer belt stalk region is larger .
when we calculate the increase in area outside the stalk region , we find it is equal and opposite to the decrease in open magnetic flux , suggesting that the total magnetic flux in the region outside the stalk region remains constant in each solar minimum .
the implication for the transport models of open flux developed by fisk and colleagues is then discussed .
the _ ulysses _ 18-year mission started in 1991 @xcite and terminated in 2009 , providing sufficient data to compare the different conditions in the two minima . here
we use the data from the year of 1995.07 - 1998.2 ( carrington rotation 1892 - 1933 ) at last minimum and 2005.83 - 2008.96 ( carrington rotation 2036 - 2077 ) at the current minimum and compare the difference .
as shown in figure [ figure1 ] , the radial component of the heliospheric magnetic field , the so - called open magnetic flux of the sun ( @xmath3 ) , decreases by 35.4% ; @xmath2 , @xmath4 , and fe / o all decrease by 61.5% , 66.2% and 10.1% , respectively . especially , when considering the region outside of the streamer stalk ( as identified later ) , we find the open magnetic flux decreased by 30% . , @xmath2 , @xmath5 , and fe / o at the previous ( black ) and the current ( dotted ) minimum from _
ulysses_.,title="fig : " ] + .in - situ signatures of three types of solar wind [ cols="^,^,^,<",options="header " , ]
fisk and colleagues developed a model for the global transport of open magnetic flux on the sun , which is illustrated in figure [ figure3]a @xcite .
differential rotation drives the open flux across the polar coronal hole and then into closed field regions where open flux does not disconnect at the current sheet , but rather the flow patterns turn as shown .
the process by which the magnetic field is transported through the closed field region is diffusion due to reconnection with loops .
this model accounts for a number of features of the observed behavior of open magnetic flux ; e.g. , the slow solar wind appears to come from large coronal loops outside of coronal holes , and be released by reconnection @xcite .
-axis is the solar rotation axis .
p marks the open line ( green ) that connects to the pole .
the curves with arrows ( red ) are the trajectories of the open field lines , and the yellow region is the streamer stalk region .
( b)the open lines reconnects and diffuses outside the streamer stalk region . , title="fig : " ] + this picture now needs to be revised , as shown in figure [ figure3]b .
the open magnetic flux in regions outside the streamer - stalk region is unable to penetrate into this region .
thus , disconnection of this component of open flux , which must occur at the heliospheric current sheet , is not possible .
rather , the turning of the flow patterns of open flux must occur outside the streamer stalk region , as shown .
the total open magnetic flux outside of the streamer - stalk region , which can not now disconnect , is conserved , as is observed to be the case .
there are several points worth emphasizing .
the signature we use to identify our streamer - belt - stalk wind is the @xmath2 ratio , or the inferred coronal electron temperature , not the solar wind speed , as was used in other studies .
moreover , it is important to note that the streamer - stalk wind is not the entire slow speed solar wind .
rather , it is only the very slow , high coronal electron temperature wind , which we identify as originating from the streamer stalk underlying the heliospheric current sheet .
there is a broader slow solar wind region @xcite , as constrained by the black dotted line in figure [ figure3]b .
the conservation of the total magnetic flux in the non - streamer - stalk region during the two solar minima suggests that the open magnetic field of the sun in the current solar minimum is behaving as it did in previous minima , the only difference being the width of the streamer belt stalk region , which controls the magnetic field strength in the region outside the streamer belt stalk region . this work was supported in part by nasa headquarters under the nasa earth and space science fellowship program - grant nnx09av13h , by the heliophysics theory program , by nasa / jpl contract 1268016 , and by nsf grant atm 0632471 | to explore the difference between the most two recent solar minima , we analyze the in - situ _ ace _ and _ ulysses _ observations and examine the distributions of the three types of solar wind ( streamer - stalk - associated wind , wind from outside the streamer stalk that can be associated , in part , with coronal holes , and interplanetary coronal mass ejections ) .
we use the taxonomy provided by @xcite to identify the three types of solar wind .
we then map the in - situ observations to the 2.5 solar radii surface . with the aid of the potential - field - source - surface model ( pfss )
, we calculate the normal distance from the solar wind `` foot point '' to the local helisopheric current sheet on that surface .
we find that the source region of the streamer stalk wind is narrower ( @xmath0 ) compared to the previous minimum ( @xmath1 ) .
the area outside the streamer stalk is accordingly larger , but the magnetic field strength is observed to be lower , with the result that the total amount of the magnetic open flux from the outside of streamer stalk region is conserved in the two successive solar minima .
the implications of the conservation of open magnetic flux for models of the behavior of the solar magnetic field are discussed . |
[ [ numerical - calculations . ] ] numerical calculations .
+ + + + + + + + + + + + + + + + + + + + + + + starting from the master equations , we can formulate equations of motion for the elements of the density matrix @xmath81 with the first index being the cavity photon number and the second being the atomic excitation ( @xmath2 ) .
the explicit equations can be written as @xmath82\varrho_{n,1;m,1}-ig[\sqrt{n}\varrho_{n-1,2;m,1}-\sqrt{m}\varrho_{n,1;m-1,2}]\nonumber\\ & -i\omega_\text r[\varrho_{n,2;m,1}-\varrho_{n,1;m,2}]+\gamma\varrho_{n,2;m,2}+\kappa\sqrt{(n+1)(m+1)}\varrho_{n+1,1;m+1,1},\\ \dot\varrho_{n,1;m,2}=&[i(\delta_\text a-(n - m)\delta_\text c)-\tfrac{\gamma+\kappa(n+m)}{2}]\varrho_{n,1;m,2}-ig[\sqrt{n}\varrho_{n-1,2;m,2 } -\sqrt{m+1}\varrho_{n,1;m+1,1}]\nonumber\\ & - i\omega_\text r(\varrho_{n,2;m,2}-\varrho_{n,1;m,1})+\kappa\sqrt{(n+1)(m+1)}\varrho_{n+1,1;m+1,2},\\ \dot\varrho_{n,2;m,1}=&-[i(\delta_\text a+(n - m)\delta_\text c)+\tfrac{\gamma+\kappa(n+m)}{2}]\varrho_{n,2;m,1}-ig[\sqrt{n+1}\varrho_{n+1,1;m,1 } -\sqrt{m}\varrho_{n,2;m-1,2}]\nonumber\\ & - i\omega_\text r(\varrho_{n,1;m,1}-\varrho_{n,2;m,2})+\kappa\sqrt{(n+1)(m+1)}\varrho_{n+1,2;m+1,1},\\ \dot\varrho_{n,2;m,2}=&-[i\delta_\text c(n - m)+\gamma+\tfrac{\kappa}{2}(n+m)]\varrho_{n,2;m,2}-ig[\sqrt{n+1}\varrho_{n+1,1;m,2}-\sqrt{m+1}\varrho_{n,2;m+1,1}]\nonumber\\ & -i\omega_\text r(\varrho_{n,1;m,2}-\varrho_{n,2;m,1})+\kappa\sqrt{(n+1)(m+1)}\varrho_{n+1,2;m+1,2}.\end{aligned}\ ] ] we truncate the set of equations at a sufficiently large photon number @xmath83 . by varying @xmath83 ,
the validity of the calculations can be checked .
using @xmath84 , we can eliminate one element of the main diagonal , in our case , we chose @xmath85 .
this introduces an inhomogeneity into the equations , allowing us to calculate the steady state density matrix simply by inverting the matrix of coefficients and multiplying with the inhomogeneity .
finally , the expectation values of interest can be directly obtained .
the normally ordered variance of a light field is usually measured via balanced homodyne detection , see e.g. @xcite . in case of single atom fluorescence the complications stem from the small collection efficiency , substantially reducing the effect to be measured .
this problem can be resolved by correlation measurements @xcite , since in this case all correlation functions include the quantum efficiencies only as proportionality factors .
one may detect the intensity correlation function @xmath86 by the scheme in fig . 2 of ref .
@xcite . here
the indices @xmath87 refer to the different output channels of a beamsplitter .
following @xcite , we consider the difference between correlations at equal times and the corresponding steady state value , @xmath88 for ( stationary ) single atom fluorescence as the signal and a 50/50 beamsplitter we obtain @xmath89 with fl and lo denoting fluorescence and local oscillator , respectively , and @xmath90 is the intensity . for @xmath91 ,
the second term is dominant .
squeezing is detected if @xmath92 .
the effect of our optimization of squeezing , which yields a factor of two , is clearly observed by this method . | squeezing of atomic resonance fluorescence is shown to be optimized by a properly designed environment , which can be realized by a quasi - resonant cavity .
optimal squeezing is achieved if the atomic coherence is maximized , corresponding to a pure atomic quantum state .
the atomic - state purification is achieved by the backaction of the cavity field on the atom , which increases the atomic coherence and decreases the atomic excitation . for realistic cavities ,
the coupling of the atom to the cavity field yields a purity of the atomic state of more than 99% .
the fragility of squeezing against dephasing is substantially reduced in this scenario , which may be important for various applications . [
[ introduction . ] ] introduction .
+ + + + + + + + + + + + + a single atom and its coupling to the electromagnetic field is a system of fundamental interest for the understanding of the quantum phenomena of light and matter . it was predicted that a driven two - level atom emits antibunched light @xcite , which can not be described by the classical maxwell theory .
the first experimental demonstration of this effect was based on the resonance fluorescence of an atomic beam @xcite . in a related experiment
it was demonstrated that a sub - poissonian photon statistics may occur @xcite .
later on , photon antibunching could be demonstrated with single trapped ions @xcite .
squeezing was predicted to occur in the single - atom resonance fluorescence @xcite .
it can also be realized in the fluorescence of many atoms , via regular arrangement of the atoms @xcite , detection in the forward direction with respect to the pump - beam @xcite , and bistability in a strong driving field @xcite .
the latter two cases , could be experimentally demonstrated @xcite . squeezing in single - atom resonance fluorescence
could not be observed yet .
based on homodyne correlation measurements with a weak local oscillator , an efficient measurement technique was proposed @xcite , which is not limited by the collection efficiency of the fluorescence light .
its feasibility was demonstrated in resonance fluorescence experiments @xcite .
very recently , squeezed light has been observed in the output channel of a weakly driven high - q cavity , containing a single atom @xcite .
since an empty driven cavity can not produce squeezing , the observed squeezing of the cavity output field is clearly based on the coupling of the atom to the cavity field .
this work demonstrates , that squeezed light originated from a single atom is a prevailing subject .
the squeezed light in the output field of a cavity containing a single atom is undoubtedly a fundamental issue for its own . under general conditions , however , one can not expect that this is equivalent to the demonstration of squeezing in resonance fluorescence . hence a direct fluorescence measurement would still be of fundamental interest . the present letter deals with the optimization of atomic resonance fluorescence with respect to squeezing .
it is shown that squeezing becomes optimal , when the atomic coherence is perfectly controlled , which is equivalent to the purification of the atomic quantum state . atomic coherence control and state - purification
can be realized by a properly adjusted cavity , even for different choices of the mean atomic excitation .
this implies the possibility to control the fluorescence intensity to some extend .
similar to ordinary fluorescence measurements , the light is observed out the side of the cavity .
the setup under study substantially reduces the fragility of squeezing against dephasing .
this achievement is expected to be of great relevance for applications in miniaturized systems , such as quantum dots in semiconductor microcavities . [ [ optimal - squeezing . ] ] optimal squeezing .
+ + + + + + + + + + + + + + + + + + let us consider a general two - level atom ( tla ) in an arbitrary environment .
the atomic source field can be written as @xmath0 where @xmath1 ( @xmath2 ) is the flip operator of the atom with ground state @xmath3 and excited state @xmath4 . here
@xmath5 describes the atom - light - field coupling and the phase @xmath6 includes the phase of the driving laser .
the field is squeezed , if the normally ordered field variance becomes negative , corresponding to a noise reduction below the vacuum level .
optimizing with respect to the phase , we get for a tla @xmath7 see @xcite .
the full field , @xmath8 , is composed of the free field @xmath9 ( assumed to be in the vacuum state ) and the atomic source field @xmath10 .
the `` @xmath11 '' prescription denotes normal ordering .
the atomic expectation values in eq .
( [ eq.atvarsol1 ] ) are readily derived from the atomic density operator , @xmath12 .
the density matrix @xmath13 reads as @xmath14 from the positive semidefiniteness of quantum states it follows that @xmath15 , that is @xmath16 here we made use of the completeness relation of the tla , @xmath17 .
this inequality defines the maximal atomic coherence , @xmath18 , for any atomic excitation @xmath19 . using this result , for arbitrary atomic excitation the minimal variance follows for the maximal atomic coherence as @xmath20 the absolute minimum follows for @xmath21 , @xmath22 this value
can not be attained in free - space resonance fluorescence @xcite .
let us consider the structure of the atomic quantum state for optimal squeezing .
the purity of the state is given by @xmath23 compared with eq .
( [ eq.csi ] ) , purity of the atomic state is equivalent to maximal atomic coherence .
that is , optimal squeezing of the resonance fluorescence is achieved for a pure state of the atomic subsystem .
hence , to optimize squeezed emission from a single atom , the task is to find an environment for which the atomic subsystem is in a ( nearly ) pure state . note that the above results may be used to estimate the squeezing in the resonance fluorescence of a tla , without the need of homodyne detection . the minimal variance , optimized with respect to the phase
, @xmath24 can be expressed by the minimal variance for maximal atomic coherence ( first term ) , and the atomic - state purity ( occurring in the second term ) . the first contribution is solely determined by the atomic excitation , cf
eq .
( [ var - min ] ) .
the excitation can be observed by comparison with the saturation intensity .
simple methods also exist for detecting the purity of low - dimensional systems @xcite . in view of the relevance of purity measurements in the field of quantum information
, this may open an alternative possibility to infer squeezing in resonance fluorescence from independent measurements .
[ [ squeezing - in - cavity - assisted - fluorescence . ] ] squeezing in cavity - assisted fluorescence .
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + in the following we will deal with a method for the practical realization of optimal squeezing by atomic - state purification .
we will show that a single - mode cavity may serve as an environment of the tla to optimize squeezing in resonance fluorescence .
in fact , our system may purify the atomic state for different values of the atomic excitation @xmath19 .
the cavity - assisted optimization of squeezing from a tla is feasible with current technology , cf . the required scheme in fig . [ fig.sys ] .
consider the tla being driven by a coherent light source of frequency @xmath25 , with the rabi frequency @xmath26 ( chosen to be real ) .
its spontaneous emission is characterized by the energy relaxation rate @xmath27 .
furthermore the atom is coupled to a single mode cavity of frequency @xmath28 , with coupling strength @xmath29 .
the cavity excitation is described by bosonic creation and annihilation operators , @xmath30 and @xmath31 , respectively .
the cavity emits light with a rate @xmath32 .
the hamiltonian for this system , in the frame rotating with @xmath25 and in the rotating - wave approximation , reads as @xmath33 where @xmath34 and @xmath35 .
the density operator @xmath36 of the full system obeys the von - neumann equation with lindblad terms for the different decay channels , @xmath37+\frac{\gamma}{2}\mathcal{l}_{\hat a_{12}}[\hat\varrho]+\frac{\kappa}{2}\mathcal{l}_{\hat a}[\hat\varrho],\\ \mathcal{l}_{\hat x}[\hat\varrho]&=2\hat x\hat\varrho\hat x^\dagger-\hat x^\dagger\hat x\hat\varrho-\hat\varrho\hat x^\dagger\hat x.\end{aligned}\ ] ] in general this system can not be solved analytically .
the numerical calculations are based on solving the steady - state equations of the density matrix , by truncation at a sufficiently large number of cavity photons , for details see @xcite .
let us now consider the cavity - assisted scenario for a strong driving field , @xmath38 , but detuning of the atom by @xmath39 .
hence the effective pumping is still limited , so that no saturation occurs , @xmath40 . a similar scenario has been studied in @xcite , but not in the context of squeezing . under such conditions the mollow - triplet is clearly visible in the spectrum , and the sidebands are well separated , at ( nearly ) the same frequencies as in free space : @xmath41 following the argumentation in @xcite , for a detuning of the cavity mode of @xmath42 its excitation depends on the ratio of the atomic decay to the cavity damping . if the cavity emission rate significantly exceeds the atomic decay , the excitation of the cavity is proportional to @xmath43 , hence the cavity is almost empty . in this case
the outcoupling of the cavity photons is fast compared to the emission rate of the atomic fluorescence out the side of the cavity .
it should be noted that we do not need a very good cavity , solely one with @xmath44 . despite the tiny excitation ,
the cavity effects become visible if a fluorescence sideband is close to a cavity resonance .
single - photon transitions in the cavity occur if the detuning , @xmath45 , is resonant to a sideband according to eq .
( [ eq.rfsidebands ] ) , @xmath46 at such a resonance , besides the fluorescence out of the side of the cavity , we also obtain enhanced emission of the cavity itself .
the excitation of the cavity increases slightly , which is consistent with the argumentation in @xcite .
nevertheless , the cavity emission increases strongly , as it scales with @xmath32 which is large compared to @xmath27 .
a similar situation was recently considered in @xcite , where steady - state inversion of a tla in a cavity was predicted . in our scenario
the cavity mode diverts a significant portion of the energy from the atom , which would otherwise contribute to the fluorescent light .
this yields a reduction of the atomic excitation . from this point of view
a not too good cavity is needed , in order to avoid a too strong backaction onto the atom . on the other hand , it has to be good enough to preserve the coherence of the atom , which would be lost in free - space fluorescence .
the coherent part of the atomic excitation ( cpae ) , @xmath47 , is determined by the interaction of the atom with both the cavity mode and the vacuum modes in free space , leading to the fluorescence . as a consequence of the above discussion , for the resonance condition ( [ eq.cavres ] ) ,
the cpae is increased due to the coupling to the cavity .
hence , we expect @xmath19 to decrease , while @xmath18 increases , yielding an obvious purification of the atomic state , according to eqs .
( [ eq.csi ] ) , ( [ eq.purity ] ) .
a critical condition in this setup is the requirement of @xmath44 and @xmath48 , so that the atom - cavity coupling significantly exceeds the atomic decay , @xmath49 .
experimental works , such as @xcite , suggest that large ratios of @xmath50 can be achieved in the optical frequency range . in this experiment a value of @xmath51
was realized , which will be used in our calculations reported below . combining the above arguments
, we can determine the regime of optimized squeezing in cavity - assisted resonance fluorescence .
we need strong pumping and atomic detuning , such that the atomic excitation in free space would slightly exceed @xmath52 .
for example , this would be the case for @xmath53 and @xmath54 , for details see @xcite .
the cavity , which obeys the condition @xmath55 , is tuned to a resonance according to eq .
( [ eq.cavres ] ) .
this yields a reduction of the atomic excitation to approximately @xmath52 , as needed for maximal squeezing according to eq .
( [ abs ] ) .
the cpae increases , resulting in a purification of the atomic state together with optimized squeezing , cf .
eq .
( [ eq.sq-pur ] ) .
the cavity emission rate @xmath32 is chosen to be intermediate , @xmath56 , since for large @xmath32 values the situation becomes close to that in free space . for smaller cavity losses
the atomic excitation is not sufficiently reduced , due to the backaction of the cavity photons on the atom . [
[ numerical - results . ] ] numerical results .
+ + + + + + + + + + + + + + + + + + in fig .
[ fig.sqmax ] we show the dependence of the atomic excitation and cpae on the atomic detuning @xmath57 .
the other parameters are chosen according to the requirements discussed above .
the atomic excitation @xmath58 behaves similar to the free - space scenario . for a wide parameter range ,
the cpae is rather close to its maximum value , cf .
eq .
( [ eq.csi ] ) , indicating significant purity of the atomic state .
the purity is given by @xmath59 .
the cavity excitation is very small , even at the cavity resonance according to eq .
( [ eq.cavres ] ) , occurring for the chosen parameters at @xmath60 .
this is consistent with the results of @xcite at the cavity resonance , which would predict @xmath61 for our parameters . :
atomic excitation @xmath19 ( blue , dashed line ) , cpae @xmath18 ( green crosses ) and maximum cpae @xmath62 ( red circles ) , cavity excitation @xmath63 ( violet , dashed - dotted line ) , normally ordered field variance of the fluorescence of a tla in the cavity ( light blue , solid curve ) , and in free space ( black , dotted curve ) .
the straight line ( black , solid ) marks the free space maximal squeezing of @xmath64 .
the system parameters are : @xmath65 , @xmath66 , @xmath67 , @xmath68.,width=302 ] around the cavity resonance we see , that the normally ordered field variance attains the value of @xmath69 .
this is more than 94% of the maximum possible squeezing of @xmath70 , which can be readily measured as discussed in @xcite .
the purity tr@xmath71 of the atomic subsystem ( not depicted in fig .
[ fig.sqmax ] ) , shows a clear maximum of about 99.5% at the cavity resonance .
the corresponding atomic excitation is @xmath72 . our numerical results for the obtained squeezing effect , the excitation and purity of the atomic state are in full agreement with the analytical relations of these quantities as given in eq .
( [ eq.sq-pur ] ) together with ( [ var - min ] ) . for larger values of @xmath50 , even more
than 99% of the absolute squeezing limit , @xmath73 , can be achieved .
this exceeds the free - space result substantially .
let us now consider , for our optimized environment , the sensitivity of squeezing with respect to dephasing , which is crucial in free - space fluorescence .
for this purpose we assume that , in addition to dephasing due to radiative damping , there is also radiationless dephasing described by the rate @xmath74 . for our considerations of the cavity - assisted atomic fluorescence we supplement the equations of motion ( [ eqmo ] ) with another lindblad - term , @xmath75+\frac{\gamma}{2}\mathcal{l}_{\hat a_{12}}[\hat\rho]+\frac{\gamma_\text d}{2}\mathcal{l}_{\hat a_{22}}[\hat \rho]+\frac{\kappa}{2}\mathcal{l}_{\hat a}[\hat\rho].\ ] ] the additional dephasing only increases the decay of the off - diagonal matrix elements of the density operator , that is , the atomic coherence and hence the cpae . in free space , squeezing does not occur anymore if the dephasing rate @xmath74 exceeds the energy relaxation @xmath27 . the atomic coherence needed for squeezing decays on a time scale which is faster than that of the emission of the fluorescence radiation . as stated above , in our setup , on a cavity resonance
the cpae is increased due to the increased transition amplitudes between atom and cavity .
the backaction of the cavity onto the atom preserves the coherence on a longer time scale , thus increasing the actual coherence in the steady state .
hence , the robustness against dephasing is enhanced . in this context
it is important that the cavity emission rate @xmath32 significantly exceeds the atomic decay rate @xmath27 .
this renders it possible to observe squeezing in cavity - assisted resonance fluorescence for surprisingly strong atomic dephasing . for different dephasings @xmath74 .
from bottom to top : @xmath76 .
the inset shows the dependence of the squeezing on @xmath74 at the cavity resonance , @xmath77 .
all other parameters are as in fig .
[ fig.sqmax].,width=302 ] in fig .
[ fig.deph ] , we show the normally ordered field variance for the same cavity as in fig
. [ fig.sqmax ] , for different values of @xmath74 .
the dependence of the minimal field variance on @xmath74 is shown in the inset . for @xmath78 ,
the minimal variance is below @xmath64 .
this is the maximal squeezing in free space , which could only be achieved for @xmath79 .
the squeezing in the cavity setup under study vanishes for @xmath80 .
this result may be of great importance for applications in light - emitting systems other than single atoms .
for example , significant dephasing is usually expected to occur in condensed matter systems .
a typical candidate could be quantum dots in semiconductor microstructures .
the scenario under study opens the possibility to create squeezing for relatively strong dephasing and intermediate cavity coupling , as it is typical for semiconductor microcavities @xcite .
[ [ conclusions . ] ] conclusions .
+ + + + + + + + + + + + we have studied the possibility of the optimization of squeezing in the resonance fluorescence of a two - level atom .
it is based on a special design of the environment of the atom , which can be achieved by a cavity with properly adjusted parameters .
the maximal squeezing of the light emitted from a coherently driven atom in an optimal environment is twice as strong as the maximal squeezing in free space experiments . more importantly , squeezing can be optimized for different atomic excitations , so that it is no longer limited to weakly driven systems .
the resulting possibility to increase both the fluorescence intensity and the squeezing will substantially widen the possibility of detection and application of squeezing in resonance fluorescence .
the realization of optimal squeezing is accompanied by the purification of the atomic state for different atomic excitations , which can be relevant for any other application which requires pure atomic states for different mean atomic excitations .
it is also important that the strong limitation of squeezing by dephasing can be substantially reduced in our system .
this may open important possibilities to control the emission of squeezed light from more complex , miniaturized systems , such as quantum dots in semiconductor microcavities .
[ [ acknowledgments . ] ] acknowledgments .
+ + + + + + + + + + + + + + + + the authors gratefully acknowledge stimulating conversation with p. r. rice and j. sperling .
this work was supported by the deutsche forschungsgemeinschaft through sfb 652 .
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the design and synthesis of strong organic bases have long been an active field of research @xcite .
infrared spectroscopy is a valuable tool in order to obtain information about the molecular structure and properties of the molecules .
this technique is used widely in qualitative and quantitative molecular analysis .
ir spectrum of interatomic vibrations can be used as structural probes for determining weak changes of structure or chemical bonding in molecules .
cyclohexene-2-ethanamine molecule consists of cyclohexene @xmath2 group attached to the carbon of ethylamine @xmath3 .
there are previous works on the cyclohexene and ethylamine structures .
some studies showed that the lowest energy conformations of cyclohexene are in a half - chair form and a boat structure . basically , the cyclohexene ring can interconvert from one twisted form to the other over the boat conformation with @xmath4 symmetry @xcite . the point symmetry group for trans - ethylamine ion
is @xmath4 whereas there is no such symmetry for gauge - ethylamine @xcite .
cyclohexene-2-ethanamine ( cyhea ) has also important industrial applications , that is used as chemical intermediate in rubber industry .
they demonstrated prototypical non - conjugated olefinic substrate cyhea which was not only a highly active substrate but also a mechanism - based inhibitor for dbm .
cyhea was also used as a substrate and oxidizing agent for ru complex .
sirimanne and may reported that dopamine @xmath5-monooxygenase ( dbm ) catalyzed stereo - selective allylic hydroxylation of cyhea @xcite .
cyhea was first synthesized by izgi et al .
@xcite and some of ir and nmr properties of this compound were reported by them .
density functional theory(dft ) is a widely used and very precise _ ab initio _ technique which is used to provide vibrational frequencies of organic compounds perfectly @xcite .
the vibrational modes and stm images of this molecule have not been investigated by an _ ab initio _ theoretical method . in this study , the molecule has been investigated by using planewave pseudopotential calculation based on dft .
exchange - correlation potential of dft scheme was taken into account within the lda and gga which are the commonly used approximations and both are used in calculation process .
the stable conformation of the molecule is obtained by following a relaxation procedure within the framework of dft under periodic boundary conditions .
the normal modes and stm images of the molecule were calculated with both lda and gga by using the freely available dft program pw - scf ( plane wave self consistent field ) @xcite which uses plane wave basis sets for electronic wavefunctions .
for all calculations , we have used perdew - zunger @xcite and perdew - burke - ernzerhof @xcite exchange - correlation parameterizations for lda and gga , respectively and vanderbilt @xcite ultrasoft pseudopotentials .
the electronic wavefunctions were expanded in terms of plane waves with kinetic energy cut - off up to 25 ry .
the special k - points of the molecule in the cubic cell is selected as @xmath6 gamma point . the lattice constant of cubic cell is 20 bohr(au ) . for experimental work
, the pure cyclohexene-2-ethanamine in liquid form was obtained from aldrich chemical co. , usa and was used without further purification .
the ir spectra of the molecule in liquid form was recorded to be in the range of @xmath0 @xmath1 using perkin elmer ft - ir 2000 spectrometer with a resolution of @xmath7 @xmath1 .
the calculated stable structure of cyhea is shown in fig.[eps1 ] which was drawn by xcrysden ( crystalline structures and densities ) program @xcite . the vibrational assignments and frequencies of cyclohexene-2-ethanamine
was reported experimantally by izgi et al .
the spectral properties of the molecule were evaluated through the calculated vibrational frequencies of the free ligand molecule .
the calculated and experimental infrared spectra data of the molecule are given in table.[table1 ] .
the experimental , gga and lda results are also compared in fig.[eps2 ] .
[ table1 ] [ cols="^,^,^,^,^,^",options="header " , ] the strong n - h asymmetric and symmetric stretch bands seen in table.[table1 ] are due to the contribution of ethylamine ( see fig.[eps4 ] ) .
c - h stretch bands between @xmath8 @xmath1 are attributed to cyclohexene group and the very strong c - h stretch bands at @xmath9 @xmath1 and @xmath10
@xmath1 result from ethylamine .
the very strong bands are attributed to the attachment of ethylamine and cyclohexene and appear between @xmath11 @xmath1 .
most of the modes below the @xmath12 @xmath1 arise from cyclohexen .
if the vibrational assignments of the molecule involving these groups are investigated , it is seen that the assignments obtained for the molecule also involve the group frequencies .
furthermore , the observed medium broad band appears at @xmath13 @xmath1 is an n - h bending band as well as a group frequency .
there is also a good agreement between the experimental and the theoretical vibrational frequencies in the region of @xmath0 @xmath1 except some gga and lda results .
the ground state energy of the molecule was obtained to be -128.66 ryd and -128.53 ryd for gga and lda , respectively .
finally , we examined the electronic properties by using calculated stm images for cyclohexene-2-ethanamine . in fig.[eps4 ] and fig.[eps5 ] which were drawn by using xcrysden , we calculated the stm images at constant current and bias voltage -2.5 ev and 2.5 ev , respectively .
these results supply a microscopic model for stm images and can serve as a source for stm experiments for organic molecules .
the experimental and the theoretical investigation of cyhea molecule have been performed successfully by using ft - ir and density functional theory calculations . for all calculations
, it is shown that the results of gga and lda methods are in excellent agreement with all experimental findings .
thus , density functional theory ( dft ) methods are suitable for the calculation of ground state properties and potential energies .
hence , dft is an excellent method for calculating vibrational spectra and stm images from first principles .
we thank g.gokoglu and t. boz for improving our paper english .
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* 77 * , 3865 ( 1996 ) . | we have investigated the structure of cyclohexene-2-ethanamine molecule both theoretically and experimantally .
theoretical investigation is based on a first principle technique density functional theory ( dft ) using plane wave basis sets and ultrasoft pseudo - potentials while the experimental technique is infrared ( ir ) spectroscopy .
exchange - correlation potential of dft was approximated in the frame of both local density approximation ( lda ) and generalized gradient approximation ( gga ) schemes .
vibrational properties of this molecule are given by the assignments in the range for wavenumber @xmath0 @xmath1 .
stable equilibrium structure of the molecule was also obtained by using lda and gga .
obtained optimized geometrical structure was used to calculate vibrational properties and stm images .
a remarkable agreement was obtained between theory and experiment , especially in the symmetric and asymmetric vibrations of nh groups . _
keywords : _
cyclohexene-2-ethanamine , first principle , ir spectrum , stm images . |
the experimental investigation of the @xmath0-decay of @xmath1xe has been started more then 20 years ago . but
both two neutrino and neutrinoless modes of this process for @xmath1xe was not observed .
the results of last experiments are presented in table [ tab1 ] .
the theoretical estimations of half lifetime for @xmath3-decay are presented in table [ tab2 ] .
it is necessary to mention that in @xcite only one spectrum ( measured with enriched @xmath1xe ) was obtained . to calculate their limit
it was assumed that at any effect / background ratio in the energy range under investigation the effect did not exceed the actually measured background increased by a systematic error given in @xmath5 units ( @xmath5 is a standart deviation ) . in our work
the measurements were performed with both enriched xenon and natural xenon simultaneously . to evaluate the @xmath6-effect the energy spectra in region 2312@xmath72646 kev were analyzed .
the data for the analysis @xmath8-mode have been taken for 17280 hours of measurements .
this energy region is determined from calculated energy resolution for 2479 kev electrons ( r=7.0@xmath9 , @xmath10 kev ) and systematic error in definition of peak position ( @xmath11 kev ) .
number of events in the energy region @xmath12 kev registered by cpc _ _ n__1 and cpc _ _ n__2 in each run of measurements are presented in table [ tab4 ] . using recommendation given in @xcite and assuming that mean background is 10 events and measured one is 8 events , we obtain : @xmath13 where @xmath14 h @xmath15 yr and @xmath16 .
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cousins , phys.rev.*d 57 * , 7 , 3873 ( 1998 ) . | search for @xmath0-decay of @xmath1xe with two high pressure proportional counters is carried out in baksan neutrino observatory .
the experiment is based on comparison of spectra measured with natural and enriched xenon .
the measured half life is equal to t@xmath2 yr ( 67% c.l . ) for @xmath3 decay mode .
no evidence has been found for neutrinoless @xmath0-decay .
the decay half life limit based on data measured during 17280 h is t@xmath4 yr ( 90% c.l . ) . |
event shapes belong to the most widely used variables to study qcd dynamics , especially at @xmath0 and @xmath1 colliders .
event - shape observables are defined in terms of the four - momenta of jets in the final state . recently a large set of new hadronic event - shape variables has been proposed in ref .
an important aspect of these variables is their normalization to the total transverse momentum or energy in the event .
therefore it is anticipated that energy scale uncertainties should cancel out to a large extent .
thus we believe that they represent an useful tool for very early measurements of the properties of qcd events at lhc and the tuning of monte carlo models .
analogously to the @xmath0 event shapes , one can define hadronic event shapes in the transverse plane , for example the central transverse thrust : @xmath2 where @xmath3 are the transverse momenta with respect to the beam axis @xmath4 .
the transverse axis , for which the maximum is obtained , is the thrust axis @xmath5 .
the variable which is typically used for perturbative calculations is @xmath6 .
the central thrust minor is a measure for the out - of - plane momentum : @xmath7 below the results of a first simulation study @xcite of these event - shapes variables at the compact muon solenoid ( cms ) are summarized .
@xmath8 is used to simulate proton - proton collisions with a centre of mass energy @xmath9 @xcite .
the events have been passed through a full geant based simulation of the cms detector .
events are preselected by requiring two or more calorimeter jets , corrected in their relative and absolute response , with a transverse energy @xmath10 within a region of @xmath11 .
if the two hardest jets of the event are not in this central region , the event is rejected .
only central corrected calorimeter jets with @xmath10 are used for the event - shape calculation .
the threshold on the transverse energy of the leading jet is set at @xmath12 .
[ sec : corrections ] the effect of jet energy corrections on the normalized event - shape distributions can be judged by comparing the corrected and uncorrected distributions with the corresponding generator level distribution .
a threshold of 30 @xmath13 on the transverse energy of uncorrected jets is applied , which corresponds to a generator level jet threshold of approximately 60 @xmath13 .
similarly , the threshold on the uncorrected leading jets is @xmath14 .
all three distributions agree well with deviations within 5 - 7 % over most of the range as fig [ fig : l2l3_thrust ] illustrates .
[ fig : l2l3_thrust ] often , the leading source of systematic errors in qcd data analysis is the limited knowledge of the jet energy scale ( jes ) and , to a lesser extent , the jet energy resolution . by definition
, event - shape variables are expected to be rather robust against both sources of systematic errors .
we assume a global uncertainty of 10% on the knowledge of the jet energy scale .
the resulting normalized event - shape distributions deviate by 5 - 10% from the reference distribution over the whole energy range as can be seen in fig .
[ fig : calo_thrust ] .
the effect of the jet energy resolution is studied by applying the jet energy resolution smearing function [ eq : smear_ass ] on generator level jets : @xmath15 the smeared event - shape distributions deviate by less than @xmath16 from the unsmeared distribution over most of the energy range ( fig .
[ fig : smear ] ) .
in order to demonstrate the sensitivity of hadronic event - shape distributions to different models of multi - jet production , we compare the central transverse thrust and thrust minor distributions to the generator level predictions as obtained from two generators that contain different models of qcd multi - jet production , @xmath8 and @xmath17 @xcite . the @xmath18 samples used in our study contains qcd processes from 2 up to 6 jets . in fig .
[ fig : alp_pyt_trthr ] the distributions of the central transverse thrust and central thrust minor can be seen .
these events are selected from a jet trigger , based on the calibrated transverse energy of the hardest jet @xmath19 with a prescale of 100 .
the error bars on the data points include the statistical uncertainties corresponding to @xmath20 of integrated luminosity and the systematic errors due to jet energy scale and jet energy resolution as discussed in the previous section .
the corrected calorimeter jets correspond to the samples , and they are found to be compatible with the generator level jets from . it can be seen that there is a significant difference with respect to the distribution , reflecting the different underlying matrix element calculations in the generators and the different parameter choices .
the result shows that hadronic event shapes can be powerful handles in comparing and tuning different models of multi - jet production . with the statistical and dominant systematic errors expected after @xmath20 of integrated luminosity .
the prescale of the trigger is assumed to be 100 .
the distributions are compared to the generator level distributions of @xmath21 and @xmath18 .
, scaledwidth=90.0% ] with the statistical and dominant systematic errors expected after @xmath20 of integrated luminosity .
the prescale of the trigger is assumed to be 100 .
the distributions are compared to the generator level distributions of @xmath21 and @xmath18 .
, scaledwidth=90.0% ]
in this note we demonstrate the use of hadronic event shapes at the lhc .
the event - shape variables are evaluated using calorimeter jet momenta as input .
they are shown to be not very dependent on the effect of jet energy corrections .
we present an estimate of the dominant systematic uncertainties at the startup , resulting from jet energy resolution effects and from the limited knowledge of the jet energy scale . using the examples of the central transverse thrust and central thrust minor
, we show that early measurements of event - shape variables allow to study differences in the modeling of qcd multi - jet production . the cms collaboration , `` study of hadronic event shape variables '' , + cms pas qcd-08 - 003 , _ http://cms-physics.web.cern.ch/cms-physics/public/qcd-08-003-pas.pdf _
t. sjostrand , s. mrenna and p. skands , `` pythia 6.4 physics and manual '' jhep * 05 * ( 2006 ) 026 [ hep - ph/0603175 ] . | in this note a study of hadronic event shapes in qcd events at the large hadron collider ( lhc ) is presented .
calorimetric jet momenta , determined by various jet clustering algorithms , are used as input for calculating various event - shape variables which probe the structure of the hadronic final state .
it is shown that the normalized event - shape distributions are robust under variations of the jet energy scale and resolution effects , which makes them particularly suitable for early data analysis and tuning of monte carlo models . |
the authors would like to acknowledge fapesp , capes and cnpq for financial support .
the calculations were carried out at cce - usp , center for high performance computing at ufabc and cenapad / sp . | nitrogen - doped carbon nanotubes can provide reactive sites on the porphyrin - like defects .
it s well known that many porphyrins have transition metal atoms , and we have explored transition metal atoms bonded to those porphyrin - like defects in n - doped carbon nanotubes .
the electronic structure and transport are analized by means of a combination of density functional theory and recursive green s functions methods .
the results determined the heme b - like defect ( an iron atom bonded to four nitrogens ) as the most stable and with a higher polarization current for a single defect .
with randomly positioned heme b - defects in a few hundred nanometers long nanotubes the polarization reaches near 100% meaning an effective spin filter .
a disorder induced magnetoresistance effect is also observed in those long nanotubes , values as high as 20000% are calculated with non - magnectic eletrodes . since their discovery by iijima in 1991 ,
carbon nanotubes@xcite ( cnt ) have become the subject of intense research due to their potential for applications,@xcite such as in novel electronic devices.@xcite furthermore , in a seminal paper by tsukagoshi _
et al _ cnts entered the realm of spintronics , whereby one envision the possibility of using the electron spin , instead of its charge , as information carrier.@xcite in that work the authors demonstrated that the spin coherence length of polarized electrons injected onto cnts is larger than 300 nm .
thus , carbon nanotube devices could be used to manipulate spins in a coherent manner .
the prototypical spintronics device uses spin - polarized electrons , which are injected from a source into an unpolarized region and analyzed by a polarized drain . within this arrangement the so - called giant magnetoresistance effect ( gmr)@xcite manifests itself by altering - via an external magnetic field - the relative orientations of the magnetic moments of the electrodes . from a practical point of view
this setup usually involves sandwiching different materials .
an alternative to this has been given by kirwan et al .
whereby initially unpolarized electrons are scattered by magnetic impurities adsorbed on the surface of a segment of a carbon nanotube .
this way , both the electrodes as well as the device itself are made of the same material .
an alternative to this has been given by kirwan _
et al . _
@xcite whereby initially unpolarized electrons are scattered by magnetic impurities adsorbed on the surface of a segment of a carbon nanotube.@xcite this way , both the electrodes as well as the device itself are made of the same material , thus avoiding issues related to surface matching at the interface consequently hindering spurious scattering .
however , one of the issues concerning the use of cnts as spintronics devices is the need to incorporate dopants or defects in order to change their electronic transport properties . closed shell species
do not interact very strongly with the pristine wall of a carbon nanotube.@xcite furthermore , transition metal atoms are more likely to form clusters when interacting with the pristine wall of the nanotube .
@xcite even linear chains of fe atoms are more energetically favorable than free standing iron atoms .
@xcite one possible path to circumvent this problem is to incorporate doping agents during the growth process . in that context , carbon nanotubes sythetized in a nitrogen - rich atmosphere - the so - called @xmath0 nanotubes - are potential candidates.@xcite it has already been demonstrated that these nanotubes could be , for example , used as gas sensors for a variety of chemical species.@xcite the most stable defect in these structures is a pyridine - like defect consisting of a 4 nitrogen divacancy ( 4nd).@xcite this defect ( shown in fig .
[ figure1]a ) is formed by two vacancies surrounded by four substitutional nitrogen atoms .
we have previously exploited the reactivity of this defect to attach ammonia molecules and study the behavior of the system as a sensor.@xcite interestingly , this defect is similar to molecules in the porphyrin class , in particular , to a molecule known as heme - b ( shown in fig .
[ figure1]b ) , which is found , for instance , in hemoglobin and myoglobin .
this heme b molecule has an iron atom bonded to the site with four nitrogens .
thus it is intuitive to assume that an iron atom - and other transition metal ( tm ) atoms - gets bonded to the 4nd defect of the carbon nanotubes .
the heme b - like defect has been recently synthesized by lee et , al .
@xcite their stability was studied by means of repeated cyclic voltammograms , and they have not observed significant differences after @xmath1 cycles , which is attributed to the stability of the covalent incorporation of the atoms . the use of carbon nanotubes - or any other long one dimensional system - with defects , however , poses an additional problem ; the position of the defects can not be controlled during growth .
the result is a device with a large number of randomly positioned defects .
thus , in order to obtain quantitatively meaningful theoretical predictions , one must take into consideration the effects of disorder .
it is generally assumed that disorder has a detrimental effect .
recently , however , we have shown that one - dimensional boron - doped graphene nanoribbons can present near - perfect conductance polarization due to disorder.@xcite such an effect should not depend on the system under consideration provided there was a difference in transmission probabilities for majority and minority spin cases for a single scatterer .
furthermore , the introduction of a large number of defects with non - zero magnetic moment leads not only to structural disorder , but also to a magnetic one .
in fact , the magnetic moments of the impurities might be pointing in random directions .
we can then consider that , in the absence of a magnetic field , approximately half of the moments are pointing up and half of them are pointing down .
a magnetic field would tend to align the magnetic moments leading to an analogous to the magnetoresistance effect without the need to rely on a multilayered material .
in this work we show that porphyrin - like cnts can exhibit a nearly - perfect polarization and extremely large disorder induced magnetoresistance ( as high as 20000% ) driven by disorder .
the disorder was simulated using cnts containing a large number of magnetic impurities randomly positioned along the tube .
for those calculations we used a combination of density functional theory@xcite coupled to recursive green s functions methods@xcite . we have initially performed _
ab initio _ calculations within density functional theory ( dft)@xcite for a segment of a ( 5,5 ) @xmath0 nanotube containing a 4nd defect ( figure [ figure1]a ) . as we have said before
, the porphyrin molecules can have different tm in the 4nd site , as shown in figure [ figure1]b .
we , thus , performed calculations using iron , cobalt , manganese and nickel atoms in the middle of the 4nd defect .
the final arrangement for the case of iron is presented in figure [ figure1]c .
as one can see , nine irreducible cells of the pristine system were used to describe the region containing the defect .
the computational code used was siesta @xcite which uses a linear combination of atomic orbitals ( lcao ) as basis set . in the particular case of this work
we have employed a double zeta basis set with polarization orbitals .
we used the generalized gradient approximation ( gga ) as parametrized by perdew - burke - ernzerhof @xcite ( pbe ) for the exchange correlation functional .
finally , the atomic coordinates have been optimized using a conjugated gradient scheme until the forces on atoms were lower than 0.03 ev / . furthermore , in order to assess whether the transition metal atoms in adjacent cells are magnetically coupled@xcite we simulated a supercell with 18 irreducible cells ( twice the initial size ) with two heme - b - like defects ; one case with ferromagnetic ordering ( @xmath2 ) , and another with a antiferromagnetic one ( @xmath3 ) .
the total energy difference ( e@xmath4-e@xmath5 ) is negligible for all transition metal atoms considered in this work , so we infer that there s no magnetic coupling in our system . for the electronic transport calculations , the system - following the procedure proposed by carolli _ _
et al__@xcite - is initially divided in three regions namely , the right and the left electrodes and a central scattering region .
the electrodes for our system are taken as semi - infinite repetitions of the pristine carbon nanotube . in the absence of spin - orbit interactions
one assumes the two spin fluid approximation , whereby one can calculate the electronic transport properties of the majority and minority spins independently of each other .
we then use the landauer - bttiker @xcite formula to calculate the transmission coefficients of the system . in order to access the electronic transport properties of a more realistic system with hundreds of nanometers we use a combination of dft and recursive green s function methods .
@xcite to do so , we split up a long nanotube into small pieces .
each piece is simulated using a separate dft calculation as already described previously , and the hamiltonian and overlap opperators respectively @xmath6 and @xmath7 are stored . for our ( 5,5 )
@xmath0 nt we also have to consider five different rotations for the position of the defect . with those smaller blocks we build up a long nanotube , ranging from 20 to 600 nanometers , by randomly placing the segments with defects together with pristine pieces , as shown in fig .
[ long ] .
one then recursively reduce the system to two renormalized electrodes coupled via an effective scattering potential that contains all the information about the central region . in the low bias limit
the differential spin - dependent conductance can be calculated by the landauer - buttiker formula for the current @xcite @xmath8 where @xmath9 is the fermi distribution function for a given temperature .
the total conductance is then given by the sum of the majority and minority conductances , @xmath10 .
we are interested in two quantities .
firstly , in order to quantify the spin filtering effect of this device , we calculate the degree of polarization@xcite @xmath11 secondly , as discussed earlier one also needs to take into consideration the relative orientations of the magnetic moments .
one can analyze the changes in conductance due to an external magnetic field that tends to align the local magnetization of each impurity .
the magnetic field in our calculations is taken into consideration only in the alignment of the magnetic moments , it has no other effect on the electronic structure of our system .
consequently , the value of this disorder induced magnetoresistance ( mr ) is given by @xmath12 where @xmath13 corresponds to the total conductance for the case where all of the magnetic moments are pointing along the same direction , and @xmath14 is the total conductance for the case where there is an equal distribution of positive and negative magnetic moments .
finally , in these long and disordered @xmath0 nanotubes , different defect distributions along the @xmath0 give different values of conductance . in order to get statistically meaningful values of conductance
we have calculated about 200 random arrangements for each concentration and length of the nanotubes .
for cn@xmath15 nanotube containing an iron atom ( heme - b - like defect ) .
the net magnetic moment of the system is localized in the iron atom.,scaledwidth=50.0% ] upon placing the different tm atoms in the 4nd , we observe that they strongly bind with a similar final structure in all situations .
table [ table1 ] shows the binding energies and the final magnetization of the system for each one of the tm atoms .
as can be seen , the binding energies are relatively high ( the reference is the isolated atom infinitelly separated from the nanotube ) .
one also sees a local magnetic moment in all cases , except for the nickel atom . a similar behavior was also observed by shang , _ et al .
_ .@xcite in fig .
[ rhoupdn ] we present the local magnetic moment , @xmath16 of the heme b - like defect . from this figure
we can notice a highly localized magnetic moment in the iron atom . .binding energy , magnetization and polarization for different transition metal atoms bonded to the 4nd defect . [ cols="^,^,^,^,^",options="header " , ] [ lengths100 ] in order to address the effect of a magnetic field applied to the system and the possibility that not all the magnetic moments are completely aligned we also considered that only 80% of the defects are magnetically aligned .
the results are shown in figure [ condpol2 ] , and the linear fits for the localization lengths also are presented in table [ lengths100 ] .
we can note a decrease ( increase ) in localization length for majority ( minority ) spin compared to the 100 % case .
this is to be expected since one is moving towards higher magnetic disorder , _ i.e. _ the 50 % case . from fig .
[ condpol2]c we can see a polarization near 100% for 700 nm long @xmath0 nanotubes .
most importantly , the magnetoresistance ( fig . [ condpol2]d ) presents values which are one order of magnitude lower than the fully aligned arrangement , but it is still in the 1000 % range .
thus , even in the case where not all spins are aligned , there is still an extremely large disorder induced magnetoresistance .
thus , this disorder - driven gmr effect is extremely robust toward fluctuations in the alignment of the magnetic moments .
we have used an ideal paramagnet model to estimate the needed magnetic field to obtain a 80% magnetization at 300k and 3k .
unfortunately the needed magnetic field at ambient temperature is about 200 t , making it impracticable for ambient temperature devices .
for a temperature of 3k the needed field will be about 2 t for an 80% magnetization and about 5 t for a 95% magnetization , so it s possible to observe the predicted effects in this paper in low temperature experiments .
in summary we have observed that transition metal atoms bind strongly to nitrogen defects in cn@xmath15 carbon nanotubes in a fashion similar to heme b molecules .
the end result is a scattering site with a localized magnetic moment on the transition metal atom that leads to a small conductance polarization in the case of a single impurity . for a large number of such impurities randomly distributed along carbon nanotubes a few hundred nanometers long
, it leads to near perfect polarization and a large magnetoresistance ( up to 20000% ) .
an interesting feature of the system proposed here is the fact that they do not need polarized electrodes as it is usually the case .
we estimate that , at low temperature , this effect could be measured experimentally . |
in the recent years , the model of light vector particles with kinetic mixing to the standard model photon has received tremendous attention , theoretically as well as experimentally . whereas @xmath3 is mainly being probed in medium - to - high energy collider experiments , masses in the sub - mev regime are subject to severe astrophysical and cosmological constraints .
below @xmath4 ev , those limits are complemented by direct laboratory searches for dark photons in non - accelerator type experiments . among the most prominent
are the `` light - shining - through - wall '' experiments ( lsw ) @xcite and the conversion experiments from the solar dark photon flux , `` helioscopes '' @xcite ; a collection of low - energy constraints on dark photons can _ e.g. _ be found in the recent review @xcite .
helioscopes derive their sensitivity from the fact that such light vectors are easily produced in astrophysical environments , such as in the solar interior , covering a wide range of masses up to @xmath5 few kev . in general , stellar astrophysics provides stringent constraints on any type of light , weakly - interacting particles once the state becomes kinematically accessible @xcite . only in a handful of examples
does the sensitivity of terrestrial experiments match the stellar energy loss constraints . here
we review our works @xcite in which we have identified a new stellar energy loss mechanism originating from the resonant production of longitudinally polarized dark photons and derived ensuing constraints from underground rare event searches .
limits on dark photons were improved to the extent that previously derived constraints from all lsw and helioscope experiments are now superseded by the revised astrophysical and new experimental limits .
and @xmath6 .
the solid / dotted line shows the longitudinal(l)/transverse(t ) contribution .
_ right : _
constraints on @xmath7 as a function of @xmath1 .
the black solid / dashed / dotted curves show the total / longitudinal / transverse energy loss limit of the sun by requiring that the dark photon luminosity does not exceed 10% of the standard solar luminosity @xcite .
the red line shows the constraint derived from the xenon10 data .
previous and future ( = proj .
) experimental bounds / sensitivities are shown by the shaded regions . from light to dark shading these are from the cast experiment @xcite considering the contributions from only the transverse modes @xcite , from the alps collaboration @xcite , and from tests of the inverse square law of the coulomb interaction @xcite.,title="fig:",scaledwidth=50.0% ] and @xmath6 .
the solid / dotted line shows the longitudinal(l)/transverse(t ) contribution .
_ right : _
constraints on @xmath7 as a function of @xmath1 .
the black solid / dashed / dotted curves show the total / longitudinal / transverse energy loss limit of the sun by requiring that the dark photon luminosity does not exceed 10% of the standard solar luminosity @xcite .
the red line shows the constraint derived from the xenon10 data .
previous and future ( = proj .
) experimental bounds / sensitivities are shown by the shaded regions . from light to dark shading these are from the cast experiment @xcite considering the contributions from only the transverse modes @xcite , from the alps collaboration @xcite , and from tests of the inverse square law of the coulomb interaction @xcite.,title="fig:",scaledwidth=50.0% ] the minimal extension of the sm gauge group by an additional @xmath8 gauge factor yields the following effective lagrangian well below the electroweak scale , @xmath9 where @xmath0 is the vector field associated with the abelian factor @xmath8 .
the field strengths of the photon @xmath10 and of the dark photon @xmath11 are connected via the kinetic mixing parameter @xmath7 where a dependence on the weak mixing angle was absorbed ; @xmath12 is the usual electromagnetic current with electric charge @xmath13 .
because of the u(1 ) nature of ( [ eq : l ] ) , we must distinguish two cases for the origin of @xmath1 : the stueckelberg case ( sc ) with non - dynamical mass , and the higgs case ( hc ) , where @xmath1 originates through the spontaneous breaking of @xmath14 by a new higgs field @xmath15 .
the crucial difference between the two cases comes in the small @xmath1 limit : while all processes of production or absorption of @xmath16 in sc are suppressed , @xmath17 , in hc there is no decoupling , and @xmath18 .
indeed , in the limit @xmath19 the interaction resembles one of a mini - charged scalar with the effective em charge of @xmath20 @xcite . in the following
we discuss the sc and refer the reader to our work @xcite as well as to @xcite and references therein for hc .
[ [ sec : flux ] ] solar flux + + + + + + + + + + the solar flux of dark photons in the sc is thoroughly calculated in ref .
@xcite ; for further discussion see also @xcite . in the small mass region , @xmath21 where @xmath22 is the plasma frequency ,
the emission of longitudinal modes of @xmath16 dominates the total flux , and the emission power of dark photons per volume can be approximated as @xmath23 this formula is most readily obtained by noting that a resonant conversion of longitudinal plasmons into dark photons is possible whenever @xmath24 .
the energy - differential flux of dark photons at the location of the earth is shown in the left panel of fig .
[ fig : dp ] .
resonant emission stops for @xmath25 since @xmath22 is limited by the temperature in the sun s core .
[ [ sec : dds ] ] absorption of dark photons + + + + + + + + + + + + + + + + + + + + + + + + + + in the sc , the ionization of an atom @xmath26 in the detector can then be schematically described as @xmath27 .
the total dark photon absorption rate is given by , @xmath28 @xmath29 are the effective mixings for the transverse ( t ) and longitudinal ( l ) modes respectively .
the polarization functions @xmath30 are found from the in - medium polarization tensor @xmath31 , @xmath32 where @xmath33 is the dark photon four momentum and @xmath34 are the polarization vectors for the transverse and longitudinal modes of the dark photon , @xmath35 . the first relation ( [ eq : gamma ] )
is a manifestation of the optical theorem .
the polarization functions @xmath30 are related to the complex index of refraction , @xmath36 or , equivalently , to the permittivity of the medium @xmath37 . for an isotropic , non - magnetic medium @xmath38 and @xmath39 , so that for an incoming on - shell dark photon with @xmath40 , @xmath41 indeed holds .
we obtain @xmath42 from its relation to the forward scattering amplitude @xmath43 where the atomic scattering factors @xmath44 are _
e.g. _ tabulated in @xcite .
close to the ionization threshold we make use of the kramers - kronig dispersion relations to relate @xmath45 and @xmath46 for estimating @xmath36 .
alternatively , one can solve an integral equation relating @xmath47 and @xmath48 in a self - consistent manner , an approach taken in @xcite .
[ [ sec : dds ] ] limits from direct detection + + + + + + + + + + + + + + + + + + + + + + + + + + + + with flux @xmath49 and absorption rate @xmath50 at hand , the expected number of signal events in a given experiment reads @xmath51 where @xmath16 and @xmath52 are the fiducial volume and live time of the experiment , respectively , and @xmath53 is the branching ratio of photoionization rate to total absorption rate . given the significant infrared enhancement of the solar dark photon spectrum , left panel of fig .
[ fig : dp ] , the low - energy ionization signals measured in the xenon10 @xcite dark matter experiment have the best sensitivity to constrain a dark photon flux that is also supported by the sun . with @xmath5412
ev ionization energy in xenon , the absorption of a dark photon with 300 ev energy can produce about 25 electrons . from @xcite
we estimate a 90% c.l upper limit on the detecting rate to be @xmath55 events kg@xmath56day@xmath56 ( similar to limits deduced in ref .
@xcite ) . in the region
@xmath57 ev the ionization process dominates the absorption , and therefore @xmath53 in this region can be set to unity .
the 90% c.l .
upper limit on @xmath7 as a function of @xmath1 is shown by the thick red curve in fig .
[ fig : dp ] . as can be seen it surpasses other current experimental limits as well as the solar energy loss bound in a mass interval from @xmath58 .
given the enormous amount of experimental progress in the field of direct dark matter detection , one can be optimistic that future sensitivity to dark photons , and other light particles is bound to be further improved .
the speaker would like to thank the conference organizers for financial support . | `` dark photons '' , light new vector particles @xmath0 kinetically mixed with the photon , are a frequently considered extension of the standard model . for masses below 10 kev
they are emitted from the solar interior . in the limit of small mass @xmath1
the dark photon flux is strongly peaked at low energies and we demonstrate that the constraint on the atomic ionization rate imposed by the results of the xenon10 dark matter experiment sets the to - date most stringent limit on the kinetic mixing parameter of this model : @xmath2 .
the result significantly improves previous experimental bounds and surpasses even the most stringent astrophysical and cosmological limits in a seven - decade - wide interval of @xmath1 . |
the gross properties of a star , such as broad - band colours and flux distributions , are significantly affected by the effects of convection in stars later than mid a - type .
consequently , our modelling of convection in stellar atmosphere models can significantly alter our interpretation of observed phenomena . by comparison with stars of known @xmath0 and/or @xmath1 ( the fundamental stars ) , we can evaluate different treatments of convection in model atmosphere calculations .
photometric indices are a fast and efficient method for determining approximate atmospheric parameters of stars . for the commonly - used strmgren @xmath2 system a vast body of observational data exists which can be used to estimate parameters using calibrated model grids ( e.g. ( * ? ? ?
* moon & dworetsky 1985 ) , ( * ? ? ?
* smalley & dworetsky 1995 ) ) .
conversely , knowing atmospheric parameters from other methods , allows observed colours to be compared to model predictions .
this method has been used to compare various treatments of stellar convection .
the effects of convection on the theoretical @xmath2 colours of a , f , and g stars was discussed by @xcite , who compared the predicted colours for the @xcite ( cm ) model with that from the standard @xcite mixing - length theory ( mlt ) models with and without `` approximate overshooting '' .
comparison against fundamental @xmath0 and @xmath1 stars revealed that the cm models gave better agreement than mlt without overshooting .
models with overshooting were clearly discrepant .
this result was further supported by stars with @xmath0 obtained from the infrared flux method ( irfm ) and @xmath1 from stellar evolutionary models .
the observed stellar flux distribution is influenced by the effects of convection on the atmospheric structure of the star . as we have seen with photometric colours ,
these effects have a clearly observable signature ( see fig .
[ smalley - fig ] ) . in their discussion of convection
@xcite presented model stellar atmospheres using a modified mixing - length theory .
they found small , systematic differences in the optical fluxes .
their figures also demonstrate that convection can have a measurable effect on stellar fluxes .
hence , high precision stellar flux measurements will provide significant and useful information on convection .
= 7000k , @xmath1 = 4 models with cm and mlt ( @xmath3 = 0.5 and 1.25 ) , compared to that for a model with zero convection .
note that the region 4000 @xmath4 5000 is especially sensitive and the effect of overshooting is considerable . ]
unfortunately , very little high - precision stellar spectrophotometry exists .
this situation will be rectified , once the astra spectrophotometer ( see below ) begins operation .
this will allow spectrophotometry to be added to our observational diagnostic toolkit .
the temperature sensitivity of balmer lines makes them an excellent diagnostic tool for late a - type stars and cooler . the @xmath5 and @xmath6 profiles behave differently due to convection :
@xmath5 is significantly less sensitive to mixing - length than @xmath6 ( ( * ? ? ?
* vant veer & mgessier 1996 ) ) .
both profiles are affected by the presence of overshooting .
since @xmath5 is formed higher in the atmosphere than @xmath6 , balmer lines profiles are a very good depth probe of stellar atmospheres .
balmer profiles are also affected by microturbulence , metallicity and , for hotter stars , surface gravity ( ( * ? ? ?
* heiter 2002 ) ) . in their comparison of balmer line profiles
, @xcite found that both cm and mlt without overshooting gave satisfactory agreement with fundamental stars .
overshooting was again found to be discrepant .
in addition , @xcite found evidence for significant disagreement between all treatments of convection for stars with @xmath0 around 8000 @xmath4 9000 k. subsequently , @xcite reviewed this region using binary systems with known @xmath1 values and their revised fundamental @xmath0 values of the component stars .
they found that the discrepancy found was no longer as evident .
however , this region was relatively devoid of stars with fundamental values of both @xmath0 and @xmath1 .
further fundamental stars are clearly required in this region .
the automated spectrophotometric telescope research associates ( astra ) have developed a cassegrain spectrophotometer and its automated 0.5-m f/16 telescope .
there are being integrated at the fairborn observatory near nogales , arizona .
scientific observations are expected to begin in 2007 ( ( * ? ? ?
* ; * ? ? ?
* adelman 2007 , smalley 2007 ) ) . in an hour
the system will obtain s / n = 200 ( after correction for instrumental errors ) observations of stars as faint as 9.5 mag .
the spectrograph uses both a grating and a cross - dispersing prism to produce spectra from both the first and the second orders simultaneously .
the square 30 arc second sky fields for each order do not overlap .
the resolution is 7 in second and 14 in first order .
the wavelength range is of approximately @xmath73300 - 9000 .
the effects of convection on the stellar atmospheric structure can be successfully probed using a variety of observational diagnostics ( ( * ? ? ?
* smalley 2004 ) ) .
the combination of photometric colours and balmer - line profiles has given us a valuable insight into the nature of convection in stars .
high quality observations that are currently available and those that will be in the near future , will enable further refinements in our theoretical models of convection and turbulence in stellar atmospheres . | convection and turbulence in stellar atmospheres have a significant effect on the emergent flux from late - type stars .
the theoretical advancements in convection modelling over recent years have proved challenging for the observers to obtain measurements with sufficient precision and accuracy to allow discrimination between the various predictions .
an overview of the current observational techniques used to evaluate various convection theories is presented , including photometry , spectrophotometry , and spectroscopy .
the results from these techniques are discussed , along with their successes and limitations .
the prospects for improved observations of stellar fluxes are also given . |
ss 433 is a peculiar binary system , consisting of a black hole ( as proposed by lopez et al . , 2005 ) and a massive companion .
this system is accreting at a super - eddington rate , and is expelling two - sided relativistic jets at a velocity of 0.26c .
these jets precess in a cone of half - opening angle of 20@xmath0 @xcite .
ss 433 is near the center of w50 , a large 2@xmath11@xmath0 nebula stretched in the east - west direction , and catalogued as an snr @xcite.the ss 433/w50 system is the only galactic object known of its kind , giving rise to a unique laboratory to study the association between snrs and black holes as well as the interaction between relativistic jets and the surrounding medium .
this system has been studied extensively in radio continuum and hi @xcite , millimetre wavelengths @xcite , and in x - rays with and ( * ? ? ? * and references therein ) and with _ rxte _ ( safi - harb & kotani , 2002 , safi - harb & petre , 1999 ) . from this multi - wavelength study , it was concluded that the morphology and energetics of w50 are consistent with the picture of the jets interacting with an inhomogeneous medium and likely hitting a denser cloud in the west .
the observation presented here provides the highest resolution x - ray image obtained to date of the bright region of the western lobe of w50 .
this region was chosen because it coincides with ir emission and can probe the jet - cloud interaction site .
we performed a spatially resolved spectroscopy of this region to primarily determine the nature of the emission and correlate the x - ray emission with radio and ir observations .
the paper is organized as follows . in 2 , we summarize the observation imaging and spectral results and compare them to the and data . in 3 , we study the x - ray emission in correlation with the infrared and radio emission , and finally present our conclusions in 4 .
the western lobe of w50 was observed with the acis - i chips on board on 2003 august 21 at a ccd temperature of -120@xmath0c .
the charge transfer inefficiency was corrected using the apply_cti tool on the level 1 raw data .
a new level 2 file was then obtained using the standard ciao 3.0 routines .
the final exposure time was 71 ksec . to illustrate the w50 region covered by , we show in fig .
1 the the radio image of w50 ( grey scale ) , and the regions covered by observations in infrared ( large box ) and x - ray ( small box ) . the projection on the sky of the precession cone axes of the ss 433 jets is also overlayed .
the radio image shows that the eastern wing of w50 exhibits a corkscrew pattern , which mimics the precession of the arcseconds - scale jets from ss 433 ( dubner et al . , 1998 , hjellming & johnston , 1981 ) .
interestingly , there is a hint of a corkscrew pattern visible in the chandra image ( fig . 2 and 3 ) , supporting the conclusion that the ss 433 subarcsecond - scale relativistic jets are affecting the large scale radio and x - ray emission from w50 . in fig .
2 , we show the energy image in which red corresponds to the soft energy band ( 0.3 - 2.4 kev ) and blue corresponds to the hard energy band ( 2.4 - 10 kev ) . in fig .
3 , we show the intensity image in the 0.3 - 10 kev energy range .
we resolve many point sources in the field ( a list of which will be provided elsewhere ) and note the knotty structure of the nebula .
the x - ray emission peaks at @xmath2 ( j2000 ) = 19@xmath3 09@xmath4 42@xmath5.86 , @xmath6 ( j2000 ) = 05@xmath0 03@xmath7 38@xmath8.8 .
( measured from n to e ) , and half - opening angle of 20@xmath0,width=384 ] .
+ to perform spatially resolved spectroscopy of the remnant , we excluded the point sources in the field , and extracted spectra from the diffuse emission for 11 regions shown in fig .
the w2 and irknot2 regions correspond to the x - ray w2 region presented in @xcite and the infrared knot2 region presented by @xcite , respectively .
these regions will be the focus of this paper and are selected in order to compare the results with those found in x - rays with and and in infrared with _
the proximity of the western lobe to the galactic plane complicates the spectral analysis because of contamination by the galactic ridge . to minimize this contamination
, we extracted several background regions from source - free regions around the diffuse emission from w50 and from the same acis chip .
we subsequently determined the spectral parameters using the resulting average background .
spectra were extracted in the 0.5 - 10.0 kev range .
the background subtracted count rate for the w2 and irknot2 regions are @xmath9 counts s@xmath10 and @xmath11 counts s@xmath10 respectively .
to determine whether the emission is thermal or not , we fitted the spectra with thermal bremsstrahlung and power - law models ( following * ? ? ? * ) .
the bremsstrahlung model is characterized by the shock temperature , @xmath12 , and the power - law model is characterized by the photon index , @xmath13 .
[ h ] = 0@xmath8.5 . * fig .
3 . ( right ) : 0.3 - 10 kev image of w50 showing regions used for spectroscopy ( see 2.2 ) . the dots hint to a corkscrew pattern.*,title="fig:",width=528 ] * * 3 for details.,width=384 ]
both models give adequate fits in each region .
however , we find that the power - law models give slightly lower reduced @xmath14 values , and that the temperatures derived from the thermal bremsstrahlung models are high ( unrealistically high for even the youngest snrs ) .
this , together with the absence of line emission in the spectra , leads us to favor the non - thermal interpretation for the x - ray emission .
table [ tab1 ] summarizes the results for the w2 region in comparison to the and results .
a distance of 3 kpc ( scaled by @xmath15 ) is used in the luminosity calculations ( as in * ? ? ?
* ) , and the errors are at the 90% confidence level .
the spectroscopic results of the other regions are beyond the scope of this paper and will be presented elsewhere ; we note here that the spectrum softens with increasing distance from ss 433 except for regions 3 , 6 and 8 .
this is consistent with the energy - color image shown in fig 2 .
.thermal bremsstrahlung and power - law model results for the w2 region [ cols="<,^,^,^,^ " , ] we subsequently use the power - law fits to derive the synchrotron emission parameters .
assuming equipartition between particles and fields and integrating from radio to x - ray frequencies , the equipartition magnetic field ( @xmath16 ) , the magnetic energy density ( @xmath17 ) , the total synchrotron electron energy ( @xmath18 ) and the lifetime of the electrons ( @xmath19 ) can be determined . for the w2 region ,
we derive @xmath20 g , @xmath21 erg @xmath22 , @xmath23 ergs , and @xmath24 years .
the range of values corresponds to a=1 - 100 ( the ratio of baryon energy to electron energy ) .
the derived values of the synchrotron parameters as well as @xmath25 ( table [ tab1 ] ) agree with those found using and for the w2 region , within error . however , the spectra appear harder with the observation .
to probe the interaction between the western jet of ss 433 and the ambient medium , we study the x - ray emission in correlation with radio continuum and hi data obtained with the nrao vla and green - bank radio telescope and infrared data obtained with _ isocam_. fig .
1 shows the radio , infrared , and x - ray regions and fig .
4 shows the x - ray emission with the infrared contours .
the average value of @xmath25 found on the basis of the hi observations is @xmath26 @xmath27 .
this is slightly lower than the average found using the data , which is to be expected .
the energetics in the western lobe found with the x - ray data can then be compared to that found in @xcite .
we found the total synchrotron electron energy in x - rays to be @xmath28 ergs , which is in good agreement with the energy found from radio observations .
as seen in fig .
4 , there is no correlation between the infrared emission and the peak of x - ray emission .
this , along with the high value of @xmath25 ( n@xmath29@xmath302@xmath3110@xmath32 @xmath27 ) derived for the irknot2 region , suggests that the infrared emission is not associated with the western lobe of w50 .
the derived value of @xmath33 kev is higher than the expected temperatures for snrs , indicating that the x - ray emission in irknot2 is non - thermal .
we favor a non - thermal interpretation for the emission of the western lobe of w50 .
the derived values of @xmath25 , equipartition magnetic field , synchrotron electron energies and lifetimes agree with those derived previously with and _ asca . _ the infrared emission is not correlated with the peak of x - ray emission .
this , in addition to the high value of @xmath25 derived for this region , suggests that the infrared emission is not originating from w50 , and could be associated with a star forming region ( work in progress ) .
the corkscrew pattern seen in both the radio and x - ray images provides strong support to the hypothesis that the relativistic jets from ss 433 are causing the morphology of the w50 nebula .
s. safi - harb acknowledges support by an nserc ufa fellowship and an nserc discovery grant ( canada ) .
y. fuchs is supported by a cnes ( france ) fellowship .
g. dubner is a member of the carrera del investigador cientfico , conicet ( argentina ) . | w50 remains the only supernova remnant ( snr ) confirmed to harbor a microquasar : the powerful enigmatic source ss 433 .
our past study of this fascinating snr revealed two x - ray lobes distorting the radio shell as well as non - thermal x - rays at the site of interaction between the ss 433 eastern jet and the eastern lobe of w50 . in this paper
we present the results of a 75 ksec acis - i observation of the peak of w50-west targeted to 1 ) determine the nature of the x - ray emission and 2 ) correlate the x - ray emission with that in the radio and infrared domains .
we have confirmed that at the site of interaction between the western jet of ss 433 and dense interstellar gas the x - ray emission is non - thermal in nature . the helical pattern observed in radio is also seen with .
no correlation was found between the infrared and x - ray emission . , ,
, binaries : close , ism : individual ( w50 ) , x - rays : stars , stars : individual ( ss 433 ) , radiation mechanisms : non - thermal , supernova remnants |
many thanks to k. a. takeuchi for numerous fruitful exchanges regarding our work and for providing his png skewness splines & 1 + 1 kpz class experimental data .
we re very grateful , as well , to m. prhofer for making available the tw - gue & goe traces , and to t. imamura for kindly sharing his numerical rendering of the baik - rains f@xmath10 limit distribution . 10 for early , bedrock kpz developments ,
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the kpz history of the baik - rains constant @xmath73 has been documented , in a nutshell , in ref .
[ 12b ] , sect .
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e*83 * , 020103 ( 2011 ) ; evident , also , ref @xcite , table 1 & figs 3,4 therein .
we extract @xmath104=4.855 via the tw - goe variance ( not shown ) , using this value to make comparison of ballistic deposit _ stationary - state _ to br - f@xmath10 limit distribution .
we are imagining , here , an experimental system size @xmath72=10@xmath105 pixels , with roughly 10@xmath105 runs being made , yielding 10@xmath56 data for each time slice . this particular _ nonuniversal behavior _ of takeuchi s png model
is quite clearly seen in his skewness insert , figure 1b , ref .
also , for increasing @xmath76 , his png traces _ fall into the minimum from above , _ rather than rise up from below , as they do for the experimental data sets .
these png features are likewise shared by our gaussian dprm and ballistic deposits . | motivated by the recent exact solution of the _ stationary - state _ kardar - parisi - zhang ( kpz ) statistics by imamura & sasamoto ( phys .
rev .
lett . * 108 * , 190603 ( 2012 ) ) , as well as a precursor experimental signature unearthed by takeuchi ( phys
. rev .
lett . * 110 * , 210604 ( 2013 ) ) , we establish here the universality of these phenomena , examining scaling behaviors of directed polymers in a random medium , the stochastic heat equation with multiplicative noise , and kinetically roughened kpz growth models .
we emphasize the value of cross kpz - class universalities , revealing crossover effects of experimental relevance .
finally , we illustrate the great utility of kpz scaling theory by an optimized numerical analysis of the ulam problem of random permutations .
extremal paths through random energy landscapes ,
i.e. , directed polymers in random media " ( dprm ) , have long been a topic of great interest to statistical physicists , condensed matter theorists , and mathematicians alike @xcite . in two dimensions ,
the exact limit distributions of the dprm problem @xcite are of the celebrated tracy - widom ( tw ) type @xcite , best known perhaps from random matrix theory @xcite , as well as the famous ulam problem of random permutations @xcite .
nevertheless , in the bulk , the statistics of these extremal trajectories remains a challenging , rich , and quite difficult problem @xcite . in all dimensions , however , the constrained free - energy @xmath0 of these directed , extremal paths is dictated by the stochastic partial differential equation @xcite of kardar , parisi , & zhang ( kpz ) : @xmath1 where @xmath2 and @xmath3 are system - dependent parameters , the last setting the strength of the _ additive _ stochastic noise @xmath4 .
rigorous mathematical approaches , by contrast , have focussed on the related stochastic heat equation ( she ) with _ multiplicative _ noise , obtained from kpz via a hopf - cole transformation , @xmath5=@xmath6 ; here , with @xmath7 and it interpretation , this becomes an elemental , rescaled version @xcite of the she : @xmath8 governing the dprm partition function @xmath9 , a much better behaved quantity , well - regularized in the uv .
inspired by imamura & sasamoto s exact solution @xcite of the kpz equation _ stationary - state _ ( ss ) statistics , as well as takeuchi s subsequent re - examination @xcite of the tour - de - force kpz turbulent liquid crystal experiments @xcite , we focus here on the 1 + 1 dimensional dprm / she , making manifest its connection to the underlying baik - rains ( br ) f@xmath10 limit distribution @xcite relevant to this kpz class .
we examine , too , dprm scaling phenomena in the pt - line & pt - pt configurations , analog of kpz stochastic growth in _ flat _ &
curved _ geometries , governed by tracy - widom distributions appropriate to gaussian orthogonal & unitary matrix ensembles ; i.e. , tw - goe & gue , respectively .
our dprm / she results in this regard provide the final installment of the kpz triumvirate , complementing prior numerical confirmation of tracy - widom universality which had focused initially on kinetic roughening models such as polynuclear - growth ( png ) @xcite , as well as single - step , or totally asymmetric exclusion processes @xcite .
in fact , we go further here in the dprm / she context , making additional suggestions regarding experimental signatures of kpz class statistics , examining the interplay of transient & ss regimes and , finally , in the pt - pt tw - gue setting , illustrate the potency of kpz scaling theory @xcite to inform key aspects of the purely mathematical ulam problem .
we thus return the favor here , reiterating the very fruitful dialog between kpz physics and tw gue mathematics . in figure 1 , for starters
, we compare to tw - gue the shifted , rescaled distributions of our _ curved _ kpz class models , among them the : i ) pt - pt g@xmath11 dprm ; i.e. , extremal paths in the xy - plane , traveling in the [ 01]-direction , gaussian random energies @xmath12 with zero mean & variance @xmath13 on the sites of the square lattice ; side - steps are permitted , but incur a microscopic , elastic energy cost @xmath14=1 .
we consider extremal paths that commence at the origin , constrained to terminate t=300 steps later on the axis .
the g@xmath11 dprm trace in fig 1 represents an average over 10@xmath15 realizations of the random energy landscape .
similarly , ii ) pt - pt w / e dprm- here , the random site energies are exponentially distributed , p(@xmath16)=e@xmath17 , and the paths , on average , cut diagonally through the plane in the [ 11 ] direction ; at each step , there are two possibilities , either vertically ( i.e. , in y - direction ) or horizontally ( x - direction ) .
there is no elastic energy cost in this model , the total energy of the trajectory simply the sum , @xmath18=@xmath19 , of the random energies collected traveling from ( 0,0 ) to ( t , t ) . for our w / e dprm ,
we averaged over 4x10@xmath15 paths of length t=400 . next , the numerically demanding iii ) constrained she - it integrations , with kpz parameter @xmath20=10 ; we evolved the system through the forward & rear light cones of the initial & final points of the trajectory , averaging over @xmath21 runs , considering paths of 4000 steps , with time increment @xmath22t=0.05 .
universal limit distributions : dprm / she , ulam - lis , & tw - gue .
insets : extraction of ulam - lis asymptotic moments & baer - brock constant , via kpz scaling theory.,width=321 ] in the case of the pt - pt dprm models , we have extracted , from a first principles krug - meakin ( km ) finite - size scaling analysis @xcite , the nonuniversal , _ system - dependent _ kpz parameters @xmath23 , @xmath24=@xmath25 , and @xmath26 . note that the km toolbox @xcite yields the asymptotic free energy per step , @xmath23 , and the _ product _ @xmath27 , so that @xmath26 , itself , must be fixed by the parabolic dprm free - energy profile @xcite .
interestingly , in the following , only @xmath23 and the combination @xmath28=@xmath29 are needed , which we record in table i. an alternative approach , which highlights the utility of cross kpz - class studies emphasized in this paper , involves fixing the kpz scaling parameter @xmath28 directly from a fit , e.g. , to the tw - goe variance and then _ using it in the service of _ both the tw - gue limit distribution , our immediate focus , as well as stationary - state baik - rains pdf , which we consider later .
this we do , for illustrative purposes , in the case of she - it integration . with @xmath30=@xmath31
the known @xcite dprm free - energy fluctuation exponent , the central kpz scaling ansatz reads- @xmath32 with @xmath33 the underlying , order one tracy - widom gue statistical variable .
thus , the pt - pt dprm / she distributions of figure 1 have been cast in terms of @xmath33 , the canonical quantity intrinsic to the _ curved _ kpz class in this dimension .
while crafting figure 1 , we have relied upon the model - dependent _ asymptotic _ values for the distribution mean and variance , @xmath34=@xmath35 , our curve fits for the latter assuming the characteristic @xmath36 dprm finite - time correction .
our most accurate values for these limit distribution characteristics are obtained via the gaussian & exponential polymers , see table i ; compare , too , our model estimates for the distribution skewness @xmath37=@xmath38 and kurtosis @xmath39=@xmath40 the accepted values @xcite for these tw - gue quantities are : @xmath41 = @xmath42 our pt - pt dprm - she results in figure 1 , stacked up against the exact , known 1 + 1 curved kpz class tw - gue distribution , provide an interesting extremal path counterpoint to efforts on radial 2d eden clusters @xcite and kinetic roughening in droplet geometries @xcite , the latter studies involving png , single - step , ballistic deposition ( bd ) , as well as corner growth in a restricted - solid - on - solid " ( rsos ) model .
l*7c kpz system & @xmath23 & @xmath43 & @xmath44 & @xmath34 & @xmath45 & @xmath46 + g5@xmath47 dprm & -0.498021 & 0.50633 & -1.77097 & 0.8167 & 0.2304 & 0.0924 + w / e dprm & -2.0003 & 1.9882 & -1.77102 & 0.8116 & 0.2227 & 0.0908 + she - it & 2.48533 & 0.13345 & -1.7908 & 0.8121 & 0.2263 & 0.0893 + finally , in homage to the pioneering efforts of baer & brock @xcite , as well as the extraordinary numerical work of odlyzko & rains @xcite a generation later , we have performed , in a post - kpz / tw context , our own analysis of the ulam problem , studying the fluctuating statistics of the length , @xmath48 , of the longest increasing subsequence ( lis ) in a permutation of @xmath49 integers .
it was established early on , with much heavy - lifting and the securing of mathematical bounds , but then definitively by vershik & kirov @xcite , that asymptotically @xmath50 .
indeed , this was well - presented by baer & brock , see figure 1 and table 2 of their early paper , where they recorded exact enumerations of the lis pdf for @xmath51 using the rsk correspondence , hook formula , & young tableau mapping @xcite , complementing these results with approximate monte carlo data reaching up to @xmath49=10@xmath52 .
later , it was conjectured by odlyzko & rains , then firmly established by kim , that the standard deviation about this mean scaled as @xmath53 ; i.e. , the ulam - lis problem possessed a well - defined limit distribution in the variable @xmath54 .
baik , deift , & johansson then proved rigorously that the underlying , asymmetric non - gaussian distribution was , surprisingly , tw - gue from random matrix theory @xcite .
in fact , odlyzko & rains provided explicit monte carlo evidence in this regard , matching their semilog lis pdf , with 10@xmath55 permutations of length @xmath49=10@xmath56 , against a precise painlev ii rendering of tracy - widom gue .
interestingly , the odlyzko - rains data show a small , but clear , finite - time offset ( they quote @xmath44@xmath571.720 ) in their lis pdf , which only stubbornly disappears as the authors heroically head toward asymptopia , pushing their simulations to @xmath49=10@xmath15 , where @xmath44@xmath571.758 , & beyond ( @xmath49=10@xmath58 ) , nearly closing the gap between themselves and the known tw - gue universal mean : @xmath44=1.7711 .
since @xmath59=@xmath60 , random permutations of @xmath49=10@xmath58 digits are equivalent , roughly , to generating pt - pt dprm with t=10@xmath55 , quite a demanding task , indeed . here
, we take a different attitude , considering rather short permutation strings , with @xmath49=10@xmath61 - 10@xmath52 , essentially the regime where baer & brock concentrated their numerical enterprise , but invoke kpz scaling wisdom to , nevertheless , pin down very precise values for the moments ; see fig .
1 , where our ulam - lis pdf follows from 10@xmath15 random permutations of length @xmath49=10@xmath52 , as well as the figure insets , which document the kpz scaling of the truncated lis cumulants , allowing us to make fine asymptotic estimates : ( -1.7715,0.8135,0.2245,0.09102 ) , close to known tw - gue values . for the ulam - lis variance , skewness & kurtosis , lower inset
, we ve invoked an @xmath62 finite-time " correction , suggested by dprm lore .
the upper inset , which examines kpz scaling of the universal tw - gue mean , amends the odlyzko - rains ansatz to include an additive constant term , resulting in an @xmath63 finite - time correction to @xmath44 , plainly visible in the data . in our ulam - lis work ,
we ve come to refer to this quantity as baer - brock s constant- here estimated to be @xmath570.51@xmath640.01 , given by the slope of the line in our plot of @xmath44 versus @xmath65 the existence of such a _ model - dependent additive constant _ is well - known to kpz practitioners @xcite , but has not , to our knowledge , been discussed for ulam - lis .
given the somewhat priviliged role of the random permutation problem amidst the menagerie of systems obeying tw - gue statistics- it is , by the hook formula , uniquely accessible to exact enumeration for finite @xmath49- we attach somewhat greater significance to this particular additive constant . 1 + 1 _ transient - regime _ & _ stationary - state _ kpz / dprm class : comparison to tw - goe & br - f@xmath10 limit distributions .
inset : universal _ variance - ratio _ as precursor signature of kpz ss statistics .
black traces document crossover scaling to the stationary - state , accessible via experiment .
, width=321 ] in figure 2 , for our g@xmath11 dprm , single - step growth , and she - it eulerian integration , we have paired up the distinct pdfs associated with the _ transient - regime _ & _ stationary - state _ statistics for the flat kpz geometry , making relevant comparisons to exact tracy - widom goe & baik - rains f@xmath10 distributions , respectively . for the _ transient _ dynamics , our dprm / she work harks back to early , pre - tw efforts @xcite , and dovetails with recent growth model studies @xcite , in which several kpz kinetic roughening pdfs , among them bd & rsos , are fit to tw - goe . as an indication of our findings here , we note specifically that the g@xmath11 dprm yields a variance , 0.63703 , quite close to the tw - goe result @xmath66=0.63805 , along with a skewness , 0.2976 , very much in line with the value , @xmath67=0.2935 , characteristic of that distribution .
more importantly , with regard to 1 + 1 kpz class _ stationary - state statistics , _ and comparison to the baik - rains limit distribution , our dprm / she results , well - matched by single - step , bd , & rsos findings , convincingly establish universality of the seminal png studies of prhofer & spohn @xcite- note the strong data collapse of our models upon the br - f@xmath10 trace , a highly nontrivial numerical matter . for the g@xmath11 dprm
, we have evolved the system to a late time t@xmath68=8x10@xmath52 , then study dynamic temporal correlations in the path _ free - energy , _
@xmath69=@xmath70 , during the subsequent time interval @xmath71=500 , averaging over 8x10@xmath52 runs in a system of size @xmath72=10@xmath52 . at @xmath71=500 , we note the approximate values : ( 1.1177,0.3432,0.252 ) which , extrapolated to infinite @xmath71 , yield ( 1.1466,0.3530,0.278 ) , quite close to the known @xcite br - f@xmath10 variance , skewness , & kurtosis : ( @xmath73,@xmath74,@xmath75)=(1.15039,0.35941,0.28916 ) . for rsos growth in the stationary - state , @xmath76=40k & @xmath71=240 , which gives an asymptotic estimate @xmath771.1331 for the baik - rains constant @xcite , while ballistic deposition , with @xmath76=50k & @xmath71=500 , produces 1.1382 for this quantity .
we emphasize that the plotted distributions of figure 2 are not the raw data , but have been rescaled , each in turn , to represent the _ system - dependent _ asymptotic variances , carefully extracted via kpz scaling theory .
included as fig 2 inset , we consider the time dependence of the _ ratio of variances _ in kpz transient & stationary - state regimes .
we are motivated here by takeuchi s recent study @xcite of the png model , as well his attempts to tease from the 1 + 1 kpz class turbulent liquid - crystal data @xcite , some sign of the ss statistics .
although the br - f@xmath10 limit distribution itself remained well - beyond the reach of these experiments , takeuchi discovered an impressive precursor signature of the kpz stationary - state , evident as a _
skewness minimum , _ which we confirm shortly with our own models , establishing its universal kpz aspect .
given the intrinsic importance of the stationary - state dynamics @xcite , we propose here an alternative signature , relying upon a more statistically tame quantity which , asymptotically , is fixed universally- @xmath78 by the ratio of the tw - goe variance & baik - rains constant . since the _ variance - ratio , _ like the skewness @xmath37 , requires no knowledge of @xmath28 , a quick examination of this quantity in experiments may provide a glimpse of a key universal property of the kpz stationary - state . within figure 2 inset ,
we document ( solid symbols ) the scaling of this interesting ratio for g@xmath11 dprm , she - it , and three distinct kpz growth models .
all 5 systems converge convincingly- even the contrarian bd , well known for its curmudgeonly behavior @xcite . for the she - it case , @xmath76=10k & @xmath71=100 as above , per our rendering of the br distribution .
however , we also include within the inset , data sets associated with lesser values of @xmath76 & hundredfold fewer runs , to study _ crossover effects , _ indicating how this scaling phenomena might appear in a more constrained experimental context .
the black traces , top down , correspond to @xmath76=3 , 20 , 100 , 500 , though all possess @xmath71=100 , with statistical averaging now done @xcite over a 10@xmath56 , rather than 10@xmath15 points .
the goal here is to provide an extra tack upon the 1 + 1 kpz class _ stationary - state _
statistics , and to further complement the spectacular experimental results already in hand for the transient _ flat _ tw - goe and _ curved _ tw - gue kpz classes .
takeuchi _ skewness minimum _ , evident in our dprm , she - it , bd , rsos & single - step kinetic roughening models .
upper & lower dot - dashed lines correspond to asymptotic skewness , @xmath74=0.35941 & @xmath67=0.2935 , of the baik - rains f@xmath10 & tracy - widom goe limit distributions , respectively .
inset : data sets , kpz turbulent liquid crystal experiments- ref .
@xcite .
the emergence of the minimum for our she - it integration , revealed as @xmath76 grows from 25 , 50 , to 100 , is manifest within the experiment proper , where the symbols indicate distinct times , smallest to largest , @xmath76=2,6,10,18,30,54,60 , right to left.,width=321 ] lastly , with figure 3 , we establish _ universality _ of takeuchi s skewness minimum @xcite , heightening its utility as an experimental precursor signature of the 1 + 1 kpz class stationary - state statistics . for our gaussian dprm , she - it integration , and kpz growth models ,
we have plotted up the fluctuation pdf skewness @xmath37 as a function of the dimensionless scaling parameter @xmath79=@xmath80 where , in each case , the numerics are evolved to a time @xmath76 , the skewness then tracked through a subsequent time interval @xmath81 . to consider the consequences of an _ insufficiently mature _ kinetically - roughened state , we include she - it results for @xmath76=25 , 50 , & 100 respectively , shown in the ascending , dashed curves , solid in the last instance .
it is interesting to observe how , with increasing @xmath76 , the traces develop to reveal a nearly full - fledged takeuchi minimum ; i.e. , for @xmath76=25 , the skewness min is entirely absent , though the curve possesses a suggestive inflection point . at @xmath76=50
, the minimum has appeared , but only gains a fuller expression at @xmath76=100 .
note , however , that once the skewness minimum has emerged , there is very little movement in its precise location- this is especially true of the @xmath82 ordinate , slightly less so for its abscissa .
the evolution , with increasing @xmath76 , of the universal kpz class skewness minimum is tied primarily to its _ curvature _ and , in the 1 + 1 dimensional case , to the steepening slope for @xmath83 , as @xmath84 .
we mention , in passing , that our she - it , single - step , and rsos simulations share a common _ nonuniversal behavior _ at very early @xmath81 , which gives rise to a _ model - dependent _ maximum and subsequent ( @xmath85 ) monotonic decrease in @xmath86 , evident in the figure .
most interestingly , this peculiar feature is actually manifest within takeuchi s @xcite liquid - crystal kpz experimental data set proper ( ! ) , shown as an inset within figure 3 and contrasts , intriguingly , with his own png simulation results , which indicate a weakly divergent , _ increasing _
@xmath37 for the smallest @xmath79 values @xcite .
these system - dependent details are small , but curious matters , slightly off - stage , but nevertheless quite apparent to those involved in the nuts & bolts of simulation . from an experimental point of view
, however , the takeuchi minimum itself is the essential focus and sits center - stage , providing a _ crucial , tell - tale precursor signature of 1 + 1 kpz class stationary - state statistics .
_ hence , see figure 3 , our g@xmath11 dprm results , for which we have devoted the greatest numerical investment , making a 1/4 million runs in a system size l=10@xmath52 , resulting in a data set of 2.5 billion samples . included , too , in the figure itself , as well as the inset , is takeuchi s skewness spline ( black traces ) , carefully crafted via his png work .
the agreement between takeuchi s png spline and our mix of kpz data sets , and that of the g@xmath11 dprm in particular , is quite suggestive , indeed . from our simulations ,
we locate the takeuchi minimum at @xmath82=0.225@xmath640.005 , for @xmath79=@xmath87=4.5@xmath640.4 .
we note , that the nonuniversal behavior at small @xmath85 evident in takeuchi s png simulation , giving rise to a climbing , positive @xmath37 is , in fact , shared by our g@xmath11 dprm and bd models .
of course , it is only in the double limit , @xmath84 , then @xmath88 , with @xmath89 that an interpolating skewness spline , originating at the tw - goe value , @xmath67=0.2935 , for large @xmath90 , would descend through the takeuchi minimum at the sweetspot near @xmath91 , then exhibit the correct asymptotic approach to the stationary - state baik - rains value , @xmath74=0.35941 , for vanishing small @xmath92 .
to manifest the latter would be quite difficult , even numerically .
finally , we mention that the _ kurtosis minimum _ we find for the g@xmath11 dprm , at @xmath93=0.117 , is quite near takeuchi s png value for this more demanding , higher cumulant ratio . given the tougher statistics , as well as the smaller difference here between the tw - goe kurtosis , @xmath94=0.1652 , and our measured k@xmath95 , eliciting this delicate feature experimentally will remain , no doubt , a most challenging task . in the interim , we await a clever experimental implementation of the kpz _ stationary - state _ initial condition , which might allow _ direct _ access to the baik - rains f@xmath10 .
given the universality established via figure 2 , with our dprm / she , single - step , bd , and rsos results , this limit distribution represents , most assuredly , the relevant fixed point pdf . |
we are studying the semileptonic decays @xmath0 , @xmath1 , @xmath2 , @xmath3 , and @xmath4 and the corresponding decays with a strange spectator quark . for a companion study of purely leptonic decays , see @xcite . the ckm matrix element @xmath5 , for example
, is obtained from the differential semileptonic decay rate for @xmath6 at total leptonic four - momentum @xmath7 @xcite : @xmath8 the unknown hadronic form factor @xmath9 is to be determined in lattice gauge theory from the matrix element of the weak vector current @xmath10 , @xmath11
since the heavy - light meson decays involve light quarks , it is important to choose an @xmath12 lattice fermion implementation with good chiral properties . to this end
we have been experimenting with an action proposed by degrand , hasenfratz , and kovcs @xcite , which introduces , in effect , a cutoff - dependent form factor at the quark - gluon vertex to suppress lattice artifacts at the level of the cutoff .
the action is the usual clover action but with a gauge background constructed by replacing the usual gauge links by ape - smoothed links @xcite with coefficient @xmath13 for the forward link and @xmath14 for the sum of staples .
the smoothed link is projected back to su(3 ) . this smoothing process is repeated @xmath15 times . for the present experiment
we take @xmath16 and @xmath17 .
these values are to be kept constant in the continuum limit , thus giving the local continuum fermion action .
this `` fattening '' process reduces problems with `` exceptional '' configurations that obstruct extrapolations to light quark mass @xcite .
calculations were done on an archive of 200 @xmath18 gauge configurations , generated with two flavors of dynamical staggered quarks of mass @xmath19 at the one - plaquette coupling @xmath20 , corresponding to a lattice spacing ( from the rho mass ) of about 0.11 fm .
the fat clover propagator was generated for three `` light '' ( spectator and recoiling ) quarks and five `` heavy '' ( decaying and recoiling ) quarks over a mass range @xmath21 .
the coefficient of the clover term @xmath22 was set to 1 .
the mass of the lightest fat clover quark was adjusted to give the same pion mass as the staggered fermion goldstone boson .
we use the fermilab program through @xmath23 for the quark wave function normalization , including the three - dimensional rotation@xcite with coefficient @xmath24 .
the light meson source is placed at @xmath25 and the heavy - light meson at @xmath26 , with antiperiodic boundary conditions in @xmath27 .
we treat three values of the heavy - light - meson momentum and 21 values of the three - momentum transfer at the current vertex .
computations are in progress .
results are presented for a subset of about half of the 200 configurations including only the two lightest spectator quark masses .
an example of the meson dispersion relation is shown in fig . [
fig : disp_rel ] .
it is quite satisfactory .
the form factor is extracted by amputating the external meson legs at present , by dividing by @xmath28 $ ] , where the @xmath29 meson energy @xmath30 and recoil meson energy @xmath31 are taken from central values of a fit to the corresponding two - point dispersion relations .
the diagonal vector form factor at zero three - momentum transfer gives the vector current renormalization factor @xmath32 .
it is shown as a function of the inverse meson mass in fig .
[ fig : z_v ] for the two currently available choices of the spectator quark mass .
we see that this nonperturbative renormalization constant is within @xmath33% of unity .
we test the soft pion theorem @xcite which states that in the chiral limit @xmath34 .
the same action and configurations are used to get @xmath35 @xcite .
both spectator and recoil quark masses ( @xmath36 and @xmath37 ) are extrapolated to zero .
if we use @xmath38 = a + bm + cm^\prime$ ] we obtain fig .
[ fig : soft_pion2 ] , a disagreement similar to that found by jlqcd @xcite .
if we include an extra term @xmath39 as advocated by maynard @xcite the theorem is satisfied , but with large extrapolated errors .
we hope our eventual full data sample will help resolve these complexities @xcite .
sample form factors for the process @xmath40 are shown in fig .
[ fig : bs_to_k ] .
fattening has allowed us to obtain results for an ostensibly @xmath12 action on unquenched lattices for quark masses at least as low as @xmath41 with no noticeable trouble from exceptional configurations .
our experiment raises a number of important questions : will a one - loop - perturbative determination of current renormalization factors be adequate ? how much fattening is good ?
does fattening push us farther from the continuum limit for some quantities ?
work is in progress .
this work is supported by the us national science foundation and department of energy and used computer resources at the san diego supercomputer center ( npaci ) , university of utah ( chpc ) , oak ridge national laboratory ( ccs ) , and the pittsburgh supercomputer center .
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presentation by v. lesk ( this conference ) .
plenary talk by s. hashimoto ( this conference ) . | we are studying a variety of semileptonic decays of heavy - light mesons in an effort to improve the determination of the heavy - quark standard - model ckm matrix elements .
our fermion action is a novel , improved `` fat '' clover action that promises to reduce problems with exceptional configurations .
dynamical sea quarks are included in a mixed approach , _
i.e. _ we use staggered sea quarks and fat - clover valence quarks . here
we report preliminary results . |
photonic crystals are artificial low - loss dielectric structures with periodic modulation of refractive index , which have attracted considerable attention in the last two decades . due to bragg reflection
, electromagnetic ( optical ) waves can not propagate through such structures in certain directions , at certain frequencies .
hence , photonic crystals can control the propagation of electromagnetic waves in novel ways , with obvious application to dielectric mirrors , dielectric waveguides , and dielectric laser cavities . as a way to efficiently inject light into a photonic crystal ( pc ) waveguide
, it has recently been proposed to use surface electromagnetic waves ( sew)@xcite . in those papers , the photonic crystal was a two dimensional array of rods , of infinite length normal to the plane of incidence .
instead , we have studied sew on a semi - infinite one - dimensional ( 1d ) photonic crystal sketched in fig .
while retaining all useful properties of 2d and 3d photonic crystals , a 1d dielectric periodic structure with high refractive index contrast is more attractive from a technological point of view
. the usual theoretical methods for wave propagation in 1d photonic crystals , including sew , are the floquet - bloch modal formalism , coupled wave theory , and the transfer matrix method . among these three ,
the coupled wave approach@xcite offers superior physical insight and gives simple analytical results in limiting cases .
unfortunately , the conventional coupled wave theory of kogelnik fails in the case of high refractive index contrast , which is essential for a functional 1d photonic crystal . in this paper
, we apply our recently developed semiclassical version of coupled wave theory@xcite to sew on 1d photonic crystals .
the method is analytically almost as simple as conventional coupled wave theory , and is practically exact for the achievable ratios ( e.g. 1.5:4.6 ) of the indices of refraction of the materials available to build devices .
we present here a unified description of te and tm sew . a detailed account of the properties of the te surface modes has recently been given by us in ref .
@xcite ; here we complement these findings with those for tm modes , which are slightly more complex due to the presence of brewster points in the bandgaps . as a result , we thoroughly clarify the systematics of solutions for surface em waves in semi - infinite 1d photonic crystals .
our method is formally quite different from that recently presented in ref .
@xcite , or those in ref .
@xcite , so in section ii we provide a short summary of the transfer matrix approach , in the notation of our previous work@xcite . in section
iii we rederive the exact equations for sew of tm modes and obtain from them various analytic approximations for a semi - infinite crystal .
the analogous equations for te modes were given in ref .
@xcite . with these in hand , we discuss systematics of sew . in section
iv we apply the semiclassical approximations of refs .
@xcite and @xcite to surface waves , and show that the second approximation is very accurate both for the dispersion relation and the bandgap boundaries .
we wish to describe surface states that form at the interface between a medium of low refractive index , @xmath0 , and a semi - infinite 1-d photonic crystal with layers of refractive indices @xmath1 and @xmath2 and thicknesses @xmath3 and @xmath4 .
we choose a coordinate system in which the layers have normal vector along oz . as shown in fig .
[ dsfig01 ] , the crystal is capped by a layer of the same material but different width , @xmath5 . for convenience of presentation , we split this termination layer of index of refraction @xmath1 and width @xmath5 into two sublayers , of lengths @xmath6 .
the first sublayer extends from @xmath7 to @xmath8 .
then the periodic array that forms the 1d photonic crystal consists of `` cells '' each made of three uniform layers of widths @xmath9 , @xmath4 and @xmath10 whose respective indices of refraction are @xmath1 , @xmath2 and @xmath1 .
( if @xmath11 , the unit cell will have reflection symmetry , which simplifies some relations , but does not change any physical results . ) the first cell , given index @xmath12 , ranges from @xmath8 to @xmath13 ; the second is given index @xmath14 , and ranges from @xmath15 to @xmath16 , etc .
the p - th cell runs from @xmath17 to @xmath18 and has @xmath19 when @xmath20 or @xmath21 and @xmath22 when @xmath23 .
we choose @xmath24 . for monochromatic te waves the electric field is parallel to the oy axis .
as in ref .
@xcite , we write @xmath25 where @xmath26 is the angular frequency , @xmath27 . is the vacuum wavenumber and @xmath28 is the ( constant ) @xmath29-component of the wavevector of modulus @xmath30 . for an electromagnetic wave entering the 1d photonic crystal from a uniform medium
, one has @xmath31 where @xmath32 is the angle of incidence measured from the normal . for monochromatic tm waves it is the magnetic field which lies parallel to the oy axis .
following ref .
@xcite , we write @xmath33 p. kramper , m. agio , c. m. soukoulis , a. bimer , f. mller , r. wehrspohn , u. gsele , and v. sandoghdar , _
`` highly directional emission from photonic crystal waveguides of subwavelength width '' _ , phys .
lett . * 92 * , 113903 ( 2004 ) . | we study surface states of 1d photonic crystals using a semiclassical coupled wave theory . both te and tm modes are treated .
we derive analytic approximations that clarify the systematics of the dispersion relations , and the roles of the various parameters defining the crystal . |
in engineering mechanics , _ damage _ is understood as a load - induced evolution of microstructural defects , resulting in a reduced macroscopic material integrity .
the phenomenological constitutive models of damage incorporate the irreversible phenomena by reducing the secant modulus of elasticity depending on the _ internal _ damage variable .
since the seminal contribution of @xcite , it has been well - understood that such description within the framework of local ( i.e. scale - free ) continuum mechanics leads to an ill - posed problem , resulting in localization of damage growth into an arbitrarily small region . as a remedy to this pathology
, a plethora of non - local rate - independent continuum theories , based on integral , explicit and implicit gradient approaches , has been proposed to introduce an _ internal length scale _ into the description , see e.g. ( * ? ? ?
* chapter 26 ) for a representative overview . despite a significant increase in objectivity offered by the enhanced continuum theories , the non - local damage formulations often suffer from the fact that the non - local variables are introduced into the model in an ad - hoc fashion , thus violating basic constraints of thermodynamics .
in addition , due to violation of the principle of local action , such inconsistencies are rather difficult to detect , especially in the multi - dimensional setting , e.g. @xcite . fortunately , as first demonstrated by @xcite and later confirmed by a number of independent studies , e.g. @xcite , a simple one - dimensional study of the localization behavior can serve as a convenient `` filter '' test , allowing to pinpoint various inconsistencies in the constitutive model formulation .
motivation of the present work arose from an energetic non - local damage model proposed by @xcite , which combines the basic features of an engineering damage model due to @xcite with recent advances in the mathematical theory of rate - independent irreversible processes @xcite .
such a connection provides a powerful modeling and analysis framework , allowing at the same time a rigorous mathematical treatment of the complete damage @xcite , theoretically supported numerical implementation @xcite as well as a thermodynamically consistent variational formulation of the non - local damage evolution problem . in this contribution
, a localization study of the model will be performed to examine its qualitative behavior from the engineering viewpoint .
numerical as well as analytical results are provided to illustrate its basic features with emphasis on the proper representation of the damage process from its initiation until complete failure .
let us consider a prismatic bar of length @xmath0 , subjected to displacement - controlled uniaxial tensile loading . in the sequel
, the bar will be represented by the interval @xmath1 , with boundary @xmath2 ( consisting of two points ) subjected to the dirichlet loading @xmath3 ( see ) , where @xmath4 denotes the ( pseudo- ) time taken from interval @xmath5 . following the standard thermodynamic approach to constitutive modeling , cf .
* chapter 25 ) , a state of the system is described using an admissible displacement and damages fields @xmath6 and @xmath7 , respectively .
formally , we write @xmath8 where @xmath9 denotes the set of kinematically admissible displacements , @xmath10 stands for the set of admissible damage values , and @xmath11 is the sobolev space of functions with square - integrable weak derivatives , e.g. @xcite , often denoted as @xmath12 . within the adopted _ global _ energetic framework @xcite ,
the constitutive description of the damage model is provided by the _ globally stored energy _ functional @xmath13 and by the _ global dissipation distance _
@xmath14 physically , @xmath15 represents the energy reversibly stored in the system , and @xmath16 is the energy dissipated by changing the damage field from @xmath17 to @xmath18 . in eqs .
( [ eq : ge ] ) and ( [ eq : gdd ] ) , @xmath19 [ pa ] denotes the young modulus of the material , @xmath20 [ jm@xmath21 is the amount of energy needed to disintegrate a unit volume of the material , and @xmath22 [ m ] is a characteristic length of the model .
later it will become clear that the `` @xmath23 '' term appearing in ensures the irreversibility of the damage evolution ; i.e. at any point , the damage variable can not decrease in time .
now , given the dirichlet loading @xmath3 , energetic functionals @xmath15 and @xmath16 and initial data @xmath24 and @xmath25 , the _ energetic solution _ of the damage problem is provided by functions @xmath26 and @xmath27 satisfying @xcite : global stability : : for all @xmath28 $ ] , @xmath29 and @xmath30 @xmath31 energy equality : : for all @xmath28 $ ] @xmath32 where @xmath33 denotes the power of external loading .
although the previous two conditions present the formal definition of the energetic solution , the analysis itself will be performed using the time discretization technique , see e.g. @xcite for a nice exposition . to that end
, we introduce a uniform partitioning of the time interval @xmath34 and inductively solve the minimization problem @xmath35 \hskip 5 mm \mbox{for } k = 1 , 2 , \ldots , n\ ] ] note that the previous problem is independent from @xmath36 , which is consistent with the assumed rate - independent character of the damage process .
the theoretical results gathered in @xcite show that , under reasonable data qualification , the solution of the time - discretized problem converge to the energetic solution as @xmath37 .
having established the essentials of the global energetic framework , we will now proceed with the main goal of this contribution the analysis of the simple uniaxial tensile test .
intuitively , we expect that as long as the energy density at all points of the structure stays below @xmath20 , the response of the bar remains elastic and no damage evolution occurs within the structure .
after the energy density reaches the value of @xmath20 at a certain time @xmath38 , damage is initiated and localization occurs .
therefore , the explicit description of the localization phenomenon will build on the incremental variational principle ( [ eq : incr_min ] ) .
note that , for the sake of brevity , the time instant @xmath38 and the time increment @xmath39 will be omitted in the rest of this paper .
dropping the constraints on @xmath40 for a moment , the optimality conditions for the minimization problem ( [ eq : incr_min ] ) read @xmath41 \de x \geq 0\ ] ] for all admissible variations @xmath42 vanishing on @xmath2 and arbitrary @xmath43 . assuming the involved fields are smooth enough , we formally obtain @xmath44_{\bnd } & \geq & 0\end{aligned}\ ] ] using the arbitrariness of the variations and imposing the constraints @xmath45 finally leads to the system of the karush - kuhn - tucker conditions , cf .
* section 15.2.4 ) @xmath46 corresponds to the uniform stress condition @xmath47 while eqs .
( [ eq : el2 ] ) , ( [ eq : el3 ] ) and ( [ eq : el4 ] ) provide the link between strain and damage and describe the elastic , damaging and fully damaged part of the structure , respectively .
note that by virtue of , the stress @xmath48 remains to be well - defined even in the fully damaged region , where the physical meaning of displacements @xmath49 and strains @xmath50 is rather questionable .
this open the way to the rigorous mathematical treatment of the complete damage problem , see @xcite for further discussion .
concentrating on the damaging zone only , we divide by @xmath20 and , employing identity ( [ eq : sigma_def ] ) , rewrite it in the form of a non - linear ordinary differential equation @xmath51 where @xmath52 parameterizes the softening process and ranges from @xmath53 at the onset of localization to @xmath54 at the stress - free state of complete failure .
it is also useful to rewrite in the rate form @xmath55 which is an ordinary second - order differential equation for the damage rate @xmath56 with possibly non - constant coefficients .
note that damage irreversibility requires @xmath57 .
observe that at the onset of damage , @xmath58 and @xmath59 .
therefore , simplifies to @xmath60 leading to the general solution @xmath61 with @xmath62 and @xmath63 denoting the integration constants , the latter specifying the position of the center of the localized profile . assuming that this zone corresponds to an interval @xmath64 located sufficiently far from the boundary , the damage rate has to verify four independent conditions @xmath65 yielding @xmath66 where @xmath67 is the width of the localized zone , cf .
a. the rate of the damage variable at the onset of damage is therefore given by @xmath68 the previous expression is consistent with the constraint @xmath69 since the stress rate @xmath70 is negative in the softening regime , which implies @xmath71 .
mielke , a. ( 2005 ) .
evolution of rate - independent systems . in dafermos ,
c. and feireisl , e. , editors , _ handbook of differential equations : evolutionary equations _ , volume 2 , pages 461559 .
elsevier b.v . ,
amsterdam , the netherlands .
mielke , a. , roubek , t. , and zeman , j. ( 2007 ) .
complete damage in elastic and viscoelastic media and its energetics .
wias preprint 1285 , weierstrass institute for applied analysis and stochastics , berlin . | the contribution presents an analysis of a rate - independent non - local damage model , recently proposed by @xcite .
an analytical as well as numerical solution of a simple one - dimensional bifurcation problem is performed , demonstrating that , for the elementary localization test , the model is free of pathological features . [ [ keywords ] ] keywords + + + + + + + + damage , non - locality , energetic solution , discretization in time , bifurcation |
the analysis of the epic data from a 30 ks observation of the seyfert 1 mrk 335 ( longinotti et al . 2006 ) shows that the 2 - 10 kev spectrum can be phenomenologically fitted with a power law , a broad gaussian line with e=6.22@xmath10.16 kev , @xmath2=0.66@xmath10.23 kev , ew 490 ev , and a narrow ( @xmath2 = 1ev ) absorption line with e=5.92@xmath10.04 kev and ew=50 ev .
these features are visible in the residuals of the spectrum plotted in fig.1 .
the significance of the absorption line estimated through monte carlo simulations is 99.7% .
the most obvious identification for the absorption feature is with redshifted iron k@xmath0 resonance absorption .
the identification with iron is favoured since the observed energy of the line is too high to be readily explained by k@xmath0 absorption in any of the other astrophysically abundant elements .
we present a simple model for the inflow ( centre and right panels of fig.1 ) , accounting approximately for relativistic and radiation pressure effects , and use monte carlo methods to compute synthetic spectra for qualitative comparison with the data .
this modeling was developed following sim ( 2005 ) and assuming spherically symmetric radially infalling gas .
it does show that the absorption feature can plausibly be reproduced by infalling gas providing that the feature is identified with fe xxvi .
a smooth continuous flow is ruled out by the poor agreement with the data : although the presence of a broad inverse p cygni fe xxvi k@xmath0 line profile is predicted , the absorption line is insufficiently redshifted and too broad .
an inflow over a limited range of radii ( as discrete blobs or section of infalling gas ) is more consistent with the data ( fig.1 ) .
the narrowness of the absorption line tends to argue against a purely gravitational origin for the redshift of the line , but given the current data quality we stress that such an interpretation can not be ruled out .
a longer ( 100 ks ) xmm - newton observation of mrk 335 has been performed this year .
the analysis of the integrated spectrum reveals a double - peaked fe line .
a broad accretion disc line is likely to be present but the peaks are due to narrower components at 6.4 and 7 kev ( oneill et al . in prep . ) .
a preliminary time - resolved analysis shows that the narrow peaks are variable .
2 shows the spectra from three portions of the light curve .
the narrow peak at 6.4 kev , clearly present in the first 30 ks , disappears in the central portion .
the 7 kev peak instead shows up only in the last 60 ks .
the variable narrow lines could be tentatively associated to the presence of flares in the light curve , but a much more detailed and careful analysis is necessary before speculating on their origin . as regard to the absorption line observed in the archival 30 ks observation ,
it is marginally detected only in the first portion of the longer exposure .
further investigation on these data will hopefully clarify all the issues reported here . | the analysis of hard x - ray features in _ xmm - newton _ data of the bright sy 1 galaxy mrk 335 is reported here .
the presence of a broad , ionised iron k@xmath0 emission line in the spectrum , first found by gondoin et al.(2002 ) , is confirmed .
the broad line can be modeled successfully by relativistic accretion disc reflection models .
regardless of the underlying continuum we report , for the first time in this source , the detection of a narrow absorption feature at the rest frame energy of 5.9 kev .
if the feature is identified with a resonance absorption line of iron in a highly ionised medium , the redshift of the line corresponds to an inflow velocity of 0.11 - 0.15 c. preliminary results from a longer ( 100ks ) exposure are also presented . |
a persistent problem in understanding the absorbing material in ngc 4151 has been reconciling the vastly different gas columns inferred for the x - ray absorption and for the uv absorption .
the x - ray absorbing column varies between @xmath1 and @xmath2 .
bromage et al .
( 1985 ) estimated a total column for the uv - absorbing material of no more than @xmath3 .
the neutral hydrogen column is variable ( kriss et al .
the bulk of the absorption is in low column density gas with @xmath4 and doppler parameter @xmath5 .
any low - b component has a neutral column no greater than @xmath6 .
one possibility for reconciling these differences has been the recent success of warm absorber models for characterizing the x - ray absorption and the associated uv absorption lines in 3c 351 and ngc 5548 ( mathur et al . 1994 ; mathur et al . 1995 ) . in such models
the absorption arises in gas photoionized by the central engine ( e.g. , netzer 1993 ; krolik & kriss 1995 ) . the x - ray absorption is dominated by highly ionized species of heavy ions ( e.g. , o vii and o viii ) .
the total gas columns can be quite high ( @xmath1@xmath2 ) , with relatively low columns in the lower ionization species responsible for the uv absorption .
warm absorber models with a reflection component can fit the x - ray spectrum of ngc 4151 ( weaver et al .
1994a , b ) .
kriss et al .
( 1995 ) find that similar models can also account for the high ionization lines in ngc 4151 ( e.g. , o vi , n v , and c iv ) , but they can not simultaneously match the particularly strong absorption in lower ionization species such as h i , c iii , and si iv .
they conclude that a single - zone warm absorber is insufficient . to search for absorption components that might possibly be identified with the x - ray absorbing gas
, i examined archival high resolution ghrs spectra of the c iv and mg ii line profiles in ngc 4151 .
fig.1 shows the spectrum of ngc 4151 in the c iv region with 14 @xmath7 resolution obtained in 8486 s using grating g160 m of the ghrs on 28 october 1994 . a model consisting of an underlying power law continuum , three broad gaussian emission lines , and 8 c iv absorption line doublets fits the data well and gives @xmath8 for 1800 points and 50 free parameters .
although the deepest and broadest c iv doublet is saturated , the bottom of the line profile is not black .
either this gas only partially covers the source ( at the 90% level , both continuum and broad line ) , or 10% of the continuum flux is scattered around the absorbing region back into our line of sight .
narrow - line emission is visible on the red side of the c iv absorption trough .
this emission is apparently unabsorbed by the broad absorbing gas ; a final layer of absorbing gas , however , lying at the systemic velocity of ngc 4151 , absorbs the core of the narrow - line profile .
this is presumably the ism or halo of ngc 4151 .
the spectrum of the mg ii region at 10 @xmath7 resolution obtained in a 1414 s integration with grating g270 m of the ghrs on 29 october 1994 is shown in fig.2 .
the best fit to the modeled emission and absorption profile gives @xmath9 for 1438 points and 22 free parameters .
as with c iv , the mg ii emission was modeled with 3 gaussians .
seven mg ii absorption doublets are required .
table 1 gives the velocities , equivalent widths , doppler parameters , and column densities of each of the absorption components fit in the c iv and the mg ii spectra .
& & & & & & & & + & & + & & & & & & & & + # & @xmath10 & ew & _ b _ & @xmath11 & @xmath10 & ew & _ b _ & @xmath12 + & @xmath13 & ( ) & @xmath13 & @xmath14 & @xmath13 & ( ) & @xmath13 & @xmath14 + & & & & & & & & + 1 & @xmath15 & 0.514 & 294 & @xmath16 & & & & + 2 & @xmath17@xmath18 & 0.120 & @xmath19 & @xmath20 & @xmath21 & 0.143 & @xmath22 & @xmath23 + 3 & @xmath17@xmath24 & 0.642 & 203 & @xmath25 & & & & + 4 & @xmath26@xmath27 & 0.310 & @xmath28 & @xmath29 & @xmath17@xmath30 & 1.259 & @xmath31 & @xmath32 + 5 & @xmath33 & 0.083 & @xmath34 & @xmath35 & @xmath36 & 0.052 & @xmath37 & @xmath38 + 6 & @xmath39 & 1.026 & 163 & @xmath40 & @xmath41 & 1.116 & 235 & @xmath42 + 7 & @xmath43 & 4.018 & 234 & @xmath44 & @xmath45 & 0.852 & 176 & @xmath46 + 8 & & & & & @xmath47 & 0.329 & @xmath48 & @xmath49 + 9 & @xmath50 & 0.407 & @xmath28 & @xmath51 & @xmath52 & 0.134 & @xmath53 & @xmath54 +
for the absorption components intrinsic to ngc 4151 , i assume that the gas is photoionized by the active nucleus .
computing photoionization models similar to those discussed by krolik & kriss ( 1995 ) and kriss et al .
( 1996 ) , i search for ionization parameters and total column densities that match the mg ii and c iv columns seen in the data .
table 2 summarizes the column density ratios of each of the absorption components and the matching ionization parameters and total column densities .
the velocities are now relative to the systemic velocity of ngc 4151 ( @xmath55 , mundell et al .
1995 ) . & & & & + # & @xmath56 & @xmath57 & log _ u _ & log @xmath58 + & @xmath13 & & & @xmath59 + & & & & + 1 & @xmath60 & @xmath61 & @xmath62 & + 2 & @xmath63 & 0.12 & @xmath64 & 18.3 + 3 & @xmath65 & @xmath61 & @xmath62 & + 4 & @xmath17@xmath66992 & 3.73 & galactic & 20.3 + 5 & @xmath17@xmath66830 & 0.060 & @xmath67 & 18.1 + 6 & @xmath17@xmath66805 & 0.085 & @xmath68 & 18.2 + 7 & @xmath17@xmath66321 & 0.004 & @xmath69 & 19.9 + 8 & @xmath17@xmath66193 & @xmath70 & @xmath71 & 17.018.0 + 9 & @xmath26@xmath661 & 0.026 & @xmath72 & 18.6 + note that all the absorbing systems have fairly low ionization parameters .
none of the systems in which mg ii absorption is visible is a good candidate for association with the warm x - ray absorbing gas , which typically has high ionization parameters @xmath73 and high total column densities log @xmath74 ( weaver et al .
1994a , b ) . while components 1 and 3 might be possible candidates , note that component 1 is visible only at this single epoch .
it is absent from all other ghrs observations at both higher and lower flux levels ( weymann et al .
observations of higher ionization species such as si iv or n v are required to set more stringent constraints on the ionization parameters and the total column densities of components 1 and 3 .
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1997 , this volume | observations of the c iv and mg ii absorption lines in the seyfert 1 galaxy ngc 4151 obtained with the ghrs in october 1994 are presented .
the data from the stsci archive show multiple broad and narrow components in both species .
in addition to galactic absorption , four narrow and four broad systems associated with ngc 4151 are identified .
two broad systems dominate the total equivalent width , and their mean blueshift and width are comparable to the broad lyman line and continuum absorption seen in far - uv spectra from the hopkins ultraviolet telescope . narrow - line c iv emission is present on the red side of the broadest absorption trough , and narrow absorption at the systemic velocity of ngc 4151 , presumably in its own ism , absorbs the core of the narrow emission line .
strong mg ii absorption is present in all but two velocity systems .
ratios relative to the corresponding c iv components suggest a low ionization parameter for the absorbing gas : @xmath0 .
this makes none of the identified uv absorption systems a good candidate for association with the warm x - ray absorbing gas . |
silicon is an indirect gap semiconductor with six minima ( valleys ) in the conduction band . in the case of ( 001)-oriented wafers , the long axes of two of the fermi ellipsoids are perpendicular to the @xmath1 plane of a @xmath2 interface ( with @xmath3 ) , while the long axes of the other four have an in - plane orientation ( @xmath4 ) .
a quantum well is formed at the interface by applying a positive voltage @xmath5 to the gate , and the electron motion in @xmath6 direction is quantized .
the difference in @xmath7 causes a splitting of the energy spectrum of bound states into two independent ladders of levels : the twofold - degenerate ladder of eigenenergies @xmath8 and a fourfold - degenerate ladder @xmath9 . due to the higher effective mass in the @xmath6-direction , the lowest energy level in the potential
well is @xmath10 .
the self - consistent calculations ( see e.g @xcite ) predicts that the excited levels @xmath0 and @xmath11 are very close on energy scale and become occupied ( cross the fermi energy @xmath12 ) at the carrier concentration @xmath13 . while @xmath14 increases linearly with @xmath5 , the fourfold - degenerate @xmath0 stays `` pinned '' to the fermi energy and @xmath15 is almost constant even for the highest possible gate voltages . in both cases
the difference between the fermi energy and the eigenenergies of excited states is at most a few percent of @xmath16 , the difference between the fermi energy and the ground level , for all gate voltages .
in our experiments we have employed the hall bar samples of russian provenance , with 200 nm thick gate oxide and the top mobilities @xmath17 above @xmath18 at liquid helium temperature .
the concentration of electrons in the inversion layer is related to the gate voltage by @xmath19 with the threshold voltage close to @xmath20 .
the samples are 0.25 mm wide and 0.5 mm long with the distance between potential leads 0.625 mm .
the highest concentration of carriers @xmath21 is reached for @xmath22 .
this is well above @xmath23 , the onset voltage of the occupation of excited subbands . according to our numerical modeling of the electronic structure @xcite , @xmath24 while @xmath25 at the highest concentration .
the samples exhibit the previously unreported features , which turned out to be important in experiments with high carrier concentration .
the metallic ( aluminium ) gate of samples overlaps to the thicker oxide outside the lithographically defined hall bar shape .
the thin molybdenium layer separates the aluminum gate and the silicon oxide .
the mo layer can be seen by cross - sectional electron microscopy ( fig .
[ sample ] ) and allows identification of a step in the thickness of oxide layers . therefore , a parallel channel is formed at the sample edges .
this explains two series of magnetoresistance oscillations at high concentration of carriers we reported in our previous publications ( see @xcite and references therein ) .
an attempt to attribute the second series to the sdh oscillations of electrons from the second subband turned out to be wrong , the ratio of periods of the two series of sdh oscillation was 9 : 2 , i.e. it corresponds to the ratio of the two oxide layers . to suppress the effect of parallel edge - channels , approximately @xmath26 of the gate metal was lithographically removed on the sample edges .
after this procedure the second series of sdh oscillations , corresponding to the sample edge channels , disappeared .
the high mobility of samples was not reduced by this procedure .
the magnetoresistance of si(001 ) mosfets with high density of electrons in the inversion layer was measured as a function of the magnetic field @xmath27 up to 11 t for a series of fixed gate voltages in the bath of pumped @xmath28he . the standard ac technique was used with a frequency 13 hz .
the measuring current @xmath29 yields the current density @xmath30 . here
we report results obtained for two samples .
the sample a has a top mobility @xmath31 at 0.45 k. the magnetoresistance and the hall resistance of this sample are presented in figs .
[ resa ] and [ halla ] for a dense set of gate voltages .
the sample b magnetoresistance ( the top mobility @xmath32 is shown in fig .
[ resb ] only for selected gate voltages @xmath5 . for this sample
we also show the current - density and temperature dependence of the magnetoresistance at the maximum gate voltage @xmath33 ( see figs .
[ current ] and [ temperature ] ) .
anomalous behavior was observed for all gate voltages corresponding to occupied excited subbands .
first , a novel series of sdh oscillations appeared , most pronounced at the highest gate voltage 120 v where the amplitude of sdh oscillations of the first subband is very small .
the oscillations are periodic in @xmath34 .
their period is almost independent of @xmath5 and close to @xmath35 for both samples .
second , a strong negative magnetoresistance and the nonlinear field dependence of the hall resistance accompany the novel oscillations at high carrier concentrations .
both the novel oscillations and the negative magnetoresistance are most pronounced at the lowest temperatures ( @xmath36 0.4 k ) and the smallest density of current ( @xmath37a ) used in our measurements .
the influence of the current density on the observed effect is illustrated in fig .
[ current ] .
the current was first increased by an order of magnitude and then by two orders of magnitude .
both amplitudes of the novel oscillations and the negative magnetoresistance are gradually suppressed , while the amplitude of sdh oscillations from the main series remain unchanged .
an independent measurement , in which the current density was kept low and the bath temperature was increased to 4.2 k , confirmed that the suppression of amplitudes of the novel oscillations and of the negative magnetoresistance is really due to the overheating of 2d electron gas in the inversion layer .
again , the amplitude of oscillations from the main series are unchanged .
we attribute the observed anomalies to the large difference between the electron structure of the ground subband and excited subbands .
the twofold - degenerate ground subband contains many landau levels even for highest magnetic fields .
the electron mobility in this subband quickly decreases with increasing gate voltage .
the roughness of si / sio interface dominates the electron scattering .
the dingle temperature is well above the electron layer temperature as witnessed by the temperature independent amplitude of the sdh oscillations . the quasiclassical picture of the electric conductivity seems to be relevant .
the occupation of excited subbans is very small and only a small number of landau levels should be occupied even at relatively week @xmath27 .
the electrons in the subband attached to the level @xmath11 have an effective mass 0.19 , the same as the electrons in the ground subband . with the difference @xmath38 of a few mev at high concentration limit
, the first landau level can cross the fermi energy at relatively week @xmath39 .
then the subband is emptied and the density of states of electrons belonging to the twofold - degenerate ladder is halved .
this can contribute to reduction of the scattering rate and to the negative magnetoresistance .
on the other hand , we believe that the fourfold - degenerate subband is not emptied by increasing @xmath27 and that the level @xmath0 stays pinned to the fermi energy also in the presence of the magnetic field .
we suggest that it is responsible for the novel oscillations the period of which does not depend on @xmath5 .
the landau level separation in this subband is smaller due to the larger cyclotron effective mass @xmath400.43 .
therefore , the amplitude of oscillations should be more sensitive to the temperature , in agreement with the experimental data .
the experiments also indicate that the dingle temperature of these electrons is rather low . assuming the fourfold degeneracy
, the concentration of electrons corresponding to @xmath41 would be close to @xmath42 .
two very different groups of electrons contribute to the magnetoresistance of a sample with high electron concentrations : the electrons from the ground subband and the more mobile electrons from the excited subbands . while the transport mediated by the ground state electrons should by described quasiclassically ,
the quantization of electron states is important for excited subbands . therefore , the deviations from the standard quasiclassical model of transport by two groups of carries should be anticipated . with increasing temperature
the energy @xmath43 becomes comparable with the separation between landau levels .
the electron - electron scattering increases , the importance of a small group of electrons from the excited subband decreases and the observed anomalies are suppressed .
this work was supported by avoz 1 - 010 - 914 and in part by the grand agency of the czech republic under grants no .
202/01/0754 and 202/96/036 . | we present an experimental study of electron transport in inversion layers of high - mobility si(001 ) samples with occupied excited subbands .
the second series of oscillations , observed in addition to the main series of shubnikov - de hass oscillations , is tentatively attributed to the occupation of a subband associated with the @xmath0 level . besides
, a strong negative magnetoresistance and nonlinear field dependence of the hall resistance accompany the novel oscillations at high carrier concentrations .
the heating of the 2d electron layers leads to suppression of the observed anomalies . , , , , and si mosfet , magnetoresistance , hall effect 73.40.qv , 73.50.jt |
non - local quantum correlations or entanglement between space - separated parties is one of the most fertile and thought - generating properties of quantum mechanics .
recently it has become a very useful resource for many of the applications in quantum information theory and this has led to a lot of work devoted to understanding how it can be quantified and manipulated .
bipartite pure state entanglement is almost completely understood , while many questions are still open for the mixed state case . for pure states ,
the schmidt decomposition @xcite has proven to be a very useful tool , since it allows to write any pure state shared by two parties a and b in a canonical form , where all the information about the non - local properties of the state is contained in the positive schmidt coefficients .
the non - local properties of quantum states can be also specified by means of other quantities invariant under the action of local unitary transformations .
an interesting type of these invariants are given by polynomial combination of the coordinates of the state in a product basis , and the relation between these invariants and the schmidt coefficients is well known .
some novel aspects , compared to the bipartite case , appear for entangled systems of more than two parties . in this work we study the canonical forms of three - qubit pure states , extending the results of bipartite systems .
first we analyze the forms proposed for generalizing the schmidt decomposition for three - qubit pure states .
then , we relate one of these decompositions to the polynomial invariants studied in @xcite .
we give a one - to - one correspondence between a canonical form for a three - qubit pure state and a complete set of polynomial invariants describing its entanglement properties .
we also classify the different types of canonical forms by means of the minimal number of local bases product states ( lbps ) , i.e. the minimal number of non - local parameters , needed for the specification of a state . for any three - qubit pure state we give its decomposition with the minimal number of lbps and the procedure that has to be applied in order to build it .
finally we indicate how to generalize the results to systems of @xmath0-qubits , where many difficulties arise .
the schmidt decomposition has been a very useful tool for the study of entanglement properties of bipartite systems . for a generic bipartite pure state @xmath1 it reads [ bischmidt ]
|=_i=1^l _ i|ii , _ i0 , where @xmath2 , @xmath3 , being @xmath4 orthonormal vectors in each subsystem , and @xmath5 are the schmidt coefficients
. it would be very interesting to find for three - qubit pure states a canonical decomposition generalizing the features of the schmidt decomposition .
however , the trivial generalization is not possible @xcite and it is not evident how to extend the schmidt decomposition to the case of @xmath0-party systems ( @xmath6 ) .
indeed several forms have been proposed ( see for instance @xcite ) . in recent work
@xcite we gave a generalization of the schmidt decomposition for three - qubit pure states , in the sense that the coefficients of this decomposition carry all the information about the non - local properties of the state , and do so minimally and unambiguously , i.e. the decomposition is not superflous . starting from a generic state shared by three parties , a , b and c , [ state ] | in this paper we analyze the canonical forms into which any pure three - qubit state can be cast .
the minimal forms , i.e. the ones with the minimal number of product states built from local bases , are also presented and lead to a complete classification of pure three - qubit states . this classification is related to the values of the polynomial invariants under local unitary transformations by a one - to - one correspondence . |
the cosmological principle ( cp ) is one the most fundamental hypothesis upon which the concordance model based . in this work ,
we discuss the validity of the cosmological isotropy with different compilations of type ia supernovae ( sne ) , namely the union2.1 @xcite ) and jla data sets @xcite , using a hemispherical comparison method , hence determining whether the cosmological isotropy actually holds in large angular scales , and whether such hypothesis is not only a mathematical simplification , but a valid assumption .
we test the isotropy of the universe expansion by mapping the @xmath0 and @xmath1 parameters through the celestial sphere , so that an opposite hemisphere comparison is performed following ref .
( see also ref . ) .
each pair of these hemispheres is well defined by the healpix pixelization scheme @xcite , such that we fit @xmath0 and @xmath1 by minimising the following quantity @xmath3 where the set @xmath4 contains the observational information of the sne data , i.e. , redshift , distance moduli and associated uncertainty of the _ i - th _ object , respectively , where @xmath5 is the distance modulus given by a specific cosmological model according to @xmath6 } + 42.38 - 5\log_{10}(h ) \;,\ ] ] where @xmath7 , @xmath8 , and @xmath9 is the adimensional luminosity distance , whose arguments are the redshift @xmath10 , in addition to the set of cosmological parameters @xmath11 which describe the underlying cosmological model , @xmath9 is given by a cosmographic expansion up to second order , where @xmath12 . ] .
furthermore , we quantify the angular non - uniformity of the data sets using the method named sigma - map , as performed in ref .
( see also ref . ) , which is based upon the two - point angular correlation function of the cosmic objects distribution computed inside each assigned hemisphere .
in other words , this estimator constructs a pixelised map in which its colour ranges from blue , when the actual distribution of sne is less correlated than the mean value expected in a random catalogue , to red , in the case when the correlation is larger .
in addition , we analyse the anisotropies of the cosmological parameters and the angular sne distribution not only in the pixel space , but in the multipole space as well , so that @xmath13 represents the quantity scanned through the celestial sphere , such as the @xmath0 and @xmath1 parameters . ] , and @xmath14 is the angular power spectrum of the hubble- , q- and sigma - map .
since we are interested in large scale angular correlations , we limit our analyses to @xmath15 .
the statistical significance of the hubble and q - maps analyses is estimated with two different approaches . in the first approach ,
the galactic coordinates of each sne is fixed , yet the set @xmath16 is shuffled ( hereafter _ shuffle _ test ) .
the second approach also keeps the original @xmath16 of each object yet the sne positions are isotropically redistributed on the celestial sphere ( hereafter the _ mc _ test ) . hence , we can test whether the directional dependence of these parameters are statistically significant in its amplitude as well as in its direction .
the results of the sigma - map analyses are shown in fig .
[ fig1 ] ( pixel space ) and fig .
[ fig2 ] ( multipole space ) for both sne data sets .
it is possible to note that they present a preferred direction on the celestial sphere , as discussed on the description of fig .
[ fig1 ] , and that the both sne catalogues are highly inconsistent with a perfectly isotropic distribution , since the analyses performed in multipole space present much higher @xmath17 s than their average values obtained by the mcs . moreover , the hubble- and q - map results are featured in fig .
[ fig3 ] ( [ fig4 ] ) for the union2.1(jla ) compilations , for the analyses performed in pixel space , whereas fig
. [ fig5 ] ( [ fig6 ] ) refer to the analyses carried out in multipole space for the union2.1 ( jla ) compilations as well .
+ we note that the direction @xmath18 obtained for the union2.1 hubble - map is consistent with the bulk flow motion direction estimated in ref . , that is , @xmath19 km / s towards @xmath20 , as well as many works which probed the cosmological isotropy with a similar approach @xcite .
moreover , the anisotropy of the @xmath0 can possibly explain the tension between the @xmath0 determinations @xcite ) from low-@xmath10 standard candles @xcite and planck cmb temperature @xcite .
it was found that the maximal @xmath0 variance through the celestial sphere is consistent with their values , and that its direction is consistent with the bulk flow motion as well .
this reinforces the idea that such anisotropy arises as a local effect , instead of an intrinsic cosmological anisotropy .
we also evaluate the strength of the correlation between these maps , finding a negligible correlation between the hubble- and q - maps with the sigma - map of the union2.1 data set ( @xmath21 and @xmath22 , respectively ) , even though the correlation is moderate in the jla analyses : @xmath23 and @xmath24 , respectively .
thus , we conclude that the anisotropy detected on the hubble and q - maps in the jla data is possibly explained by the incompleteness of the sample in terms of sky coverage , while the anisotropy pointed by the union2.1 sne is most likely of local origin .
+ the results of the statistical significance are depicted , in multipole space , in figs .
[ fig5 ] and [ fig6 ] for the union2.1 and jla case , respectively .
it is possible to note that the union2.1 hubble - map present mild disagreement with the _ mc _ and _ shuffle _ tests specially in the lower @xmath25 ( @xmath26 ) , and that the q - map strongly disagrees with both realisations except for the dipole case , thus showing significant evidence for anisotropy in this analysis .
nevertheless , this signal can be ascribed to the limited constraining power of the union2.1 data on this parameter , besides the degeneracy with the hubble parameter . for the jla catalogue
, there is a better agreement between the real data and the _ shuffle _ realisations in both hubble- and q - maps , except for the dipole contributions , whereas the data presents stronger disagreement with the _ mc _ runs specially in the q - map analysis .
this result shows , once again , the fact that the angular non - uniformity of the jla sample indeed biases the hubble and q - map analyses .
we have shown that the anisotropy detected on the @xmath0 mapping with the sne sample can be attributed to the bulk flow motion due to its proximity of reported directions in the literature , and the @xmath1 significant anisotropy probably arises due to the limitation of this data set . on the other hand ,
the jla directional analyses show a significant dependence with its celestial coverage , then biasing the hubble and q - map results .
therefore , we conclude that there is no significant violation of the cosmological isotropy with the latest sne data in the @xmath27 range , albeit next - generation surveys such as lsst and euclid may improve this test with the greater precision and much larger data sets that they shall provide .
we thank roy maartens , ribamar reis and ivan soares ferreira for helpful discussions .
we acknowledge the healpix package for the derivation of our analyses .
this work is supported by cnpq , faperj and capes . | we investigate the validity of the cosmological principle by constraining the cosmological parameters @xmath0 and @xmath1 through the celestial sphere .
our analyses are performed in a low - redshift regime in order to follow a model independent approach , using both union2.1 and jla type ia supernovae ( sne ) compilations .
we find that the preferred direction of the @xmath0 parameter in the sky is consistent with the bulk flow motion of our local universe in the union2.1 case , while the @xmath1 directional analysis seem to be anti - correlated with the @xmath0 for both data sets .
furthermore , we test the consistency of these results with monte carlo ( mc ) realisations , finding that the anisotropy on both parameters are significant within @xmath2 confidence level , albeit we find a significant correlation between the @xmath0 and @xmath1 mapping with the angular distribution of sne from the jla compilation .
therefore , we conclude that the detected anisotropies are either of local origin , or induced by the non - uniform celestial coverage of the sne data set . |
understanding sea quark effects in the light hadron spectrum is an important issue , sharpened by the recent finding of a systematic deviation of the quenched spectrum from experiment@xcite . to this end , we have been pursuing @xmath0 qcd simulations using an rg - improved gauge action and a tadpole - improved clover quark action @xcite , to be called * rc * simulations in this article .
the parameters of these simulations are listed in table [ tab : param ] .
the statistics at @xmath3 have been increased since lattice98 , and the runs at @xmath4 are new .
in addition we have carried out quenched simulations with the same improved action , referred to as * qrc * , for a direct comparison of the full and quenched spectrum .
the @xmath5 values of these runs , given in table [ tab : param ] , are chosen so that the lattice spacing fixed by the string tension matches that of full qcd for each value of sea quark mass at @xmath6 and 2.1 .
quenched hadron masses are calculated for valence quark masses such that @xmath7 0.80.5 , which is similar to those in the * rc * runs . in this report we present updated results of the full qcd spectrum and light quark masses .
we also discuss sea quark effects by comparing the * rc * and * qrc * results . for reference
we use quenched results with the plaquette gauge and wilson quark action @xcite as well , which we denote as * qpw*. [ tab : param ] lllll + lattice & @xmath8 & # traj . &
@xmath9 & @xmath10 [ fm ] + @xmath11 & 0.1409 & 6250 & 0.806(1 ) & 0.289(3 ) + @xmath12 & 0.1430 & 5000 & 0.753(1 ) & 0.152(2 ) + @xmath13 & 0.1445 & 7000 & 0.696(2 ) & 0.269(3 ) + @xmath14 fm & 0.1464 & 5250 & 0.548(4 ) & 0.248(2 ) + @xmath15 & 0.1375 & 7000 & 0.805(1 ) & 0.204(1 ) + @xmath16 & 0.1390 & 7000 & 0.751(1 ) & 0.193(2 ) + @xmath17 & 0.1400 & 7000 & 0.688(1 ) & 0.181(1 ) + @xmath18 fm & 0.1410 & 7000 & 0.586(3 ) & 0.170(1 ) + @xmath19 & 0.1357 & 2000 & 0.806(2 ) & 0.1342(6 ) + @xmath20 & 0.1367 & 2000 & 0.757(2 ) & 0.1259(5 ) + @xmath21 & 0.1374 & 2000 & 0.690(3 ) & 0.1201(5 ) + @xmath22 fm & 0.1382 & 2000 & 0.575(6 ) & 0.1128(3 ) + @xmath19 & 0.1351 & 2000 & 0.800(2 ) & 0.1049(2 ) + @xmath23 & 0.1358 & 2000 & 0.754(2 ) & 0.1012(3 ) + @xmath24 & 0.1363 & 2000 & 0.704(3 ) & 0.0977(3 ) + @xmath25 fm & 0.1368 & 2000 & 0.629(5 ) & 0.0947(2 ) + lllll + & & + @xmath5 & @xmath10 [ fm ] & & @xmath5 & @xmath10 [ fm ] + 2.187 & 0.2079(15 ) & & 2.416 & 0.1359(7 ) + 2.214 & 0.1977(13 ) & & 2.456 & 0.1266(13 ) + 2.247 & 0.1853(9 ) & & 2.487 & 0.1206(9 ) + 2.281 & 0.1727(10 ) & & 2.528 & 0.1130(9 ) + 2.334 & 0.1577(9 ) & & 2.575 & 0.1065(7 ) +
the analysis procedure of our full qcd spectrum data follows that in ref .
@xcite : @xmath26 and @xmath27 are used to set the scale and determine the up and down quark mass @xmath28 , while the strange quark mass @xmath29 is fixed from either @xmath30 or @xmath31 .
we tested several fitting forms for the continuum extrapolation , and found that the fit is stable ; e.g. , for the meson masses , linear extrapolations in @xmath32 and in @xmath33 are consistent with each other and a quadratic fit in @xmath32 is also consistent within 2 standard deviations . here , we present results from the linear extrapolation in @xmath32 .
= 7.5 cm = 7.5 cm fig .
[ fig : spectrum ] shows an update of results for vector meson and octet baryon masses in comparison to those from the * qpw * simulation . with increased statistics at @xmath34 and new points at @xmath35
, we find our conclusion to remain unchanged since lattice98 , _
i.e. , _ meson masses in full qcd extrapolate significantly closer to experiment than in quenched qcd . for baryons ,
the statistical errors are still too large to draw definitive conclusions .
in order to obtain a deeper understanding of the sea quark effect in meson masses , we investigate how their values depend on the sea quark mass . in this test
, the valence strange quark mass is fixed by a phenomenological value of the ratio @xmath36 . to avoid uncertainties that may arise from chiral extrapolations ,
the light dynamical quark mass is set to one of the values corresponding to @xmath37 or 0.5 .
the values of the masses `` @xmath38 '' and `` @xmath27 '' of fictitious mesons for such quark masses can then be determined by interpolations or short extrapolations of hadron mass results . in fig .
[ fig : massratio ] , we plot `` @xmath39 '' as a function of the lattice spacing normalized by `` @xmath27 '' for different sea quark masses . making linear extrapolations in @xmath32 , we observe that the continuum limits of the two quenched simulations * qrc * and * qpw * are consistent . on the other hand , the full qcd result from * rc * exhibits an increasingly clearer deviation from the quenched value toward lighter sea quark masses .
we consider that this result provides a clear demonstration of the sea quark effect on vector meson masses .
= 7.5 cm = 7.5 cm = 7.5 cm we plot our results for light quark masses in the @xmath40 scheme at @xmath412 gev in fig .
[ fig : mq ] , together with the quenched results of ref .
continuum extrapolations are made linearly in @xmath32 with the constraint that the three definitions ( using axial vector ward identity(awi ) or vector ward identity(vwi ) with either @xmath42 from sea quarks or partially quenched @xmath42 ) yield the same value .
we confirm our previous finding@xcite that i ) quark masses in full qcd are much smaller than those in quenched qcd , and ii ) the large discrepancy in the strange quark mass determined from @xmath30 or @xmath31 , observed in quenched qcd , is much reduced .
our current estimate for quark masses in @xmath43 qcd are @xmath44 mev , @xmath45 mev ( @xmath46-input ) and @xmath47 mev ( @xmath48-input ) .
the quoted errors include our estimate of the systematic errors due to the choice of functional form of continuum extrapolations and the definition of the @xmath40 coupling used in the one - loop tadpole improved renormalization factor .
our results for quark masses are smaller than the values often used in phenomenology@xcite , though the ratio @xmath49 26(3 ) is consistent with the result 24.4(1.5)@xcite from chiral perturbation theory .
the small values are quite interesting , especially for the strange quark mass ; a smaller strange quark mass raises the prediction of the standard model for the direct cp violation parameter @xmath50 , as strongly favored by the experimental results from the ktev @xcite and na31 collaborations @xcite .
this work is supported in part by grants - in - aid of the ministry of education ( nos . 09304029 , 10640246 , 10640248 , 11640250 , 11640294 , 10740107 , 11740162 ) .
se and kn are jsps research fellows .
aak , tm and hps are supported by the research for the future program of jsps , and hps also by the leverhulme foundation . | we present updated results of the cp - pacs calculation of the light hadron spectrum in @xmath0 full qcd .
simulations are made with an rg - improved gauge action and a tadpole - improved clover quark action for sea quark masses corresponding to @xmath10.6 and the lattice spacing @xmath20.09 fm .
a comparison of the @xmath0 qcd spectrum with new quenched results , obtained with the same improved action , shows clearly the existence of sea quark effects in vector meson masses .
results for light quark masses are also presented . |
as a complement to detailed simulations of wolf - rayet ( wr ) winds ( e.g. , * ? ? ?
* ; * ? ? ?
* ) , we have developed a set of simple analytic models using diffusive cak - type line driving with frequency redistribution @xcite . in this paper
, we apply these models to a preliminary study of the @xmath0 relation for wr stars , which is important for the study of wr stars as progenitors of long - duration gamma - ray bursts @xcite .
the details of the basic model are discussed in @xcite .
we compare our results with those from @xcite ( hereafter vdk ) using their wn star parameters ( see figure [ vdfig ] ) .
the metal abundances were provided by a. heger ( private communication ) from a 25 @xmath5 evolution model based on solar abundances from @xcite . while the @xmath2 from these abundances is smaller than the traditional @xmath6 , uncertainties in other model parameters
are expected to dominate over uncertainties in abundance .
figure [ vdfig ] shows the metallicity dependence of our wnl model , as compared to the model in vdk .
a least - squares fit to our result over @xmath3 gives @xmath7 , where @xmath8 , very close to the vdk result of @xmath9 .
it appears that our @xmath1 flattens more quickly than those of vdk , perhaps because fe saturates more quickly with our more complete line list .
calculations to higher @xmath2 need to be done to confirm that there is indeed a flattening , however .
log @xmath1 vs. log @xmath10 for a typical wnl star ( @xmath11 ) .
plusses and lines are from @xcite , figure 2 .
crosses are from this paper . ]
we have applied analytic wr wind models to the study of @xmath1 as a function of @xmath2 . our preliminary results for a wnl - type star show a power - law dependence of @xmath1 with @xmath2 over @xmath12 , with index @xmath8 , similar to the the findings vdk .
however , our @xmath1 seems to flatten more quickly .
we plan to cover a wider range in @xmath2 to confirm this and to perform the same analysis for wc stars .
a. onifer would like to thank alexander heger for helpful discussions and valuable data .
portions of this work were performed under the auspices of the u.s .
department of energy by los alamos national laboratory under contract no . | to better understand wolf - rayet stars as progenitors of gamma - ray bursts , an understanding of the effect metallicity has on wolf - rayet mass loss is needed . using simple analytic models , we study the @xmath0 relation of a wn star and compare the results to similar models .
we find that @xmath1 roughly follows a power law in @xmath2 with index 0.88 from @xmath3 and appears to flatten by @xmath4 . |
the fast x - ray transient source xte j1901 + 014 was discovered [ 4 ] by the all - sky monitor asm on board the rxte observatory during the powerful outburst on april 6 , 2002 lasted from 3 min to 3.15 hours and reached the peak flux @xmath10.9 crab in the 1.5 - 12 kev energy band ( fig.1 , right panel ) .
the source position was determined as ra = 19@xmath2 01@xmath3 45@xmath4.95 , dec = + 1 2415.7(j2000 ; 3uncertainty ) .
the analysis of the archival asm data [ 5 ] revealed a previous outburst from the same position on june 21 , 1997 .
this outburst was longer than 6 min and shorter than 8 hr , with a peak flux of @xmath10.4 crab ( fig . 1 , left panel ) .
the obtained information about xte j1901 + 014 was not enough to make any confident conclusions about its nature , but it was noted that the time scale of this flare is similar to those of such events observed from the black hole binary v4641 sgr . in this report
we briefly present results of observations of xtej1901 + 014 with the integral and rxte observatories .
more detail analysis will be presented separately ( see [ 2 ] ) .
during the outburst in july 1997 the source flux in the 1.5 - 3 kev energy band did not exceed the background level whereas in the harder energy bands , 3 - 5 kev and 5 - 12 kev , it reached @xmath10.13 crab and @xmath10.7 crab , respectively . during the outburst in april 2002
the peak fluxes in these three bands were detected at the levels of @xmath10.8 , @xmath11.1 and @xmath11.2 crab , respectively .
thus both observed outbursts were hard .
we analysed rxte / asm archive data from junuary , 1996 to july , 2006 and could not find other such powerful outbursts from the source .
xtej1901 + 014 was detected in the quiescent state ( outside of outbursts ) by both the spectrometer rxte / pca in september , 1998 and april , 2002 , with the full exposure @xmath11650 s and an average 3 - 100 kev flux of @xmath12.8 mcrab ( is was the same in different years ) and the detector integral / isgri in 2003 - 2004 see above with an average flux of @xmath12.7 mcrab in the 17 - 100 kev energy band .
some aperiodic variability of the source flux was detected in all rxte observations .
we found a number of small flares with a duration of 40 - 60 s and a maximal flux of @xmath16 - 8 mcrab .
the origin of such variability is most likely connected with a nonsteady accretion .
analysis of the rosat all - sky survey source catalogue , has shown that the source 1rxs j190141.0 + 012618 is located in the rxte / asm error box ( 3 ) of xte j1901 + 014 . during the pointed rosat / hri observation performed on october 3 , 1994 , the source was also detected , its position was refined and the source was renamed as 1rxh j190140.1 + 012630 [ 7 ] . using the integral / isgri data we improved an accuracy of the xte j1901 + 014 localization to @xmath11.2 . as it clearly seen from fig.2
the rosat source 1rxh j190140.1 + 012630 confidently the distance between positions of xte j1901 + 014 and 1rxh j190140.1 + 012630 is about 0.3 ) falls into the integral / isgri error box for xtej1901 + 014 , that points that xte j1901 + 014 and 1rxh j190140.1 +
012630 are the same source .
we have only very poor information of the source spectral evolution during the outbursts ( see below ) , but can precisely reproduce its spectrum in the quiescent state . to obtain the broadband spectrum of the source in the quiescent state we used rxte / pca data in the 3 - 20 kev energy band and integral / isgri data in the hard energy band ( @xmath520 kev ) analysis .
it is important to note , that the pca / rxte observations were performed in 1998 , 2002 and the isgri / integral ones - in 2003 - 2004 .
thus our spectral reconstruction is correct in the suggestion that the spectrum shape of the source does not change during this time interval .
the broadband ( 3 - 100 kev ) spectrum of xtej1901 + 014 was approximated by a simple power law model with the interstellar absorption which value was fixed at n@xmath6 = @xmath7 atom/@xmath8 that is typical for this direction to the sky ( it was evaluated from the n@xmath6 map ) . the best - fit photon index is @xmath9=2.15 @xmath10 0.03 ( fig .
3 ) . we analysed small short flares registered by rxte / pca from the source ( see above ) and found that the source spectral shape did not changed during the flares .
xtej1901 + 014 is located near the galactic plane ( l = 35.38 deg , b = -1.62 deg ) , thus the galactic ridge emission could strongly affect the result of spectral measurements with rxte / pca [ 3 ] . in this report the spectrum and lightcurves of xtej1901 + 014 were obtained taking into account this contamination . in order to estimate the galactic ridge emission intensity we used the data obtaned during pointing observations of nearby transient sources performed during their `` turned off '' state .
in particular we used pointing data of gs 1843 - 02 ( l @xmath1131 deg , b @xmath11 - 0.5 deg ) observations , that is the nearest transient x - ray pulsar to obtain the galactic ridge spectrum at its position for xtej1901 + 014 .
the analysis of this data allows us to obtain the galactic ridge spectrum near gs 1843 - 02 . due to the nature of the galactic ridge emission
its spectrum has the same form in different regions of the sky with -5 deg @xmath12 b @xmath12 + 5 deg [ 3 ] .
therefore we can just renormalize this spectrum ( using the scan data ) , to get the galactic ridge spectrum at xtej1901 + 014 position .
the importance of accounting the galactic ridge emission is demonstrated by fig.4 , where the total pca / rxte spectrum is shown along with the galactic ridge and source true spectra .
however using two energy bands of rxte / asm ( 3 - 5 and 5 - 12 kev ) it is possible to roughly estimate evolution of the photon index during the outbursts . according to [ 6 ]
the photon index @xmath13 can be expressed as : @xmath14 where r - the relation between count rates in the 3 - 5 kev and 5 - 12 kev energy bands .
note that this equation was obtained for sources with powerlaw spectra . for the outburst in june , 1997
, we found that @xmath13 was not changed significantly ; for the outburst in april , 2002 - it changed from 2.4 + /-
0.1 to 1.4 + /-
* the broadband spectrum of xtej1901 + 014 in the quiescent state was obtained and investigated for the first time .
it can be approximated by a simple power law model with the photon index of @xmath12.15 without any high energy exponential cutoff . *
the powerful outbursts of the source in 1997 and 2002 are not the 1st type x - ray bursts because they become harder with time , resembling to the well - known outburst of v4641sgr or outbursts from saxj1818.6 - 1703 [ 1 ] . *
a number of small short flares were detected from the source during pointed rxte / pca observations . *
the accuracy of the xtej1901 + 014 localization was improved from 3to @xmath11.2that strengthens the association of the source with the rosat soft source 1rxh j190140.1 + 012630 .
summarizing all the above we can suppose that xtej1901 + 014 belongs to the class of fast x - ray transient sources , but for the final answer on its origin , more observations at different wavelengths are necessary .
the authors thank to e.churazov for the developing of the methods of the analysis of the ibis data and software .
authors also thank m.revnivtsev for the help with the analysis of rxte data and a discussion of the results obtained .
this work was supported by the russian foundation for basic research ( projects no.05 - 02 - 17454 and 02 - 04 - 17276 ) , the russian academy of sciences ( the origins and evolution of stars and galaxies program ) and grant of president of rf ( nsh- 1100.2006.2 ) .
al acknowledges financial support from the russian science support foundation . | we present results of spectral and timing analysis of the fast x - ray transient xte j1901 + 014 based on data of the rxte and integral observatories . with the integral / isgri
the source was detected at a significance level of 20@xmath0 with the persistent flux of @xmath12.7 mcrab in a 17 - 100 kev energy band in 2003 - 2004 ( during long observations of the sagittarius arm region ) .
we added the rxte / pca ( 3 - 20 kev ) data obtained in 1998 to the integral / isgri data to build the broadband spectrum of the source in a quiescent state .
it was found that the spectrum can be well approximated by a simple powerlaw with a photon index of @xmath12.15 . from timing analysis
we found short time scale aperiodic variations which can be connected with instabilities in the accretion flow .
[ 2001/04/25 1.1 ( pwd ) ] |
many if not all high - luminous infrared galaxies ( ulirgs , @xmath1 ) possess regions hidden by huge amounts of dust .
this makes it difficult to ascertain whether this enormous energy output is due to a starburst activity or an accretion process onto a supermassive black hole .
one of the best known objects to study this relationship is the nearby ulirg ngc 6240 ( assuming @xmath2 ) .
infrared observations favour an energy source dominated by starburst processes , whereas observations in the x - ray range point to an agn as the central engine ( @xmath3 ) .
we have analyzed the data of ngc 6240 taken from an 24 ksec observation with _ xmm - newton _ using the epic - pn and epic - mos instruments . in order to investigate the fe line complex around 6.4 kev and the 0.3 - 10.0 kev spectrum as a whole the high sensitivity and
therefore the good photon statistics - especially in the 6.4 kev range - in combination with a higher energy resolution enables us to examine this feature in unprecedented detail .
table 1 summarizes some basic parameters ( powerlaw - @xmath4 , line energies ) of different models ( first column ) after fitting to the data .
the first of the leading three models includes line profiles with no line width ( @xmath5 ) , whereas eachone of the last two models uses a second powerlaw , but with a different number of line profiles .
each model contains a 6.4kev line as an indication of an agn contribution .
a prove of an compton - thick agn has been reported by vignati et al .
( 1999 ) using bepposax and by ikebe et al .
( 2000 ) using rxte . however , the last model seems to have the best statistical acceptance ( see fig . 1 , left ) . emission lines & powerlaw & & @xmath6 + & @xmath4 & energy - line 1 & energy - line 2 & energy - line 3 & d.o.f .
+ lines : @xmath7 & -0.18 & @xmath8 & @xmath9 & @xmath10 & 38.5/53 + lines : @xmath11 & -0.16 & @xmath12 & @xmath13 & @xmath14 & 38.4/51 + lines : 2nd broad & -0.27 & @xmath15 & @xmath16 & @xmath17 & 43.1/53 + emission lines + & powerlaw & & @xmath6 + absorp . edge : & @xmath4 & energy - line 1 & energy - line 2 & energy - line 3 & d.o.f .
+ po + 2 lines & 0.47 & @xmath18 & @xmath19 & - & 39.7/54 + po + 3 lines & 0.47 & @xmath12 & @xmath19 & @xmath20 & 39.1/54 + the analysis of the spectral data ( @xmath21 ) indicates at least two models providing an statistically acceptable fit : each of them contains two thin thermal plasmas ( @xmath22 and @xmath23 ) , a direct component ( absorbed powerlaw with @xmath24 and @xmath25 , both fixed ) as well as a reflection component ( absorbed powerlaw , either reflected from neutral matter or not ) .
finally , three gaussian lines have been added to the models ( neutral + ionized k @xmath0 and k @xmath26 ) . the right plot of fig .
1 shows the components of the second model ( incl .
reflection ) and their deviations from the data points . | a recently performed _
xmm - newton _ observation of the ulirg ngc 6240 clearly indicates the presence of an agn contribution to its x - ray spectrum . in the 5.0 - 7.0 kev energy range
there is a clear signature of the fluorescent fe k @xmath0 lines at 6.4 , 6.7 and 6.9 kev , respectively .
the line strength of the 6.4 kev line can not be produced by a thermal component .
the 0.3 - 10.0 kev spectral energy distribution is characterized by the following components : ( i ) two hot thermal components ( the starburst ) , ( ii ) one direct component ( heavily absorbed ; agn is hidden ) , ( iii ) one reflection component ( the agn ) , ( iv ) three narrow fe lines
. the model parameters for the broad - band spectral energy distribution are consistent with the results of previously works .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
the experimental setup ( fig . [ fig1 ] ) consisted of a brass container filled with solid carbon dioxide ( dry ice ) .
a clean glass slide was placed over the brass container , where a drop ( @xmath2 ) of deionized and degassed water was deposited using a syringe pump . to increase contrast and observe the freezing front
, red food dye was added to the water .
the process was recorded from the side using a long distance microscope ( vzm1000 edmund optics ) mounted on a color camera , at a frame rate of 50 frames per second .
we used both backlight and bottom light illumination provided by optic fiber lamps .
the resolution obtained was @xmath3 pixels with approximately @xmath4 .
we measured the plate temperature near the droplet using a standard thermocouple . | in this fluid dynamics video we show how a drop of water ( @xmath0 ) freezes into a singular shape when deposited on a cold surface ( @xmath1 ) .
the process of solidification can be observed very clearly due to the change in refraction when water turns into ice .
the drop remains approximately spherical during most of the process , with a freezing front moving upwards and smoothly following the interface .
however , at the final stage of freezing , when the last cap of liquid turns into ice , a singular tip develops spontaneously .
interestingly , the sharp tip of the ice drop acts as a preferential site for deposition of water vapour , and a beautiful `` tree '' of ice crystals develops right at the tip .
the tip singularity attracts the vapour in analogy to a sharp lightning rod attracting lightning . |
the electron / positron linac at kek injects 8-gev electron and 3.5-gev positron beams into kekb rings , where the cp - violation study is carried out . since the efficiency of the experiment
can be increased by shortening the injection time , several mechanisms have been introduced to accomplish this@xcite .
especially , much effort has been made to improve the positron injection time , since it is longer compared with that of electrons@xcite .
one of such effort is a two - bunch acceleration plan , which has been studied and applied@xcite . in this scheme
two bunches of positrons are accelerated in one rf pulse , which is 50 hz ; they may double the injection rate .
the time space between two bunches , however , is restricted by the rf frequencies of the linac and the rings , and the smallest space is 96.29 ns , since the common frequency is 10.38 mhz .
thus , a precise beam control and diagnosis are necessary .
the beam diagnosis used so far has been made by employing strip - line - type beam - position monitors ( bpm ) , wire scanners for transverse profiles and streak cameras for longitudinal profiles . in order to maintain stable beams , it is essential to have the beam instrumentations work for both of the two bunches .
the two - bunch read - out of bpms is especially important , because it is used in a number of orbit and energy feedback loops to stabilize the beams .
along the 600-m linac , 90 bpms are installed and their signals are transferred to one of 18 measurement stations .
signals are delayed and combined so as not to overlap each other , and are fed into a 5-gs / s waveform digitizer ( sony - tektronix tds-680b / c)@xcite , as in fig .
although the bpm signal is a fast bipolar , the readout precision is optimized using the interpolation function of the digitizer .
all 18 digitizers are triggered by a single distributed signal , which is synchronized with beam repetition and rf frequencies .
the waveform is read through the gpib , and a signal from each electrode is analyzed with a predetermined response function once per second by a vme computer ( force 68060 ) .
the response functions include 3rd - order position - mapping functions , attenuation factors of various components and position offsets against the center of the corresponding quadrupole magnet derived from a beam - based alignment .
since the timing and amplitude ranges of bpm signals are different depending on the beam modes and locations , the process is driven by a control database system@xcite .
the acquired beam positions at 18 stations are sent to central computers once per second and are served for various beam - energy and orbit feedback systems to maintain stable beam operation .
the bpm system was improved for two - bunch operation . as written above , it is important to acquire the beam positions of two bunches along the linac simultaneously to study the beams . in our instrumentation ,
signals from those two bunches appear as two signals separated by 96.29 ns on the waveform . although it was sometimes necessary to add more delay lines so as to avoid waveform overlapping , there was no need to add any specific hardware to handle such signals with small separations .
the calibration factors were re - examined since delay lines were added , and the beam - timing database for the signal analysis was extended to accommodate two - bunch information .
processing functions / commands for bpms on the central computers are also extended or added for two bunches , while keeping the old functions as before for single - bunch operations . with these modifications ,
the bpm processing system was extended for two - bunch operation without any performance loss in either precision and speed .
it has been used in beam operation since march , 2001 .
most of the operation software which utilize the bpm information was extended to meet both single- and two - bunch operations .
one of such examples is fig .
[ fig2 ] , which measures the beam energies of two bunches by correlation between a steering - magnet field and the beam - position response at the bunching section .
in order to accelerate the beams properly , the beam characteristics of two bunches need to be adjusted so as to be the same .
for example , in order to adjust the beam - energy differences , we change the beam timing and rf pulse timing .
the beam timing can be changed by 10-ps steps@xcite and the rf pulse timing can be changed by 1.75-ns steps at each sector independently .
most of other parameters in the linac are not sensitive against time separation of 96.29 ns . with such adjustments ,
the 10-nc primary electron bunches are accelerated up to 3.7 gev and positrons are generated as shown in fig .
[ fig3 ] .
the beam feedback loops in the linac for energy and orbit stabilization@xcite were also extended to control two - bunch beams .
since we do nt have many mechanisms to control two bunches independently , most feedback loops were modified to use positions derived from the charge - weighted averages of two bunches . with these changes
, those loops can maintain the average orbit and energy . in software ,
only the monitoring function was extended to read the average positions if two bunches are accelerated .
for positron injection , about 20 beam feedback loops are used , and they are all extended for two bunches . while normal energy and orbit feedback loops use charge - weighted average positions , feedback loops to minimize the energy differences use the position difference between two bunches , as shown in fig .
[ fig4 ] .
although the energy difference does not change frequently , such loops stabilize the beam over the long term .
the data - acquisition system for the linac bpms was upgraded to provide beam positions in two - bunch operation without losing any original features . along with improvements of the streak camera and wire scanner systems
, it has still been indispensable to study and operate on linac beams .
the system is also used by many operation software programs , including beam - energy and orbit feedback systems . | in order to double the positron injection rate into the kekb ring , a two - bunch acceleration scheme has been studied at the linac , in which bunches separated by 96 ns are accelerated in 50 hz . in this scheme stabilization of the energy and orbit of each bunch
is indispensable .
thus , the beam energy and orbit feedback systems have been upgraded .
since beam characteristics are acquired through beam - position monitors ( bpm ) , their read - out system was improved to meet two - bunch requirements . combined waveforms from bpm s
were adjusted with delay cables avoiding overlaps so as to enable the simultaneous measurements of the beam positions of two bunches .
the beam energies of two bunches were balanced by tuning the rf pulse timings , and the average energy was stabilized by adjusting the accelerating rf phases .
the average beam orbits were also stabilized .
slow feedback systems at the injector section for charge and bunching stabilities are being planned as well .
these systems were successfully used in the test beams and will be employed during routine operation . |
this study finds the leaky pipeline phenomenon exists for women past the postdoctoral level at a level of around 15% .
some may wonder if this is a big enough leak to be a problem . in human terms , however , a 15% leak means that we are missing one out of six women who , in an equitable society , would have been physics faculty members .
there are so few women at the faculty level in physics , that losing one out of every six is in fact a serious concern .
especially if we think about what it must take to convince someone to leave a field when , by that point in their careers , they have committed their working lives to physics , and have gone through at least a decade of higher education to get there .
not all women who become physics faculty members have experienced gender discrimination during their careers . however , many do , and it is unfortunate that the combination of gender discrimination and a ` glass ceiling ' phenomenon in the field is preventing more women from becoming physics faculty members .
the author is an experimental particle physicist , and has observed over the years the serious obstacles that her female colleagues have had to face as they try to advance in the field .
there is indeed widespread discrimination against many women in physics , and women with children seem to be particularly vulnerable ; for instance , the author is personally acquainted with three female physicists who , after having children , had to work for free or a substantially reduced rate compared to their peers , simply to remain in the field .
the only other choice available to them was to simply drop out of the academic pipeline all together .
conversely , the author knows literally hundreds of male physicists past the doctoral level , but is not aware of a single male who has had their pay cut off or substantially reduced for any reason .
given some of the chilling incidents of discrimination against females that the author has personally observed to transpire within physics academia , it is somewhat surprising that the relative leak of females in the academic pipeline past the postdoctoral level is * only * 15% .
a male colleague once mentioned to the author that he felt very sorry for many of his female colleagues in physics because he felt the message that they were persistently given was that ` yes !
the good news is that you * can * succeed in physics as a female !
( you just need to be prepared to chew your own leg off to do so ) ' .
tragically , some of the women who have ultimately made it to the faculty level likely did have to ` chew their own leg off ' to get there .
even more tragically , their stories are almost never told because they ( quite rightly ) fear repercussions to their career if they speak out .
the chilly climate that removes one out of every six female potential physics faculty members needs to be changed if particpation of women in physics is to be increased at all levels .
probability that a female who graduated in a particular year will be a physics professor in 2005 at one of the ` top 50 ' american physics universities .
points are the actual distribution , and the histogram indicates the predicted distribution , obtained assuming that females and males from the same graduating class have the same relative probability of being a professor in 2005 . ]
year - of - phd of female professors in 2005 ( points ) , for assistant , associate and full professors . the histograms indicate the predicted year - of - phd distributions , obtained assuming that females and males from the same graduating class have the same relative probability of being a professor in 2005 . ]
year - of - phd of all female professors in 2005 ( points ) .
the histogram indicates the predicted year - of - phd distribution , obtained assuming that females and males from the same graduating class have the same relative probability of being a professor in 2005 . ]
american institute of physics 2005 report _ women in physics and astronomy _
+ http://www.aip.org/statistics/trends/reports/women05.pdf national research council 1995 report _ research - doctorate programs in the united states : continuity and change _ | the author has recently examined the departmental web pages of the ` top 50 ' physics research universities , as ranked by the national research council ( nrc ) @xcite .
most of the departmental web pages contained biographical data ( ie ; year and institute of phd , etc ) of their faculty members .
of the approximately 1750 faculty members at the ` top 50 ' universities that were examined , approximately 100 were female , and around 1425 had available biographical data .
based on this data , the * predicted * fractions of female faculty members at the ` top 50 ' universities are @xmath0,@xmath1 , and @xmath2 at the assistant , associate , and full faculty levels , respectively . the * observed * fractions are @xmath3 , @xmath4 , @xmath5 , respectively . the overall observed number of women faculty is about 15% less than expected , and the depletion is statistically significant .
unfortunately , the study finds that the `` leaky pipeline '' is found to be alive and well for women in academic physics above the postdoctoral level , at all stages of the faculty career ladder .
this result is stark contrast with the conclusion of the american institute of physics ( aip ) 2005 report on women in physics and astronomy ; the aip report concludes that women are actually * more * likely to be hired at the faculty level than their male peers . in this paper
, we will discuss the two key flaws in the aip analysis that led to their faulty conclusion , then describe in detail the analysis performed by the author that corrects these flaws to get an accurate estimate of the ` leakiness ' of the academic pipeline for women physicists past the postdoctoral level .
_ to be submitted to the american journal of physics _
many studies have documented the `` leaky pipeline '' phenomenon for women in the academic hard sciences ( see , for instance , references @xcite and @xcite ) . a recent report that caught the author s interest was the american institute of physics 2005 report on women in physics and astronomy @xcite ; this report is rather unique in that it concludes that the leaky pipeline phenomenon does not exist past the doctoral level .
in fact , the report concludes that the observed fraction of female faculty members is actually * higher * than expected .
however , careful examination of the report reveals that the analysis that led to this conclusion was flawed ; first , the report lumps faculty members at phd granting universities together with faculty members at teaching colleges . at teaching colleges ,
the faculty are more likely to be female , yet much less likely to teach physics to physicists .
thus the aip report gives little indication of the fraction of women at the faculty level at the universities in america that produce the majority of physics doctoral degrees .
second , the analysis performed for the report did not properly take into account the differing age distributions of male and female faculty members ( the report used instead the combined age distribution of both males and females , which of course is completely dominated by the males , since they constitute over 90% of the sample ) .
this flaw has a significant effect on the predicted fraction of female faculty ( the predicted fraction goes up when the analysis is performed taking the differing age distributions properly into account ) . to perform a detailed analysis that corrects both of these problems , the author began with an examination of the departmental web pages of the ` top 50 ' physics universities , as ranked by the national research council ( nrc ) @xcite .
these universities produce the majority of bsc s and phd s in america .
most of the departmental web pages contained biographical data ( ie ; year and institute of phd , etc ) of their faculty members . in this study astronomers
were excluded because they have a different fraction of women participating in the field than other areas of physics .
adjunct , visiting , research , and affiliated professors were also excluded .
the study also excluded faculty members who had received their degree from a non - american institution . of 1743 faculty members at
the ` top 50 ' universities that were ultimately examined , 101 were female , and a total of 1425 had available biographical data . to obtain the predicted fraction of female professors from this data , we begin with the number of phd s granted each year to both males and females in america @xcite ( see figure [ fig : phd ] ) .
we then work out the probability that a male in a particular phd graduating class will be a professor at one of the ` top 50 ' universities in 2005 ; we do this by dividing the year - of - phd distribution of male professors with the distribution of the number of male phd s graduating each year .
if the leaky pipeline does not exist , the female ` be - a - professor - in-2005 ' probability will be exactly the same as for the males in each graduating class . in this manner , we obtain a prediction of the number of female professors we expect to see at the ` top 50 ' universities in 2005 .
figure [ fig : prob ] shows the actual probability versus year - of - phd that a female physicist will be a faculty member at one of the ` top 50 ' universities in 2005 . the histogram indicates the predicted distribution ,
obtained assuming that females have the same relative probability of being a professor in 2005 as males from the same graduating class .
the actual distribution is systematically lower than the predicted distribution .
figure [ fig : all ] shows the year - of - phd distributions of female assistant , associate , and full professors .
the histograms again indicate the predicted distribution , obtained assuming that females and males from the same graduating class have the same relative probability of being a professor in 2005 .
figure [ fig : summary ] shows the year - of - phd distributions of all female professors .
every point in the actual distribution is lower than the predicted .
based on this data , the * predicted * fractions of female faculty members at the ` top 50 ' universities are @xmath0,@xmath1 , and @xmath2 at the assistant , associate , and full faculty levels , respectively .
the * observed * fractions are @xmath3 , @xmath4 , @xmath5 , respectively .
it is interesting to note that the fraction of female associate professors is actually higher than predicted .
however , figure [ fig : summary ] shows an overall depletion of professors for years - of - phd 1984 and onwards .
it thus appears that the excess may well be due to women languishing longer at the associate professorship level than their male peers ( ie ; the excess probably reflects a ` clog ' in the academic pipeline at the associate professor level ) . the overall observed number of women faculty is about 15% less than expected , and the depletion is statistically significant at a level of @xmath6 standard deviations . |
we acknowledge partial support of fondecyt ( chile ) projects 1060627 and 1060651 , conicyt / pbct proyecto anillo de investigacin en ciencia y tecnologa act30/2006 and u.s .
national science foundation grant dms 06 - 00037 . | we establish rigorous upper and lower bounds for the speed of pulled fronts with a cutoff .
we show that the brunet - derrida formula corresponds to the leading order expansion in the cut - off parameter of both the upper and lower bounds . for
sufficiently large cut - off parameter the brunet - derrida formula lies outside the allowed band determined from the bounds . if nonlinearities are neglected the upper and lower bounds coincide and are the exact linear speed for all values of the cut - off parameter .
the reaction diffusion equation @xmath0 provides a simple description of phenomena in fields such as population dynamics , chemical reactions , flame propagation , fluids , qcd , among others @xcite .
it is one of the simplest models which shows how a small perturbation to an unstable state develops into a moving front joining a stable to an unstable state .
the reaction term @xmath1 satisfies different conditions depending on the physical problem of interest .
one of the first , and most studied cases , is the fisher reaction term @xmath2 for which the asymptotic speed of the propagating front is @xmath3 , a value determined from linear considerations .
a more general case was studied by kolmogorov , petrovskii and piscounov ( kpp)@xcite who showed that for all reaction terms which satisfy the kpp condition @xmath4 the asymptotic speed of the front joining the stable @xmath5 point to the unstable @xmath6 point is given by @xmath7 these fronts are called pulled since it is the leading edge of the front which determines the velocity of propagation . in the rest of this work
we assume that @xmath8 .
the evolution of localized initial conditions for general reaction terms , and rigorous properties of the fronts were studied by aronson and weinberger @xcite .
the asymptotic speed of the front for all reaction terms can be found from the integral variational principle @xcite @xmath9 where the supremum is taken over all positive monotonic decreasing functions @xmath10 for which the integrals exist and where @xmath11 .
the supremum is always attained for reaction terms which are not pulled .
two effects not included in the classical reaction diffusion equation ( [ rd ] ) , are the effect of noise and the effect of a finite number @xmath12 of diffusive particles .
it was shown by brunet and derrida that such effects can be simulated by introducing a cut - off in the reaction term . in the case of noise
the cut - off parameter measures the amplitude of the noise while in the case of finite number of @xmath12 diffusing particles the cut - off parameter @xmath13 .
there is substantial numerical evidence that introducing a cut - off in the reaction terms reproduces accurately the effect of noise and finiteness in the number of diffusing particles @xcite . by means of an asymptotic matching brunet and derrida showed that for a reaction term @xmath14 a small cut - off changes the speed of the front to @xmath15 in recent work it has been show that the brunet - derrida formula for the speed is correct to @xmath16@xmath17 for a wider class of reaction terms @xcite .
the purpose of this work is to show that for reaction terms of the form @xmath18 where @xmath19 satisfies the kpp condition eq .
( [ kppcondition ] ) and @xmath20 is the step function , the speed @xmath21 of the front with the cutoff satisfies @xmath22 with @xmath23 we see that for @xmath24 , @xmath25 .
the function @xmath26 depends on the nonlinear terms of the reaction function . for small @xmath27 the series expansion of the upper bound @xmath28
is @xmath29 the contribution of the nonlinearities , contained in the term @xmath26 , appears at @xmath16@xmath17 , so that the leading order terms in the expansion of the upper and lower bounds give the brunet - derrida formula .
if nonlinearities are neglected the value @xmath30 is the analog of the kpp value @xmath3 for reaction terms which satisfy the kpp condition , but with a cutoff . in what follows we derive the bounds and apply them to the fisher reaction term @xcite @xmath31 and to the reaction term studied by brunet and derrida @xmath32 .
the main tool to obtain the bounds is the variational principle for the speed . as shown in previous work @xcite
, we may perform the change variables @xmath33 where @xmath34 in eq.([vp1 ] ) and write the variational expression for the speed as @xmath35 where @xmath36 is an arbitrary parameter , @xmath37 and the supremum is taken over positive increasing functions @xmath38 such that @xmath39 , @xmath40 and for which all the integrals in ( [ newvp ] ) are finite .
therefore , for any suitable trial function @xmath38 we know that @xmath41 consider now reaction terms @xmath1 with a cut - off @xmath27 of the form @xmath42 where @xmath43 , the nonlinearity , is such that @xmath44 .
we find @xmath45 where @xmath46 assume now that @xmath1 satisfies the kpp criterion eq.([kppcondition ] ) .
since @xmath47 , it follows that @xmath48 where @xmath49 and therefore @xmath50 \equiv \sup_{u(s ) } 2 \,\frac { g(1)/s_0 + \int_0^{s_0 } g(u(s))/s^2 d\,s}{\int_0^{s_0 } \left ( d u /d s\right)^2 d\,s}.\ ] ] one can prove ( rigorous details will be given elsewhere ) that @xmath51 is bounded above and that there exists a function @xmath52 for which the supremum is attained .
this function is the monotonic increasing solution to the euler - lagrange equation for @xmath51 satisfying the boundary conditions @xmath53 .
one can also prove that the variational parameter @xmath54 is finite and @xmath55 .
in summary , the maximizing function for @xmath51 is the solution of @xmath56 @xmath57 subject to the boundary conditions @xmath58 with the function and its derivative continuous at @xmath59 .
the solution to this problem is given by @xmath60 with @xmath61 where @xmath62 is the first positive solution of @xmath63 the maximum of @xmath64 $ ] can be calculated easily .
we obtain after performing the integrals , @xmath65 = 4 \sin^2 ( \phi _ * ) \equiv c^2_{up}. \label{top}\ ] ] to obtain the lower bound we shall use the optimizing function @xmath52 as a a suitable trial function in eq .
( [ lowerbound ] ) .
we obtain @xmath66 \label{bottom}\ ] ] since @xmath67 is negative , we may combine eqs.([top ] ) and ( [ bottom ] ) and write our main result as given in eq .
( [ main ] ) . as an example
consider the reaction term studied by brunet and derrida , @xmath32 .
the lower bound can be written explicitly as @xmath68 the integral has a long analytic expression which we omit here . from the explicit expression above it
is not difficult to show that the contribution of the two last terms , which arise from the nonlinear terms , are of @xmath69 . in figures 1 and 2
we show the bounds together with the brunet - derrida formula as a function of @xmath27 .
the solid lines correspond to the upper and lower bounds .
the dashed line is the brunet - derrida formula . .
the solid lines correspond to the bounds , the dots to the brunet - derrida formula .
, height=188 ] as a second example we consider the fisher reaction term @xmath70 with a cut - off .
the lower bound becomes @xmath71 again , the integral can be done analytically and we do not show it here . in fig .
3 we show the upper and lower bounds and the brunet - derrida formula . in this case
the brunet - derrida formula leaves the allowed band at larger value of @xmath27 . in general for reaction terms @xmath72 , the gap between the upper and lower bounds becomes narrower and the brunet - derrida formula valid for a smaller range of @xmath27 . .
lines as in fig . 1 ,
height=188 ] in summary , we have studied the effect of a cut - off on reaction terms which satisfy the kpp condition eq.([kppcondition ] ) .
we have found upper and lower bounds valid for all values of the cut - off parameters , which allow to assess the accuracy of the brunet derrida formula .
if we consider only the linear terms , the upper and lower bounds coincide and give the exact linear value for the speed , of which the two leading order terms are the brunet - derrida formula . |
here we will provide the formulas describing the time - evolution of the mechanical oscillator along with the formula for the qfi of the steady state . assuming that the mechanical oscillator is continuously monitored with efficiency @xmath19 , the evolution is described by the following stochastic master equation @xmath83 \ : dt+ ( \gamma_{\sf env } + \gamma_{\sf fun } ) \ : \mathcal{d}[\hat{x}]\varrho \ : dt \nonumber \\ & \qquad + \sqrt{\eta \gamma_{\sf env } } \mathcal{h}[\hat{x } ] \varrho \ : dw \label{eq : smesm}\end{aligned}\ ] ] where @xmath6 , @xmath7\varrho = o\varrho o^\dag - ( o^\dag o \varrho + \varrho o^\dag o)/2 $ ] and @xmath20\varrho = o \varrho + \varrho o^\dag - \tr[(o+o^\dag)\varrho]$ ] . this equation can be translated in the following equations for first moments and covariance matrix , fully describing the evolution for gaussian quantum states @xmath84 where @xmath85 is a vector of wiener increments such that @xmath86 and the matrices read @xmath87 the steady state covariance matrix can be derived analytically as @xmath88 where @xmath89 notice that , typically , the steady state above is a squeezed state , in the sense that its smallest eigenvalue will be smaller than one . obtaining the decomposition , in terms of diagonal single - mode squeezers and orthogonal phase shifters , of the symplectic operation that relates the vacuum state to this steady state is a straightforward task , that just requires one to diagonalise the matrix @xmath46 .
the corresponding quantum fisher information can be easily evaluated by using the formula @xcite @xmath90}{1+\mu_\phi^2 } + 2 \frac{(\mu_{\sf ss}^{\prime})^2}{1-\mu_{\sf ss}^4 } \ : , \label{eq : gaussqfi}\end{aligned}\ ] ] where @xmath91 = 1/\sqrt{\det[\sigmacm_{\sf ss}]}$ ] represents the purity of the state , and primed quantities corresponds to derivative with respect to the parameter @xmath10 .
one then obtains @xmath92 + \gamma_{\sf fun } \left ( \omega_m - 3 \upsilon\right ) } { 8\upsilon ( \gamma_{\sf env } + \gamma_{\sf fun } ) \left [ \eta^2 \gamma_{\sf env}^2 - ( \gamma_{\sf env } + \gamma_{\sf fun})^2 \right ] } .\end{aligned}\ ] ] | inspired by the notion that environmental noise is in principle observable , whilst fundamental noise due to spontaneous localisation would not be , we study the estimation of the diffusion parameter induced by wave function collapse models under continuous monitoring of the environment .
we take into account finite measurement efficiencies and , in order to quantify the advantage granted by monitoring , we analyse the quantum fisher information associated with such a diffusion parameter , identify optimal measurements in limiting cases , and assess the performance of such measurements in more realistic conditions . _
introduction . _ - spontaneous localization models @xcite , in their many flavours and variations , were introduced from the late eighties primarily as an attempt to unify the dynamics of microscopic and macroscopic systems , encompassing measurement apparata , which customary quantum mechanics only describes through ad hoc prescriptions that can not be relied to the fundamental dynamical principles .
while such models reproduce quantum and classical mechanics in the extreme regimes of few ( @xmath0 ) and very many ( @xmath1 ) elementary constituents , they do deviate substantially from standard quantum mechanics in the intermediate mesoscopic regime . as molecular interferometry @xcite and quantum opto - mechanics , especially in the levitating paradigm @xcite , are swiftly advancing into this mesoscopic middle ground , there is currently a lively interest in designing and carrying out experiments that would falsify either standard quantum mechanics or its spontaneously localized variants @xcite . in a nutshell ,
spontaneous localization models postulate the presence of an additional stochastic term in the schrdinger equation , that would be responsible for the wave - function collapse and the perceived discontinuous dynamics of quantum projective measurements .
this would essentially imply the existence of a source of `` fundamental '' decoherence , in the form of momentum dissipation , acting on a mesoscopic system , such as a levitating opto - mechanical nanosphere .
it has hence been recently noted that , if the sources of `` environmental '' decoherence due to the interaction and entanglement with the environment are well known , the additional fundamental decoherence could be directly observed by tracking the system s dynamics @xcite .
the detection of fundamental effects over the background of environmental ones is however obviously difficult , as the two may take the same form and imply qualitatively similar effects .
the primary intent of this work is emphasising that a possible distinction between fundamental and environmental decoherence is that , while the former is unavoidable and beyond repair , the latter can in principle be reversed through measurements : if the physical degrees of freedom of the environment are completely or partially accessible , one can perform measurements on them that partly restore information about the quantum state @xcite .
drawing from this notion , we will hence consider the estimation of the free parameter of qmupl ( `` quantum mechanics with universal position localization '' ) or of an equivalent function of the two parameters of the csl ( `` continuous spontaneous localization '' ) wavefunction collapse model , under time - continuous measurements on the environment of a quantum degree of freedom , such as the centre of mass of a levitated nanosphere @xcite .
the latter will be our system of reference , bearing in mind that similar results would apply to more general settings .
the monitoring we consider , aided by markovian linear feedback , has the added bonus of stabilising the dynamics @xcite , so that we will be in a position to base our investigation entirely on steady state properties and not on the features of the transient dynamics , which may be more elusive to record in practice . as a further element of novelty
, we will not just consider specific empirical signatures of the different values of the collapse parameter but instead address their systematic , ultimate discrimination by applying quantum estimation techniques and deriving the quantum fisher information ( qfi ) associated with such a parameter @xcite .
thus , we will quantify exactly the advantage provided by continuous monitoring as a decrease in the achievable uncertainty on the parameter estimation , and hence on the discrimination between different theories .
we shall derive analytical expressions for both the qfi and the optimal final measurement for parameter discrimination in limiting instances , and show the latter performs remarkably well in realistic situations too . _
the dynamics . _ - to fix ideas , we shall consider a single noisy continuous variable quantum degree of freedom subject to a positive definite harmonic hamiltonian and to momentum diffusion , as would be the case for a trapped nanosphere undergoing heating via photon scattering , background gas collisions and blackbody radiation @xcite . in order to simplify our treatment , we shall not include the typically smaller effects of position diffusion and friction @xcite , which could be accounted for promptly within our formalism but would not add much conceptual insight .
the additional stochastic term acting on the state vector according to the qmupl model is equivalent to a momentum diffusion lindblad superoperator entering the master equation for the quantum state @xmath2 .
the same is approximately true for the centre of mass of motion of mesoscopic objects in the csl model , since the position fluctuations are expected to be much smaller than the model localization length and one can perform a first order expansion of the superoperator @xcite .
hence , the overall dynamics we shall consider is the following : @xmath3 + \gamma \ : \mathcal{d}[\hat{x}]\varrho \ ; , \label{eq : me}\end{aligned}\ ] ] where @xmath4=i$ ] ( @xmath5 ) , @xmath6 and @xmath7\varrho = o\varrho o^\dag - ( o^\dag o \varrho + \varrho o^\dag o)/2 $ ] . the momentum diffusion rate is the sum of two contributions : @xmath8 , where @xmath9 is due to environmental effect , while @xmath10 is fundamental .
our aim is analysing the estimation of @xmath10 .
notice that such a parameter is equivalent to the only fundamental parameter of qmupl and constrains the parameters of the csl models through the formula @xmath11 @xcite , where @xmath12 is the mass of the object , @xmath13 is a factor that depends on its geometry , and the parameters @xmath14 and @xmath15 characterise the model ( the value for the intrinsic length scale is typically chosen at @xmath16 nm , while bounds on the collapse rate are currently placed at @xmath17 @xcite ) . since we will consider only one mode , we will assume that after having trapped the nanosphere and cooled its motion down by sideband cooling , one will either turn off or detune the driving field in order to decouple the nanosphere motion and the cavity field .
hence , we will focus on the evolution of the mechanical oscillator alone .
as already argued , in principle one can always counter the environmental decoherence by monitoring the environment . here , we suppose to monitor the nanosphere position through the scattered light , obtaining a conditional dynamics described by the following conditional master equation @xcite : @xmath18 \varrho \ : { \rm d}w \ : , \label{eq : sme}\end{aligned}\ ] ] where @xmath19 denotes the monitoring efficiency , @xmath20\varrho = o \varrho + \varrho o^\dag - \tr[\varrho ( o + o^\dag)]$ ] and @xmath21 represents a standard wiener increment . as the hamiltonian @xmath22 is quadratic in the position and momentum operators , the evolution described by eq .
( [ eq : sme ] ) sends gaussian states into gaussian states , and thus we can fully describe it by looking at the evolution of the covariance matrix @xmath23 and the first moments vector @xmath24 of the quantum state @xmath2 , defined in components as @xmath25 $ ] and @xmath26 $ ] for the operator vector @xmath27 . remarkably , due to a very specific property of quantum and classical conditional gaussian statistics , one obtains @xcite that , while the evolution of the first moments is , as expected , stochastic , _
i.e. _ depends on the results of the measurement performed on the environment , the covariance matrix evolves deterministically . in formulae : @xmath28 where @xmath29 is a vector of independent wiener increments .
the matrices @xmath30 , @xmath31 and @xmath32 are given in the supplemental material @xcite as functions of the dynamical parameters .
notice that the efficiency parameter @xmath33 $ ] will allow us to describe realistic situations where the environmental degrees of freedom are only partially accessible ( as would be the case for the imperfect collection of light scattered by a nanosphere ) .
note also that setting @xmath34 obviously yields the original , unmonitored dynamics .
thanks to the deterministic evolution of the second moments , one can prove that real - time linear feedback ( _ i.e. _ real - time displacement in phase space depending on the measurement current ) can be applied in order to obtain a steady state with zero first moments and thus remove the stochasticity of the evolution @xcite .
this may not be the optimal strategy in terms of the estimation of @xmath10 , but we will nonetheless consider this regime in what follows and set the first moments to zero , as it does allow for a deterministic steady state and will let us illustrate the advantage granted by the monitoring with a very compact , entirely analytical treatment .
also , in an experiment , a stable steady state is certainly much more desirable than a stochastically fluctuating one , on which one would have to perform an optimal discriminating measurement that would also fluctuate stochastically .
now , if all the other dynamical parameters are known , the steady state solutions of eq .
( [ eq : evolutioncm ] ) yield a family of gaussian states with zero first moments parametrized by the different values of @xmath10 . to assess the effectiveness of our strategy , in the following we will derive the ultimate limits on the estimation of @xmath10 , quantified by the quantum and classical cramr - rao bound evaluated on such a family of states . _ quantum estimation theory . _
- let us consider a family of quantum states @xmath35 parametrized by a parameter @xmath36 that we want to estimate .
if one performs a measurement described by a positive operator valued measure ( povm ) @xmath37 , the ultimate limit on the precision of any unbiased estimator for the parameter @xmath36 is set by the cramr - rao bound @xcite @xmath38\ : , \end{aligned}\ ] ] where @xmath39 is the number of measurements performed , @xmath40 is the so - called ( classical ) fisher information ( fi ) , and @xmath41 $ ] denotes the conditional probability describing the whole measurement process . by optimizing over all the possible povms ,
one derives the quantum cramr - rao bound ( qcrb ) @xcite @xmath38 \geq 1/[m h(\gamma ) ] \ : , \label{eq : qcrb}\end{aligned}\ ] ] where @xmath42 $ ] is the quantum fisher information ( qfi ) and @xmath43 is the symmetric logarithmic derivative ( sld ) that is implicitly defined by the equation @xmath44 . as apparent from eq .
( [ eq : qcrb ] ) , the qfi quantifies with how much precision one can estimate the parameter @xmath36 independently from the specific measurement performed .
geometrically , the qfi corresponds to the bures metric in the hilbert space @xcite : large values of the qfi correspond to large bures distances between two quantum states @xmath35 and @xmath45 obtained via an infinitesimal variation of the parameter @xmath36 .
we also remark that for single - parameter estimation it is guaranteed that an optimal povm saturating the quantum cramr - rao bound always exists @xcite .
_ fundamental diffusion estimation . _ - as detailed above , we want to assess the estimation of the parameter @xmath10 , whose information is encoded in the gaussian steady state obtained through the monitoring described by eq .
( [ eq : sme ] ) .
in particular , we will focus only on the steady state covariance matrix solution @xmath46 of the riccati equation ( [ eq : evolutioncm ] ) , as we can assume that the first moments will be equal to zero .
it should be remarked here that the linear driving needed to set the first moments to zero does depend on the parameter @xmath10 we need to estimate . and so will the final optimal quantum measurement to be performed on the steady state .
however we can invoke , as customary in _ local _ quantum estimation problems , a multi - step adaptive protocol in order to solve this possible conundrum : one can apply the optimal protocol valid for an initial rough guess of the parameter @xmath10 ( say , in our case , @xmath47 ) , estimate the parameter through the measurement just performed , and then refine the operation and optimal measurement to be implemented given the latest estimate of the parameter .
it has been shown in several cases that , after a few adaptive steps , one obtains an estimator giving the true value of the parameter and saturating the cramr - rao bound @xcite . as a function of the monitoring efficiency @xmath19 , for @xmath48 , @xmath49 and and for different values of the estimated fundamental diffusion @xmath10 . from top to bottom : @xmath50 .
[ f : qfi ] right : ratio between the classical fi for the povm introduced in the main text ( optimal for perfect monitoring and no collapses ) , and the qfi @xmath51 as a function of the monitoring efficiency @xmath19 and of the ratio between fundamental decoherence @xmath10 and environmental decoherence @xmath9 ( the environmental decoherence is kept fixed to @xmath49 ) .
[ f : optimalpovm],title="fig : " ] as a function of the monitoring efficiency @xmath19 , for @xmath48 , @xmath49 and and for different values of the estimated fundamental diffusion @xmath10 . from top to bottom : @xmath50 .
[ f : qfi ] right : ratio between the classical fi for the povm introduced in the main text ( optimal for perfect monitoring and no collapses ) , and the qfi @xmath51 as a function of the monitoring efficiency @xmath19 and of the ratio between fundamental decoherence @xmath10 and environmental decoherence @xmath9 ( the environmental decoherence is kept fixed to @xmath49 ) .
[ f : optimalpovm],title="fig : " ] under these assumptions ( gaussian steady state with zero first moments ) , the qfi can be evaluated analytically from the covariance matrix @xmath46 , as described in @xcite .
the general analytical formulae for the steady state covariance matrix @xmath46 and the qfi @xmath51 are rather cumbersome and are reported in the supplemental material @xcite .
we start our analysis by discussing the general properties of the qfi by looking at fig .
[ f : qfi ] .
firstly , it is apparent from the graph that the qfi increases monotonically with the detection efficiency @xmath19 , providing one with a quantitative confirmation that countering the environmental decoherence through continuous measurements would help in the estimation of the collapse - induced diffusion .
also , the qfi decreases monotonically with @xmath10 , implying that , in principle , smaller values of the parameter can be estimated more efficiently in terms of absolute error .
next , it is instructive to consider the limiting case of perfect monitoring efficiency ( @xmath52 ) , where the qfi takes the compact analytical form @xmath53 one can easily check that in the limit of both perfect monitoring and zero fundamental decoherence ( @xmath47 ) , the qfi diverges .
this can be intuitively understood by looking at how the steady state @xmath54 changes in the hilbert space by varying the parameter of interest : as we have already remarked , for perfect monitoring and zero fundamental decoherence , the steady state is pure ; however , increasing the value of @xmath10 from zero introduces a diffusion that can not be neutralized by monitoring the environment and , therefore , a mixed steady state ( the same reasoning applies to the case of fixed @xmath47 and measurement efficiency @xmath19 decreasing from the maximum value ) .
the abrupt change from pure to mixed states is responsible for the diverging qfi , and also yields insight as to the identification of the optimal quantum measurement saturating the qcrb . in point of fact , this argument singles out a dichotomic measurement corresponding to projecting either on the steady state itself @xmath55 or on the rest of the hilbert space , in order to be sensitive to the change from a pure to a mixed state .
the corresponding povm , described by the operators @xmath56 and @xmath57 , is indeed optimal , as it can be shown to achieve the quantum cramr - rao bound .
this povm can be realized by first applying the symplectic operation that sends the vacuum state into the pure steady state @xmath55 ( this operation involves some squeezing @xcite , that could be obtained by modulating the trap potential @xcite ) , and then by performing a vacuum projection ( which , in optomechanics , could in principle be achieved by a mapping of the mechanical state onto the light mode through red sideband driving , followed by a measurement of the latter with an avalanche photodiode , that distinguishes between zero and any positive number of photons ) .
more revealing than the quantum fisher information itself is the associated signal to noise ratio @xmath58 quite simply , the ratio between the estimated value and its standard deviation which can be easily determined from eq .
( [ eta1 ] ) in the case of perfect monitoring , and reads @xmath59 which , in the regime @xmath60 , goes like @xmath61 ( let us remind the reader that @xmath39 is the number of estimation runs ) , and hence vanishes as @xmath10 vanishes .
the limits of perfect continuous monitoring of the environment and zero fundamental decoherence are clearly idealizations .
however , the continuity of the qfi assures us that very high precision can be obtained in their neighbourhood , _
i.e. _ for high but not perfect efficiency @xmath62 and for the interesting case of small csl decoherence , when @xmath63 .
we have in fact also investigated the performance of the povm just described also for different values of @xmath19 and @xmath10 , where we know it is no longer optimal .
as apparent from fig .
[ f : optimalpovm ] , the ratio between the classical fi and the qfi is still above @xmath64 for a reasonably large region of values of @xmath19 and @xmath10 .
this is particularly relevant since the optimal measurement , as is often the case , depends on the parameter to be estimated ; given these results , one can indeed apply the optimal measurement for the case of zero fundamental decoherence , and still achieve a very high precision in the most interesting region of small , but not zero , values of @xmath10 .
the most convincing evidence for the advantage granted by the continuous monitoring comes from considering the number of measurements needed to achieve a signal to noise ratio of one in the plausible scenario of continuous spontaneous localization with @xmath65 , for a hypothetical nanosphere of radius @xmath66 , mechanical frequency @xmath67 khz and subject environmental diffusion @xmath68 as a function of the monitoring efficiency @xmath19 , as shown in fig .
[ f : snr ] .
it can be seen that the number of runs goes from around one million for the unmonitored case to around @xmath69 for perfect monitoring .
hence , one concludes that environmental monitoring would help in designing experiments able to improve the existing bounds on @xmath10 . as a further piece of analysis , one can consider the dependence of the signal to noise ratio @xmath70 on the mechanical frequency @xmath71 in the csl model , where @xmath71 and the oscillator mass @xmath12 determine @xmath10 . for perfect efficiency
, this reads @xmath72 with @xmath73 .
this is a decreasing function of @xmath74 , confirming that oscillators at lower frequencies ( which , however , are more challenging to cool down to the quantum regime ) would prove advantageous in this context , as already indicated in proposals such as @xcite , where an ion trap , rather than optical tweezers , was considered . and for @xmath65 ( other parameters are set considering a nanosphere of radius @xmath66 , with mechanical frequency @xmath67 khz and with environmental diffusion @xmath68 kzhz ) .
[ f : snr ] right : ratio between the qfi @xmath75 obtained for the state at time @xmath76 and the steady state qfi @xmath51 as a function of the evolution time @xmath76 , for @xmath77 khz , @xmath68 khz and @xmath78 .
[ f : finitetime],title="fig : " ] and for @xmath65 ( other parameters are set considering a nanosphere of radius @xmath66 , with mechanical frequency @xmath67 khz and with environmental diffusion @xmath68 kzhz ) . [
f : snr ] right : ratio between the qfi @xmath75 obtained for the state at time @xmath76 and the steady state qfi @xmath51 as a function of the evolution time @xmath76 , for @xmath77 khz , @xmath68 khz and @xmath78 .
[ f : finitetime],title="fig : " ] _ finite time analysis . _ - all the results reported above have been derived considering the mechanical oscillator steady state . in order to validate such an analysis
, we investigate the transient dynamics of the qfi and in particular its ratio with the qfi obtained at steady state .
the results are plotted for experimentally reasonable values of the parameters in fig .
[ f : finitetime ] .
we focus in particular on small values of the fundamental decoherence parameter @xmath10 , but we have numerical evidence that similar results are obtained for larger values .
as can be seen from the graph , the ratio goes indeed to one in a relatively small time ( around @xmath79 with our parameters ) , _ i.e. _ the precision on the estimation of the parameter @xmath10 can be safely obtained at finite time . while in the case of perfect monitoring ( @xmath80 ) , the ratio increases monotonically to @xmath81 , in the case of @xmath82 one observes a maximum , indicating the possibility of a better estimation at finite times .
however , this marginal advantage would come at the price of having to perform fast measurements at a certain fixed time : as argued above , in a laboratory it may be more expedient to wait for the stable steady state . _ discussion and outlook .
_ - it should be noted that our estimation analysis assumed perfect knowledge of all the dynamical parameters other than our target @xmath10 .
this may be particularly delicate , especially in regard to the environmental diffusion @xmath9 , which would have to be inferred from other parameters through theoretical considerations @xcite .
quantum estimation theory could however be adapated to allow for uncertainties in dynamical parameters other than the estimated one ( see e.g. @xcite ) . in the optomechanical paradigm
, one could also take into account the coupled light field : the extension of the present study to the full , two - mode optomechanical system , and the identification of associated optimal global detection strategies , will be an interesting development of this line of inquiry .
nevertheless , as it stands , our study clearly highlights the substantial advantage that monitoring environmental decoherence , whenever and to whatever extent possible , would grant .
this notion , we argue , should hence inform the design of experiments aimed at setting bounds on wave function collapse models . here
monitoring would be , in a sense , an active way of `` putting aside the impediments of matter '' that hinder the detection of fundamental effects , much in the same fashion as friction was standing in the way of galileo s analysis of free fall motion @xcite .
+ _ note added _ : after the completion of this work , we became aware of a related analysis where the qfi is employed to assess non - interferometric tests of wave - function collapse models ( see @xcite ) .
_ acknowledgments . _ - we thank p. barker and d. goldwater for discussions .
mgg and as acknowledge support from epsrc through grant ep / k026267/1 .
mgg acknowledges support from the marie skodowska - curie action h2020-msca - if-2015 .
osd acknowledge support from grant 2015/12747 - 9 , so paulo research foundation ( fapesp )
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( to appear ) . |
aim of this contribution is to present a fully covariant model for describing the electromagnetic ( em ) decay of vector mesons ( vm s ) , both in light and heavy sectors . to this end ,
a simple analytic form for the bethe - salpeter ( bs ) amplitude of vm s is adopted in order to perform without any further approximation the calculations of the decay constants . moreover , with such an ansatz one can easily evaluate the so - called transverse momentum distribution of a constituent inside the vm ( see de melo et al @xcite for the pion case ) , that plays an essential role for fixing the value of the parameters appearing in our approach , and in turn for including some non perturbative inputs in our analytical ansatz . a possible form of the bs amplitude for an interacting @xmath0 system with @xmath1 ,
can be written as follows _ ( k , p)=s(k , m_1 ) _ vm(k , k
- p ) s(k - p , m_2 ) where @xmath2 is the dirac propagator of a constituent with mass @xmath3 , @xmath4 the four - momentum of a vm with mass @xmath5 , @xmath6 its polarization four - vector , @xmath7 the helicity , @xmath8 the dirac structure of the amplitude and @xmath9 the momentum dependence of the bs amplitude .
in particular , the adopted covariant form for the dirac structure is the familiar one ( transverse to @xmath4 ) , viz v^(p ) = m m+m_1+m_2 that in the limit of non interacting system leads to the melosh rotations for a @xmath10 system @xcite , as expected .
for the present preliminary calculations , the momentum dependence has the following simple form with single poles , viz _
vm(k , k - p)= n _ i=1,3 1 [ lambda ] where @xmath11 , @xmath12 are the free parameters of our ansatz ( to be determined as described below ) , @xmath13 the normalization factor , that can be derived by imposing the standard normalization for the bethe - salpeter amplitude , in impulse approximation ( i.e. with free propagators for the constituents ) . the form chosen for @xmath9 allows one both to implement the correct symmetry under the exchange of the quark momenta ( for equal mass constituents ) and to avoid any free propagation of the constituents ( cf the numerator in eq .
( [ lambda ] ) ) . to determine @xmath11 in eq .
( [ lambda ] ) , we first define the constituent transverse momentum distribution inside the vm , @xmath14 , along the same guidelines adopted by de melo et al .
@xcite for the pion , within a light - front hamiltonian dynamics approach . in a frame where @xmath15 , one has n(k_)=n_cp_q|q(2)^3 ^ 2 _ 0 ^ 2 d_k__0 ^ 1 d m^2_0(1- ) @xmath16 and @xmath17 is the valence wave function associated to a given bs amplitude , see , e.g. , huang and karmanov@xcite and frederico et al@xcite . in eq .
( [ nk ] ) , the probability @xmath18 of the valence component reads p_q|q=
n_c(2)^3 ^ 2 _ 0 ^ 1 d ( 1-)d*k*_m^2_0 |(,*k _ * ; m_r_i)|^2 finally , @xmath14 is normalized as : @xmath19 . in spite of the simple form assumed for @xmath20
, one can nicely fit the constituent transverse momentum distributions obtained within 3-d approaches , that i ) retain only the valence component of the vm s and ii ) are able to yield a reasonable description of the spectrum . in this work
we have extracted the parameters @xmath21 in eq .
( [ nk ] ) by fitting @xmath22 to the corresponding quantity obtained from i ) a harmonic oscillator model ( see , e.g. figs . 1 and 2 ) , ii ) the godfrey - isgur model @xcite and iii ) an adapted version of the model by salcedo et al @xcite ( ita model ) .
in order to evaluate the em decays constants , @xmath23 , we adopted a mandelstam - like formula@xcite ( see also de melo et al.@xcite ) ) .
the starting point is the _ macroscopic _ definition of @xmath23 , through the transition matrix element of the em current for a given neutral vm , viz 0|j^(0)| p,= f_v _ ^ [ eq : fv ] the decay constant @xmath23 is related to the em decay width as follows _
e^-= [ eq : gamma ] in our model , the transition matrix element in eq .
( [ eq : fv ] ) can be approximated _ microscopically _ _ la _ mandelstam through 0|j^(0)| p,= f_vm n_cn ( 2)^4d^4 k _ vm(k , k - p , m_1,m_2 ) ( k^2-m^2_1 + ) [ ( p - k)^2-m^2_2 + ] [ _ ( p ) v(p ) ( k -p + m_2)^(k+m_1 ) ] [ eq : mandel ] where @xmath24 with @xmath25 the quark charge . in tabs .
[ tab : hosci ] , [ tab : gi ] , [ tab : qcd - in ] , the preliminary results for both valence probability , @xmath18 , and em decay widths , @xmath26 are shown . even if a more refined evaluations are in progress , some comments are in order : i ) for the harmonic oscillator model the light meson decay widths can be reasonably well described ( in the light sector the confining interaction is quite relevant ) , while the @xmath27 one is largely underestimated ; ii ) for the godfrey - isgur model @xcite , the heavy sector is well reproduced , while the light sector is overestimated , and this appears correlated to the poor estimate of the valence probability ( work in progress suggests that an ansatz for the bs amplitude with a more rich structure substantially improves the comparison ) ; iii ) for the adapted version of the ita model @xcite the same pattern of the harmonic oscillator case has been found , even if more dynamical contents are present in this model .
._preliminary vm em decay widths within the harmonic oscillator model
. adopted quark masses : @xmath28 0.310 gev , @xmath29 0.460 gev , @xmath30 1.749 gev , @xmath31 5.068 gev , _ [ tab : hosci ] [ cols="^,^,^,^,^,^",options="header " , ] and @xmath32 vs the quark transverse momentum .
dashed line : harmonic oscillator model .
solid line : fit by using the analytic ansatz in eq .
( [ lambda])_,title="fig:",width=207 ] ._,title="fig:",width=207 ]
in this contribution we have presented the main ingredients of our model for evaluating both the em decay width of the ground states of vm s and the probability of the valence component of the state . in our fully covariant model ,
a simple , analytic ansatz for the bs amplitude is proposed , and the three parameters , @xmath21 , for each neutral vm , are determined through a fitting procedure , based on the transverse momentum distribution of a constituent inside a given vm , obtained within a light - front hamiltonian dynamics framework . from this first comparisons between our results and the experimental data , one could argue that two different regimes occur in the light ( @xmath33 , @xmath32 ) and in the heavy sector ( @xmath27 ) . from the theoretical side , indeed , the harmonic oscillator and the adapted ita@xcite models seem to better reproduce the light mesons ( cf tab . [
tab : hosci ] , [ tab : gi ] ) while for the heavy sector the godfrey - isgur model@xcite seems to work better ( cf . tab .
[ tab : qcd - in ] ) .
the work in progress will substantially improve the present calculations , in two respect : both introducing a more refined ansatz for the bs amplitude and extending our investigation to the em decay of the @xmath34 .
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d 73 * , 074013 ( 2006 ) . | a fully covariant model for describing the electromagnetic decay of vector mesons , both in light and in heavy sectors , is presented .
the main ingredients of our approach are i ) an ansatz for the bethe - salpeter vertex for vector mesons , and ii ) a mandelstam - like formula for the electromagnetic decay constant .
the free parameters of our approach are fixed through a comparison with the transverse momentum distribution obtained within a light - front hamiltonian dynamics framework with constituent quarks .
preliminary results for both the decays constants and the probability of the valence component are shown .
= 11.6pt |
we are investigating whether or not interacting but not yet merging galaxies have heightened star formation properties . in our spitzer spirals , bridges , and tails interacting galaxy study ( @xcite ) ,
we have compiled a sample of interacting galaxies selected from the arp atlas of peculiar galaxies @xcite .
we have previously presented a detailed study of one of these galaxies , arp 107 , in @xcite . in the current proceeding
we investigate a second system , the interacting pair arp 82 ( ngc 2535/6 ) @xcite .
we have obtained uv , visible , and ir images of arp 82 from galex , sara , and spitzer telescopes respectively .
figure 1 displays various images of arp 82 .
the top left is a galex far - uv image with the 26 clumps identified .
the northern galaxy is ngc 2535 and southern galaxy is ngc 2536 .
the top right image in figure 1 is arp 82 in the spitzer irac 3.6 @xmath0 m band with h@xmath1 contours from the sara telescope .
the bottom left image in figure 1 is arp 82 in the spitzer irac 8 @xmath0 m band with sara h@xmath1 contours .
the tail is more prominent in the uv than in the ir while the center is much less prominent .
note that there are fuv and 8 @xmath0 m clumps in the tail region that are not seen in h@xmath1 .
the star forming regions at 8 @xmath0 m and in the fuv are more prominent than at 3.6 @xmath0 m .
the bottom right image in figure 1 is a snapshot of a smooth particle hydrodynamics model of the gas in red and old stars in blue .
this image shows arp 82 about 1 gyr after the initial closest approach .
the dotted curve shows the companion s passage .
the orbit is nearly planar .
the long duration is needed to allow particles to propagate out to the large distances observed .
four individual plots are seen in figure 2 .
the top left plots the galex fuv / nuv distribution .
a starburst99 @xcite stellar population synthesis model reddened with e(b - v)=0.0(blue ) , 0.2(green ) , and 0.6(red ) mag according to the @xcite reddening law is shown at the top of the histogram .
selected ages are marked .
the top axis is in magnitudes .
most of the clumps have an e(b - v ) between 0.2 and 0.6 mag and ages @xmath2 myr while a few clumps may be @xmath3 myr .
we have determined the star formation rate ( sfr ) for the clumps using two independent methods .
first , we estimated them from the l(ir ) using the calibration in @xcite .
the clumps have a total sfr@xmath4 of @xmath5 m@xmath6 yr@xmath7 .
second , we estimated the sfr from the l@xmath8(fuv ) using the uv sfr calibration in @xcite .
the total sfr@xmath9 of the clumps is @xmath10 m@xmath6 yr@xmath7 , in good agreement with the sfr@xmath4 .
no reddening correction has been applied to the l@xmath8(fuv ) .
the top right plot in figure 2 shows the star formation rate ( sfr ) versus distance from ngc 2536 .
the red symbols are the sfr determined from l(ir ) and the blue symbols are the sfr determined from l@xmath8(fuv ) .
the open boxes represent clumps in ngc 2536 , x s represent clumps in the bridge region , stars represent clumps in the spiral ( ngc 2535 ) region , and filled boxes represent clumps in the tail region .
the top axis is in arcseconds . from this figure
it can be seen that the sfr is greatest in the spiral region of ngc 2535 and in ngc 2536 , with much less star formation in the bridge and tail regions .
it can also be seen that the sfr s of clumps in the bridge and tail regions have much better agreement than do the sfr s of clumps in ngc 2536 and the spiral regions . in most cases
the sfr@xmath9 is greater than the sfr@xmath4 .
if an extinction correction were applied to the l@xmath8(fuv ) the sfr@xmath9 would be greater and the agreement with sfr@xmath4 would be worse .
the clumps in the bridge and tail regions account for about 7% of the total clump sfr@xmath4 , while the 2 clumps in the small companion , ngc 2536 , and the 2 largest clumps in the spiral region of ngc 2535 ( # 13 and # 16 ) make up about 42% of the total clump sfr@xmath4 .
the sfr@xmath4 of the entire arp 82 system is 1.2 m@xmath6 yr@xmath7 , while the entire system sfr@xmath9 is 2.7 m@xmath6 yr@xmath7 .
the total clump sfr@xmath4 accounts for about 36% of the entire system sfr@xmath4 .
the bottom left graph in figure 2 plots the irac [ 4.5]@xmath11[5.8 ] vs [ 3.6]@xmath11[4.5 ] colors of the clumps .
the data symbols are the same as above .
also included in this figure are the predicted irac colors for interstellar dust @xcite , the sloan digitized sky survey quasars in the spitzer wide - area infrared extragalactic survey ( swire ) elais n1 field @xcite , and the colors of m iii stars from m. cohen ( 2005 , private communication ) and field stars from @xcite .
the quasars have redshifts between 0.5 and 3.65 ; since their spectral energy distributions are power laws , their infrared colors do not vary much with redshift . from these figures
, it can be seen that clumps # 23 and # 26 have colors consistent with those of quasars and field stars respectively and may not be part of arp 82 .
most of the clumps have [ 4.5]@xmath11[5.8 ] colors between those of the ism and stars , indicating contributions from both to this color .
clumps # 24 and # 25 , which are in the northern tail , have colors similar to those of ism ( but with large uncertainties ) .
thus these appear to be very young star formation regions with little underlying old stellar population .
the bottom right graph in figure 2 plots the irac [ 4.5]@xmath11[5.8 ] color vs distance from ngc 2536 . the data symbols and horizontal axis
are the same as above . from this plot
it can be seen that clumps in the bridge and tail regions seem to have different relative ages than those in the spiral region .
the [ 4.5]@xmath11[5.8 ] colors are generally very red ( i.e. , very ` starbursty ' ) , except for the two low s / n clumps in the tail , # 23 and # 26 .
this work is based in part on observations made with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology under contract with nasa .
galex is a nasa small explorer mission , developed in cooperation with the centre national detudes spatiales of france and the korean ministry of science and technology .
this research was supported by nasa spitzer grant 1263924 , nsf grant ast 00 - 97616 , nasa ltsa grant nag5 - 13079 , and galex grant galexgi04 - 0000 - 0026 .
this work has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , california institute of technology , under contract with nasa . | to help understand the effects of galaxy interactions on star formation , we analyze spitzer infrared and galex ultraviolet images of the interacting galaxy pair arp 82 ( ngc 2535/6 ) , and compare to a numerical simulation of the interaction .
we investigate the uv and ir properties of several star forming regions ( clumps ) . using the fuv / nuv colors of the clumps
we constrain the ages .
the 8 @xmath0 m and 24 @xmath0 m luminosities are used to estimate the far - infrared luminosities and the star formation rates of the clumps .
we investigate possible gradients in the uv and ir colors .
see smith et al .
( 2006a , b ) for global results on our entire interacting sample . |
simulation of hadron production at low energies ( @xmath1 gev ) is relevant for various physical problems . as the cross - section in this region
is considered to be saturated with intermediate resonances , it is possible to study the properties of these resonances through mass , momentum and angular distributions .
simulation of different channels allows one to better account for selection rules and interference effects .
in particular , the problem of measuring r ( total cross - section of @xmath0 annihilation into hadrons ) is a crucial information for contemporary high energy physics , especially for the @xmath2 problem @xcite . at low energies this value
can only be obtained from an experiment .
simulation allows to calculate the ratios between different channels and estimate the accuracy of measurements
. of other related problems we can highlight the studies of @xmath3 at @xmath4 and @xmath5 decays allowing to check the vector current conservation hypothesis in the standard model @xcite , studies of the @xmath6 decay mode as well as @xmath7- and @xmath8-meson decays .
at this moment there is no theory , describing the strong interactions reliably at low energies .
we used a common phenomenological approach , assuming the production of a final state in consequent resonance decays : + @xmath9 only tree - level diagrams including 2- and 3-body decays , are considered ; + @xmath9 there may be several interfering mechanisms ( e.g. @xmath10 ) which may contribute to different final states ( e.g. @xmath11,@xmath12 ) in accordance with charge and strong isospin conservation ; + @xmath9 possible permutations of final particles are taken into account .
+ to simplify adding new matrix elements , we introduced the following requirements : + @xmath9 the tensor structures are chosen according to the field transformation properties ( spin , isospin , parities ) ; + @xmath9 expressions for matrix elements are written in gauge - invariant form with the help of specialized tensor library ( e.g. , @xmath13 ) ; + @xmath9 indices contraction and particles permutations are performed by the software . + allowed charge states and relative phases of permutations are based on the strong isospin part of the matrix element .
scalar parts of propagators may have arbitrary forms , including form - factors and dependence of width on virtuality . in case of the vector intial state ( @xmath14 )
, the absolute value of the transverse part of hadronic current is used as the value of matrix element .
several interfering matrix elements with arbitrary complex relative coefficients may be used .
by now the package has been used to calculate 4 and 6-pion production cross - sections in @xmath0-collisions .
some distributions of simulated data vs. experimental results @xcite are given in fig .
[ 2picomp ] ( parameters not fitted ) .
comparison with analytical calculations given in ref .
@xcite show a reasonable agreement .
+ at the vepp-2000 collider ( the major upgrade of vepp-2 m , binp , novosibirsk ) @xmath15 production will become possible . despite the lack of absolute normalization factor in matrix elements , the ratio of cross - sections of different final charge states with the same production mechanism
can be tested for @xmath15 data . in the channel @xmath16
our simulation ( left ) and experimental data ( right).,title="fig:",width=260 ] in the channel @xmath16 our simulation ( left ) and experimental data ( right).,title="fig:",width=260 ]
the package for simulation of multipion production has been developed .
it includes generators for @xmath17 @xmath18 , @xmath19 , @xmath20 , and @xmath21 production mechanisms
. this tool may be useful for many problems involving production of multipion final states .
we are thankful to o.yu .
dashevskij , i.f .
ginzburg , p.p .
krokovny , a.s .
kuzmin , a.i . milstein and n.i .
root for useful discussions and helpful contributions .
d.a . thanks dfg foundation for support of his participation in pic2003 .
the work is supported by rfbr grants 02 - 02 - 17884-a and 03 - 02 - 06651-mac .
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kopylov , the basics of resonance kinematics , nauka , moscow , 1970 . | software package for monte - carlo simulation of @xmath0 exclusive annihilation channels written in the c++ language for linux / solaris platforms has been developed .
it incorporates matrix elements for several mechanisms of multipion production in a model of consequent two and three - body resonance decays .
possible charge states of intermediate and final particles are accounted automatically under the assumption of isospin conservation .
interference effects can be taken into acccount .
package structure allows adding new matrix elements written in a gauge - invariant form .
= 14.5pt |
let @xmath8 be a simple arrangement formed by @xmath0 hyperplanes in dimension @xmath1 .
we recall that an arrangement is called simple if @xmath9 and any @xmath1 hyperplanes intersect at a distinct point .
the closures of connected components of the complement of the hyperplanes forming @xmath10 are called the cells , or @xmath1-faces , of the arrangement . for @xmath11 ,
the @xmath12-faces of @xmath10 are the @xmath12-faces of its cells .
a facet is a @xmath13-face of @xmath8 , and a facet belonging to exactly one bounded cell is called an external facet .
equivalently , an external facet is a bounded facet which belongs to an unbounded cell . for @xmath14 ,
an external @xmath12-face is a @xmath12-face belonging to an external facet .
let @xmath15 denote the number of external @xmath12-faces of @xmath10 .
the set of all external facets forms the envelope of the arrangement .
it was hypothesized in @xcite that any simple arrangement @xmath8 has at least @xmath2 external facets . in section [ 2d ] , we show that a simple arrangement of @xmath0 lines has at least @xmath4 external facets for @xmath16 , and that this bound is tight . in section [ 3d ] , we show that a simple arrangement of @xmath0 planes has at least @xmath6 external facets for @xmath17 , and exhibit a simple plane arrangement with @xmath7 external facets . for polytopes and arrangements
, we refer to the books of edelsbrunner @xcite , grnbaum @xcite and ziegler @xcite and the references therein .
[ ext2dlb ] for @xmath16 , a simple line arrangement has at least @xmath4 external facets .
the external vertices of a line arrangement can be divided into three types , namely @xmath18 , @xmath19 and @xmath20 , corresponding to external vertices respectively incident to 2 , 3 , and 4 bounded edges .
let us assign to each external vertex @xmath21 a weight of 1 and redistribute it to the 2 lines intersecting at @xmath21 the following way : if @xmath21 is incident to exactly 1 unbounded edge , then give weight 1 to the line containing this edge , and weight 0 to the other line containing @xmath21 ; if @xmath21 is incident to @xmath22 or @xmath23 unbounded edges , then give weight @xmath24 to each of the @xmath22 lines intersecting at @xmath21 .
see figure [ fig_weight_distribution ] for an illustration of the weight distribution .
a total of @xmath25 weights is distributed and we can also count this quantity line - wise .
the end vertices of a line being of type @xmath18 or @xmath19 , we have three types of lines , @xmath26 and @xmath27 , according to the possible types of their end - vertices .
as a line of type @xmath27 contains @xmath22 vertices of type @xmath19 , its weight is at least @xmath22 .
similarly the weight of a line of type @xmath28 weight is at least @xmath29 . remarking that a line of type @xmath30 contains at least one vertex of type @xmath20 yields that the weight of a line of type @xmath30 is at least @xmath31 . for @xmath16
the number of lines of type @xmath28 is at most 2 as otherwise the envelope would be convex which is impossible , see for example @xcite .
therefore , counting the total distributed weight line - wise , we have @xmath32 .
since for a line arrangement the number of external facets @xmath33 is equal to the number of external vertices @xmath34 , we have @xmath35 . for @xmath16 ,
consider the following simple line arrangement : @xmath36 is made of the @xmath22 lines @xmath37 and @xmath38 forming , respectively , the @xmath39 and @xmath40 axis , and @xmath41 lines defined by their intersections with @xmath37 and @xmath38 .
we have @xmath42 and @xmath43 for @xmath44 , and @xmath45 and @xmath46 where @xmath47 is a constant satisfying @xmath48 .
see figure [ a072 ] for an arrangement combinatorially equivalent to @xmath49 .
one can easily check that @xmath49 has @xmath4 external facets and therefore the lower bound given in proposition [ ext2dlb ] is tight . for @xmath16 ,
the minimum possible number of external facets of a simple line arrangement is @xmath4 .
, height=377 ]
let @xmath50 for @xmath51 be the planes forming the arrangement @xmath52 . for @xmath51 , the external vertices of the line arrangement @xmath53 are external vertices of the plane arrangement @xmath52 . for @xmath17 ,
the line arrangement @xmath53 has at least @xmath54 external facets by proposition [ ext2dlb ] , i.e. , at least @xmath54 external vertices .
since an external vertex of @xmath52 belongs to 3 planes , it is counted three times . in other words ,
the number of external vertices of @xmath52 satisfies @xmath55 for @xmath17 . as the union of all of the bounded cells is a piecewise linear ball ,
see @xcite , the euler characteristic of the boundary gives @xmath56 .
since an external vertex belong to at least 3 external edges , we have @xmath57 .
thus , we have @xmath58 . as @xmath55 , it gives @xmath59 for @xmath17 , we consider following simple plane arrangement : @xmath60 is made of the @xmath61 planes @xmath37 , @xmath38 and @xmath62 corresponding , respectively , to @xmath63 , @xmath64 and @xmath65 , and @xmath66 planes defined by their intersections with the @xmath39 , @xmath40 and @xmath67 axis .
we have @xmath68 , @xmath69 and @xmath70 for @xmath71 , and @xmath72 , @xmath73 and @xmath74 where @xmath47 is a constant satisfying @xmath75 .
see figure [ a073 ] for an illustration of an arrangement combinatorially equivalent to @xmath76 where , for clarity , only the bounded cells belonging to the positive orthant are drawn .
we first check by induction that the arrangement @xmath77 formed by the first @xmath0 planes of @xmath78 has @xmath79 external facets .
the arrangement @xmath77 is combinatorially equivalent to the plane cyclic arrangement which is dual to the cyclic polytope , see @xcite for combinatorial properties of the ( projective ) cyclic arrangement in general dimension . see figure [ a63 ] for an illustration of @xmath80 .
let @xmath81 denote the half - space defined by @xmath62 and containing the positive orthant , and @xmath82 the other half - space defined by @xmath62 .
the union of the bounded cells of @xmath83 in @xmath82 is combinatorially equivalent to the bounded cells of @xmath84 and therefore has @xmath85 facets on its boundary by induction hypothesis , including @xmath86 bounded facets contained in @xmath62 .
these @xmath86 bounded facets also belong to a bounded cell of @xmath83 in @xmath82 and therefore are not external facets of @xmath83 .
thus , the number of external facets of @xmath83 belonging to a bounded cell in @xmath82 is @xmath87 .
the union of the bounded cells of @xmath83 in @xmath81 can be viewed as a simplex cut by @xmath88 sliding down planes .
it has @xmath89 facets on its boundary , including the @xmath86 bounded facets contained in @xmath62 belonging to a bounded cell of @xmath83 in @xmath82 .
thus , the number of external facets of @xmath83 belonging to a bounded cell in @xmath81 is @xmath90 .
therefore , @xmath83 has @xmath91 external facets .
we now consider how the addition of @xmath92 to @xmath84 impacts the number of external facets .
this impact is similar in nature to the addition of @xmath92 to the first @xmath93 lines of @xmath36 .
the addition of @xmath92 creates @xmath94 new bounded cells : one above @xmath37 that we call the _ @xmath0-shell _ , and the other ones being below @xmath37 .
the @xmath0-shell turns @xmath88 external facets of @xmath84 above @xmath37 into internal facets of @xmath60 , and adds 3 external facets .
for each external facet of @xmath84 belonging to @xmath37 which is turned into an internal facet of @xmath60 , one external facet of @xmath60 on @xmath92 and not incident to @xmath37 is added .
below @xmath37 , the addition of @xmath92 creates @xmath95 new external facets of @xmath60 with an edge on @xmath37 .
finally , @xmath88 new external facets belonging to @xmath37 and bounded by @xmath92 are created from unbounded facets of @xmath84 .
thus , the total number of external facets of @xmath96 is @xmath97 .
we do not believe that @xmath98 minimizes the number of external facets . among the 43 simple combinatorial types of arrangements formed by 6 planes ,
the minimum number of external facets is @xmath99 while @xmath100 has 23 external facets .
see figure [ a63_29 ] for an illustration of the combinatorial type of one of the two simple arrangements with @xmath101 planes having 22 external facets .
the far away vertex on the right and 3 bounded edges incident to it are cut off ( same for the far away vertex on the left ) so the 10 bounded cells of the arrangement appear not too small .
david bremner + faculty of computer science , + university of new brunswick , new brunswick , canada .
+ _ email _ : bremner@unb.ca + + antoine deza , feng xie + department of computing and software , + mcmaster university , hamilton , ontario , canada .
+ _ email _ : deza , xief@mcmaster.ca | a facet of an hyperplane arrangement is called external if it belongs to exactly one bounded cell .
the set of all external facets forms the envelope of the arrangement .
the number of external facets of a simple arrangement defined by @xmath0 hyperplanes in dimension @xmath1 is hypothesized to be at least @xmath2 . in this note
we show that , for simple arrangements of @xmath3 lines or more , the minimum number of external facets is equal to @xmath4 , and for simple arrangements of @xmath5 planes or more , the minimum number of external facets is between @xmath6 and @xmath7 . |
schematic of an interferometer which implements the 2-qubit deutsch - jozsa algorithm ( a ) .
all beam splitters are 50/50 . with beam splitters c1 and c2 in place , the standard algorithm ( b ) is performed . in this work ,
we show that an alternate encoding ( c ) is preferable in the presence of random noise as indicated on rails 2 and 3 ; replacing beam splitters c1 and c2 with beam splitters d1 and d2 implements this modified algorithm .
fig 2 . experimental setup .
variable - reflectivity beam splitters are implemented using a pair of polarizing beam splitters ( pbs ) and a half waveplate .
the `` preparation '' portion of the interferometer produces the same superposition as the pair of hadamards in fig .
the oracle consists of two variable beam splitters which can each be set to swap two rails or leave them unchanged , plus two half - waveplate used to induce @xmath14 phase shifts on two of the outputs .
the random noise is generated by inducing turbulent airflow under rails 2 and 3 while they are spatially superposed .
fig 3 . experimental data : normalized intensity is a measure of the fraction of photons reaching each detector , pd1 through pd4 .
data are shown for both the dfs and standard encodings , for each of the four oracles ( 00 , 01 , 10 , and 11 ) ; c indicates `` constant '' oracles while b indicates `` balanced '' oracles .
the bottom plot shows the same data in the presence of noise .
note that the noise has a much more significant effect in the case of the standard encoding .
the probability of the algorithm returning a 0 or a 1 for each of the oracles , in each encoding , with and without the addition of phase noise .
the data are extracted by summing the normalized intensities from fig . 3 for pd1 and pd2 ( dashed line , indicating constant oracles ) and for pd3 and pd4 ( solid line , indicating balanced oracles ) .
note that the success rate is close to 1 even in the presence of noise when the dfs encoding is used . | for a practical quantum computer to operate , it will be essential to properly manage decoherence .
one important technique for doing this is the use of `` decoherence - free subspaces '' ( dfss ) , which have recently been demonstrated .
here we present the first use of dfss to improve the performance of a quantum algorithm .
an optical implementation of the deutsch - jozsa algorithm can be made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces ; we observe a reduction of the error rate from 35% to essentially its pre - noise value of 8% .
[ theorem]acknowledgement [ theorem]algorithm [ theorem]axiom [ theorem]claim [ theorem]conclusion [ theorem]condition [ theorem]conjecture [ theorem]corollary [ theorem]criterion [ theorem]definition [ theorem]example [ theorem]exercise [ theorem]lemma [ theorem]notation [ theorem]problem [ theorem]proposition [ theorem]remark [ theorem]solution [ theorem]summary one of the great stumbling blocks to building quantum computers , with their oft - touted ability to resolve certain problems more efficiently than any classical algorithm @xcite is the ubiquity of decoherence .
coupling of any element of a quantum computer to an environment destroys its unitary evolution , and introduces uncontrollable noise ; at first , it was thought by many @xcite that these errors would make quantum computation impossible in practice . since then , a variety of techniques for correcting errors and/or building in immunity to certain classes of decoherence have been developed @xcite and it has been proved that if errors are kept below a certain constant threshold , arbitrarily large quantum computers are possible@xcite .
one important technique involves computing within certain subspaces of the full system s hilbert space known as decoherence - free subspaces ( dfss ) @xcite which remain unaffected by the interaction with the environment .
such dfss exist when the interaction hamiltonian has an appropriate symmetry property .
dfss have been demonstrated in a linear - optical experiment @xcite and in nmr @xcite and recently to help circumvent the technical noise which had previously limited the operation of ion - trap quantum computers @xcite . to date , no demonstration has been made of the usefulness of dfss in the context of the implementation of an actual quantum - computing algorithm . in this paper , we present a linear - optical implementation of the two - qubit deutsch - jozsa algorithm dj92,nchuang , and demonstrate that when a certain class of noise is introduced into the system , greatly increasing the error rate of the algorithm , it is possible to ` encode ' one logical qubit into two physical qubits and take advantage of dfss , reducing the error rate to close to zero .
linear optics is well known to be an extremely powerful arena for the transportation and manipulation of quantum information , benbrassard , reckzeilinger .
although it is also well known that due to the linearity of optics , this arena does not allow for scalable construction of quantum gates @xcite , recent work has shown that the incorporation of detection and post - selection may in fact render all - optical quantum computers an attractive possibility @xcite .
work also proceeds on development of nonlinearities which would allow for the development of natural two - qubit gates in optics@xcite . while we do not yet have access to a truly scalable optical quantum - computer architecture
, many of the elements of any such system would be identical to those used in simple linear - optical geometries @xcite . for this reason
, linear optics remains an important domain for the study of quantum coherence and error correction , even while the ultimate fate of optical quantum computing is uncertain .
recently , striking demonstrations of quantum search algorithms @xcite have been carried out in linear - optical systems , as has the first verification of dfss @xcite . additionally , it is already clear that even if quantum computation never becomes truly practical , quantum information processing may have a great effect on the practice of communications and cryptography@xcite .
although some information - processing will be necessary in this area as well , the question of scalability is not crucial , and linear - optical quantum computation could well prove applicable for elements such as quantum repeaters repeatersbriegel . in this context
, we have chosen to study the applicability of dfss to a linear - optical implementation of the quantum deutsch - jozsa algorithm , despite the non - scalable nature of the present architecture .
the deutsch - jozsa algorithm is designed to distinguish between two classes of functions ( `` oracles '' ) on n - bit binary inputs .
`` constant '' functions return the same value ( 0 or 1 ) for all @xmath0 possible inputs , while `` balanced '' functions return 0 for half the possible inputs and 1 for the other half .
clearly , a classical algorithm would on some occasions require as many as @xmath1 queries to unambiguously determine to which class a given oracle belongs .
by contrast , deutsch and jozsa showed @xcite that a quantum algorithm requires only one such query . in the 2-qubit deutsch - jozsa algorithm @xcite ,
the oracle is a function on a single bit .
it takes as input a query bit @xmath2 and a signal bit @xmath3 ; its action is to perform the unitary mapping @xmath4 _ _ @xmath5 _ _ @xmath6 to perform the algorithm , the input is prepared in @xmath7\otimes \lbrack \left| 0\right\rangle -\left| 1\right\rangle ] $ ] which the oracle maps to @xmath8=\frac{1}{2}[\left| 0\right\rangle e^{i\pi
f(0)}+\left| 1\right\rangle e^{i\pi f(1)}]\otimes h\left| 1\right\rangle $ ] .
a hadamard on the query qubit then transforms it into @xmath9 which is equal to 0 for constant and 1 for balanced functions .
thus measurement in the computational basis allows one to determine a global property of @xmath10 , namely @xmath11 in a single evaluation of the function .
furthermore , the signal qubit is in fact superfluous after the oracle @xcite .
thus only one logical qubit is needed after the operation of the oracle .
if some source of decoherence is present during the propagation from the oracle to the final hadamard , one may consider encoding this logical qubit in some decoherence - free subspace of the two physical qubits . in this experiment
we represent the four basis states of two logical qubits ( @xmath12 and @xmath13 , where the first bit corresponds to the query and the second to the signal ) by a photon traveling down one of four optical rails numbered 1 , 2 , 3 and 4 respectively .
it is possible to implement a universal set of one- and two - qubit operations in a four - rail representation @xcite .
for example a not gate on the query qubit can be realized by simultaneously swapping rails 1 and 3 and rails 2 and 4 . a cnot gate on the signal qubit is implemented by swapping rails 3 and 4 .
to perform a hadamard gate on the query qubit , we combine rails 1 and 3 and rails 2 and 4 at two 50/50 beam - splitters ; a @xmath14 phase shift is also needed on two of the arms.analogous gates can be constructed for the other qubit .
the transformations introduced by the four possible functions can also be implemented in this representation by four different settings of an oracle operating as follows : if @xmath15 is 1 , rails 1 and 2 are swapped ; if @xmath16 is 1 , rails 3 and 4 are swapped .
thus the task of distinguishing balanced from constant oracles reduces to that of determining whether the number of swaps was odd or even . the schematic diagram of the interferometer is shown in fig .
1 .
each photon is sent along rail 2 corresponding to the logical state @xmath17 .
the two pairs of 50/50 beam splitters @xmath18 , @xmath19and @xmath20 , @xmath21 implement the two hadamard gates on the query and signal qubits respectively , preparing the qubits for the oracle s action .
the last two 50/50 beam splitters @xmath22 and @xmath23 realize the hadamard gate on the query qubit after the oracle .
rails 1 - 4 illuminate photodiodes @xmath24 .
a photon reaching pd1 or pd2 indicates that the value of the query qubit after the algorithm , @xmath25 , is 0 .
this constitutes a determination that the oracle is constant , while the other two detectors indicate balanced oracles .
one source of decoherence in such systems is the phase noise introduced by fluctuating optical path lengths between the different sections of the apparatus , created either by variations in distance or by temperature variations and turbulent air flow . in real optical systems ,
the stability of certain path - length differences may be larger than that of others , either because of the physical proximity of certain paths to one another or because of the particular sources of mechanical or thermal noise .
this may lead to a situation where the dominant source of decoherence exhibits a particular symmetry which can be exploited for computing within dfss . to simulate the effects
such processes could have in larger - scale , distributed quantum - information systems , we introduced a high degree of turbulence by placing the tip of a hot soldering iron below two of the optical rails .
these two optical paths ( rails 2 and 3 ) were spatially superposed in this region , distinguished only by their polarisation ; for this reason , they experienced essentially the same random phase shifts under the influence of the turbulent air flow , relative to the other optical rails .
since the outputs of the optical deutsch - jozsa setup are the outputs of two parallel interferometers , which measure the phase of rail 2 with respect to that of rail 4 and rail 3 with respect to rail 1 , this phase noise destroys the interference on which the success of the algorithm relies .
on the other hand , inspection of the optical schematic makes the physical process behind the algorithm evident : rails 1 and 3 are prepared in phase with one another , while rails 2 and 4 are also prepared in phase , but @xmath26out of phase with the former pair .
thus , constructive interference is observed either between 1 and 3 or between 2 and 4 . if a single pair ( 1 and 2 or 3 and 4 ) is swapped by the oracle , destructive interference is instead observed at both interferometers , while if an even number of swaps occurs , constructive interference is restored .
in other words , so long as each interferometer compares an output of each of the potential swap regions in the oracle with one from the other , it is possible to distinguish a balanced oracle ( one swap ) from a constant oracle ( zero or two swaps ) . the strategy to deal with phase noise impressed symmetrically on paths 2 and 3 now becomes clear : instead of interfering 2 with 4 and 1 with 3 , one can accomplish the same task by interfering 2 with 3 and 1 with 4 . in this way , the random phase appears at both inputs to the same interferometer , and has no effect on the measured results .
this modification can be expressed as an encoding of the data into a pair of dfss .
since our engineered phase noise has identical effects on the two states of odd parity ( @xmath27 and @xmath28 stored on rails 2 and 3 respectively ) and on the two states of even parity ( @xmath29 and @xmath13 , stored on rails 1 and 4 ) , each fixed - parity subspace can store a single logical qubit in a decoherence - free fashion .
the action of the soldering iron tip may be modelled by the evolution operator @xmath30 , where @xmath31 is a random , fluctuating phase . in a subspace with a definite eigenvalue of @xmath32 , the random phase
, @xmath33 does nothing but impress an overall global phase on the quantum state , leaving the information within the subspace unaffected . since the 2-qubit deutsch - jozsa algorithm relies on a single qubit ( query qubit ) after the oracle has completed its action , this single qubit may be encoded in either of these dfss , providing immunity to parity - dependent phase noise which occurs between the oracle and the final hadamard gates . as shown in fig
1c , a cnot after the oracle encodes the query qubit into these dfss , and a second cnot after the final hadamard can be used for decoding .
the decoding cnot is unnecessary since measurements are only performed on the query qubit . swapping rails 3 and 4 performs the encoding ; or equivalently ,
beam - splitters @xmath22 and @xmath23 may be replaced by @xmath34 and @xmath35 .
the actual experimental setup is shown in fig .
2 .
the light source was a diode laser operating at 780 nm . to implement the four different oracle settings a specific kind of variable beam splitter ( vbs )
was designed .
this variable beam splitter consists of a half - waveplate between two polarizing beam splitters ( pbs ) ; any desired reflectivity can be obtained with this optical arrangement . for realizing our oracles , a pair of these vbss was used , and
each was adjusted either for maximum or minimum reflectivity , essentially acting as a swap or the identity .
hadamards were constructed using similar vbss .
after the oracle rails 2 and 3 were combined into the same spatial mode in a pbs to guarantee the collective phase shift for these beams in presence of decoherence , and then separated out by another pbs .
the transformation between two different encodings was performed by applying another vbs to either swap rails 3 and 4 or not .
the experimental setup was designed such that in all of these interferometers the spatial path lengths are always balanced .
the average fringe visibility for all four output ports and all possible settings of oracle and encoding was measured to be about 95% .
this setup consists of 16 different possible mach - zehnder interferometers , of which two are in operation for any given oracle / encoding combination .
the experiment was performed by measuring the signals at detectors @xmath36 through @xmath37 as the half waveplates were adjusted to cycle through all four oracles and both encodings .
the intensities at detectors pd1 through pd4 were normalized to their sum , to yield the probabilities of a photon reaching each of the detectors .
these normalized intensities are plotted in fig . 3 for all 4 oracle settings , in both the standard algorithm and the dfs encoding .
ideally , all the photons should arrive at detectors @xmath36 and @xmath38 for constant functions and at detectors @xmath39 and @xmath37 for balanced functions . in figure 4 , we plot the probability of a photon reaching _ either _ pd1 or pd2 , and the probability of a photon reaching _ either _ pd3 or pd4 .
the average error rates were measured to be about 8% in the absence of added noise .
the sources of errors in this experiment were mostly due to imperfect visibility , ( due to alignment and waveplate setting ) , and uncertainty and drift in the optical phases setting , when a @xmath40 phase error on one beam correspond to a 2% error rate .
the drift of the interferometer during measurement was kept low by balancing all path lengths as mentioned above and enclosing the interferometer .
introduction of the turbulent airflow increased the average error rates to 35% for the standard algorithm . when the dfs encoding was used in the presence of turbulence , however , the error rates dropped to 7% , essentially equal to the value in the absence of noise .
this work demonstrates that a simple modification of a quantum algorithm may be used to encode information into dfss , and significantly reduce the error rate introduced by realistic , physical noise sources , provided that these sources have certain symmetry properties .
phase noise is an everpresent issue in coherent optical systems , and often exhibits certain correlations which should be exploitable in this manner .
we also note that since the noise characteristics are intimately tied to the particular physical realization of a quantum circuit , it may often prove easier to design the decoherence - free process by direct consideration of the multiple interferometers which constitute the optical device , than by contemplation of the very general quantum circuits .
this work was supported by the us air force office of scientific research ( f49620 - 01 - 1 - 0468 ) , nserc , and photonics research ontario .
we would like to acknowledge useful discussions with daniel lidar and also thank guillaume foucaud and chris ellenor for technical assistance .
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the authors are very much grateful to v. i. anisimov for helpful advise on the lsda+u method and for a fruitful discussion on the spin alignment of ndnio@xmath0 , and also to t. mizokawa for useful discussion about their work @xcite .
this work is supported by grant - in - aid for coe research `` spin - charge - photon '' . | electronic structures of ndnio@xmath0 and ynio@xmath0 are calculated by using lsda+u method with rotational invariance .
the jahn - teller distortion is not allowed under the observed magnetic ordering .
no orbital order on ni sites can not be observed in the calculation of both systems but different types of charge ordering . in a small distorting system
ndnio@xmath0 , all ni ions are trivalent and oxygen sites have a particular ordering , both in charge and orbital . in a large distorting system ynio@xmath0 ,
the charge disproportionation occurs , 2ni@xmath1 ni@xmath2ni@xmath3 .
therefore , the charge ordering stabilizes the asymmetry of the arrangement of ni magnetic moments in both systems .
2 perovskite transition metal oxides are now of high interest because of the large variety and the possible controllability of their physical properties .
perovskite nickelates rnio@xmath0 ( r = an trivalent rare earth or y ions ) can be classified into three different categories , according to their tolerance factor ( @xmath4 ) .
@xcite one is those whose tolerance factor is much smaller ( @xmath5 ) and has a larger distortion , such as lunio@xmath0 or ynio@xmath0 .
they are antiferromagnetic insulators at low temperatures .
this class of rnio@xmath0 undergoes transition to paramagnetic insulator at the neel temperature @xmath6 and also has another phase transition from paramagnetic insulator to paramagnetic metal ( m - i transition ) at very high transition temperature .
second is those whose tolerance factor is intermediate ( @xmath7 ) , such as ndnio@xmath0 or prnio@xmath0 .
these materials are also antiferromagnetic insulators at low temperatures and above @xmath6 they are paramagnetic metals .
@xcite third is lanio@xmath0 where @xmath8 and is paramagnetic metal . low temperature phase of above mentioned first and second classes of rnio@xmath0 have the unique magnetic structures .
@xcite its magnetic diffraction peak is characterized by the propagation vector @xmath9 and the magnetic unit cell is identified as the @xmath10 supercell of the crystallographic lattice .
@xcite the magnetic order is specified to be alternating ferromagnetic ( fm ) and antiferromagnetic ( afm ) couplings @xmath11 along three crystallographic directions . on the contrary to the asymmetric arrangement of magnetic bonds ( fm / afm ) around each nickel site , ni - o distances around each ni ion are almost equal to each other .
for instance , the difference between the longest and the shortest ni - o bonds in one nio@xmath12 octahedron is at most 2% in rnio@xmath0 .
@xcite the jahn - teller distortion is absent in rnio@xmath0 , even in the largely distorted system ynio@xmath0 , whose tolerance factor is 0.88 .
experimentally there is only one crystallographic site for ni ions in ndnio@xmath0 and two different sites for ni ions in ynio@xmath0 .
therefore , one can expect trivalent ions ni@xmath13 in ndnio@xmath0 . on the contrary , ni ions in ynio@xmath0 are divalent and quadrivalent , _
i.e. _ the charge disproportionation 2ni@xmath1 ni@xmath2ni@xmath3 occurs . in this letter , we study the electronic properties of the afm insulating phase of two perovskite nickelates , ndnio@xmath0 and ynio@xmath0 , which are typical ones of above mentioned two respective classes .
we use the lsda+u method with the rotational invariance in conjunction with the lmto - asa method .
@xcite the lsda+u method counts the electron - electron interaction between localized orbitals by the hartree - fock type interaction term .
the ionic positions and lattice parameters used in the present calculations are imported from the diffraction experiments .
@xcite the unit cell here is the @xmath14 crystallographic supercell containing 16 nd or y ions , 16 ni ions , and 48 o ions and , in addition , 32 empty spheres , totally 112 atomic spheres .
sixty - four k - points in the brillouin zone are sampled in the calculation of the density of states .
ndnio@xmath0 is antiferromagnetic up to @xmath15 , but the nd spin moment vanishes at about 30k .
@xcite therefore , three 4f electrons of nd ion are counted in the frozen core .
we also calculated the electronic structure of ndnio@xmath0 with 4f electrons in valence states , and the results show no significant difference .
the coulomb and exchange parameters @xmath16 and @xmath17 of ni ions are fixed to be 7.0 ev and 0.88 ev , respectively , through all the lsda+u calculations .
these values are consistent with photoemission experiments and the results of the lsda calculations
. calculated results are not changed much over a large range of values of @xmath16 and @xmath17 .
the crystallographic space groups of ndnio@xmath0 and ynio@xmath0 are orthorhombic @xmath18 and monoclinic @xmath19 , respectively .
the group theoretical analysis shows that , using the projection operator method , the jahn - teller distortion of one nio@xmath12 octahedron can not be transfered over the whole enlarged @xmath20 supercell with @xmath21 .
@xcite therefore , the jahn - teller distortion actually can not appear in the observed spin ordered state .
ndnio@xmath0 : there are two possible spin configurations in @xmath22 satisfying the observed transfer vectors @xmath21 .
one is that the spin magnetic moments align ferromagnetically on the ( 101 ) plane and the planes are stacked with a doubled period as @xmath23 , whose magnetic space group is monoclinic @xmath24 .
@xcite this spin configuration is assumed in the present letter . another possible spin configuration with @xmath25 spin order could be the doubled period checkerboard stacking along crystallographic @xmath26-axis , and the magnetic space group is orthorhombic @xmath27 .
@xcite the state of @xmath27 shows orbital ordering of e@xmath28 states on ni sites , but the resultant calculated total energy is higher by 0.18 ev per @xmath29 cell than that of @xmath24 .
because there is no possibility of subsidiary jahn - teller distortion to lower the total energy , @xmath27 could not be the symmetry to be considered .
the total energy is also calculated in a fictitious antiferromagnetic state of @xmath30 whose magnetic unit cell is identical to the crystallographic one and is higher by 2.0 ev per @xmath31 cell .
figure [ fig - ndnio3-pdos ] shows the projected density of states on the ni 3d orbitals in ndnio@xmath0 .
the system is insulator with a gap @xmath32ev .
each nickel ion has the local magnetic moment @xmath33 within the atomic sphere of a radius @xmath34 , contrary to the observed value of @xmath35 .
@xcite it should be noticed that the local magnetic moment can not be uniquely defined .
furthermore , ndnio@xmath0 is not a simple antiferromagnetic insulator but a dynamical effect is essential , which may be an origin of this discrepancy .
@xcite there is no distinctive variation in partial spin density of states of ni site in each magnetic sublattice .
an e@xmath28 band lies on the energy range @xmath36 .
the numbers of states in the energy ranges @xmath37 and @xmath38 are 16 , respectively , which are the one occupied and one vacant e@xmath28 states per ni ion . actually , these e@xmath28 orbitals extend over surrounding oxygen sites from ni ions due to strong hybridization between ni e@xmath28 and o p orbitals .
the extended occupied e@xmath28 orbital has a 60% weight on p orbitals on surrounding six oxygens , a 10% weight on an individual oxygen .
therefore , one would establish a model where one occupied e@xmath28 state with majority spin locates at the top of the valence bands , and it hybridizes strongly with the p states on nearby o ions .
this is the molecular orbital @xmath39 state .
@xcite then one can assign all nickel ions in ndnio@xmath0 to be trivalent ni@xmath13 ( t@xmath40e@xmath41 ) , even though the ni ion is not truly ionized by + 3 charge . in the projected density of states of ni ion site
, one observes a large amount of e@xmath28 states at the bottom of the d bands , which are the bonding states between ni d and o p , corresponding to the @xmath42 states in the molecular orbital picture .
@xcite the e@xmath28 band in the range @xmath43 does not show any orbital ordering .
in fact , off - diagonal elements within the e@xmath28 subblock of the occupation matrix @xmath44 are zero and the diagonal elements are identical
. the absence of the orbital ordering may be consistent with the fact that the @xmath45 $ ] axis has three - fold rotational symmetry in the present spin configuration , once the distortion is neglected . due to this pseudo three - fold rotational symmetry , the basis orbitals of e@xmath28 representation of the trigonal group d@xmath46 is a good basis set and those derived from e@xmath28 orbitals are @xmath47 and @xmath48 . therefore , there is no difference between the occupancies of @xmath49 and @xmath50 .
figures [ fig - ndnio3-sd ] is the spatial profiles of spin densities @xmath51 in the energy range @xmath52 ( @xmath39 state ) .
only one spin component of o p orbitals on the fm bond is bridging between two ni e@xmath28 orbitals , while both spin components on the afm bond couple with ni e@xmath28 orbitals of respective spins .
consequently , oxygen ions on the afm bond have more charge in this energy range than oxygen on the fm bond .
this is the realization of oxygen - site charge - ordered state discussed by mizokawa _
et al .
_ in the framework of the hartree - fock calculation .
@xcite however , the charge difference between oxygen sites of ni@xmath53-@xmath54-ni@xmath53 and ni@xmath53-@xmath55-ni@xmath56 in @xmath39 states is mostly compensated by hybridized @xmath42 state at lower energies . besides , all oxygen ions have no local magnetic moment .
more significant results seen in fig . [ fig - ndnio3-sd ] may be the p orbital ordering on oxygen sites .
the magnetic space group is @xmath24 and its unitary part is @xmath57 .
the unit cell and lattice primitive vectors are not identical to those in @xmath18 .
the spin density in fig .
[ fig - ndnio3-sd ] is consistent with this magnetic group @xmath24 , neither higher nor lower than this .
the symmetry lowering of the unitary part @xmath57 is the origin of the opening the band gap at @xmath58 in the majority spin band , despite to the absence of the orbital ordering on ni sites ( _ i.e. _ symmetry driven band gap ) .
therefore , one can conclude that the origin of the insulator phase at low temperatures in ndnio@xmath0 is the characteristic spin density on the oxygen sites or , equivalently , the orbital ordering there .
the energy gap @xmath59 ev is due to the symmetry of charge order . in fictitious ideal cubic structure without distortion or tilting of nio@xmath12 octahedra ,
the system becomes metal whose valence and conduction bands touch at points with each other .
@xcite the structure of @xmath39 bands is insensitive to the value of @xmath16 .
the value of the band gap is unchanged down to @xmath60 ev .
this is because the gap is driven by the symmetry .
ynio@xmath0 : one should expect larger distortion in ynio@xmath0 because ynio@xmath0 is the typical system with the small tolerance factor .
@xcite there are two different crystallographic ni sites , and the distances from each ni ion to surrounding o ion are different by 3@xmath614% from one type of ni ion to the other type .
@xcite calculated self - consistent solution is that with the apparent charge disproportionation and no orbital polarization .
since ni@xmath3 site has no spin magnetic moment , the two spin configurations discussed in ndnio@xmath0 become identical and the spin configuration of ynio@xmath0 is uniquely determined .
the magnetic space group is @xmath62 if the spins of ni@xmath3 ions are non vanishing and , on the contrary , @xmath63 if the spins of ni@xmath3 ions are zero .
the latter symmetry @xmath63 is actually the case .
figure [ fig - ynio3-pdos ] shows the projected density of states at ni ion sites . the system is insulator with a gap @xmath64ev .
the resultant magnetic moments for half of ni ions are @xmath65 within the atomic sphere of a radius @xmath66 , namely divalent ions ni@xmath67
( t@xmath40e@xmath68 ) , of larger nio@xmath12 octahedron and zero for another half of ni ions within the atomic sphere of a radius @xmath34 , namely quadrivalent ni@xmath3 ( t@xmath40 ) , of smaller octahedron . the experimentally observed magnetic moments are @xmath69 for ni@xmath67 ions and
@xmath70 for ni@xmath3 ions .
@xcite the discrepancy may be due to a possible non - collinear spin order .
the number of states in the energy range @xmath71 is 16 and dominant weight on ni@xmath67 .
because the number of ni@xmath67 in the @xmath14 cell is 8 , these states are assigned as two e@xmath28 states mainly on ni@xmath67 and surrounding oxygens .
the e@xmath28 orbitals of ni@xmath3 is lifted in the higher energy range ( @xmath72 ) without spin polarization .
a large amount of e@xmath28 orbitals in ni@xmath67 ions locates at the bottom of the d bands , in the range @xmath73 for ni@xmath67 , and in the range @xmath74 for ni@xmath3 , stabilizes the bonding between ni@xmath3 ions and oxygen ions . from these facts
, one can establish a model that deep @xmath42 molecular orbitals ( one per both ni@xmath67 and ni@xmath3 ) stabilize the system , and other two e@xmath28 states ( @xmath39 states ) per one ni@xmath67 ion located at @xmath75 .
the charge disproportionation is mainly due to the crystal field effect .
the low spin state in ni@xmath3 or ni@xmath13 ion is energetically unstable in small @xmath76 case and the ground state multiplet of ni@xmath67 is @xmath77a@xmath78 ( t@xmath40e@xmath68 ) for all arbitrary values of @xmath76 .
@xcite therefore , the small tolerance factor causes two different ni sites , compressed ni@xmath3 ( large @xmath76 ) and dilated ni@xmath67 ( small @xmath76 ) , rather than uniformly dilated ni@xmath13 ionic states .
@xcite the standard values of @xmath79 ( @xmath80 is the racah parameter ) for ni@xmath67 is presumably around 1.0 . once one estimate the crystal field effects from the ni - o bond lengths @xmath81 , the difference of @xmath82 on two ni ion sites is presumably about 20% .
two narrow e@xmath28 bands can be seen in the energy range @xmath83 and @xmath84 in fig .
[ fig - ynio3-pdos]a .
two ni@xmath67 e@xmath28 states are spatially extending over wide area and not only hybridizing with the nearest neighbor o ions but also extending over the nearest @xmath85 ions .
this situation is well depicted in the spin density .
figure [ fig - ynio3-sd ] shows the isometric surfaces of the spin density in the range of @xmath83 .
the d - wavefunctions on ni@xmath67 are extending over the ( 101 ) plane , and antiferromagnetically coupled with other ni@xmath67 ions .
charge in each ni ion is compensated in ynio@xmath0 as in ndnio@xmath0 and the difference between total charges in the muffin tin spheres on ni@xmath67 and ni@xmath3 sites is very small , equals to 0.03 .
this variation is the same order as that of oxygen ions in ndnio@xmath0 .
however , charge disproportionation is coupled with the lattice distortion , where larger oxygen octahedron is surrounding ni@xmath67 , and stabilizes the lattice system in ynio@xmath0 .
therefore , diffraction experiment can detect the charge ordering in the yttrium system easier than in the neodymium system . in conclusion ,
we have studied two typical antiferromagnetic insulating phase of rnio@xmath0 , ndnio@xmath0 and ynio@xmath0 , by using the lsda+u method . a possibility of the jahn - teller distortion is excluded by the group theoretical consideration .
no orbital order on ni sites is observed in both systems , but two different types of ordering are observed . in small distorting rnio@xmath0 such as ndnio@xmath0 , oxygen sites shows the orbital ordering and this is the origin of the gap opening in ndnio@xmath0 .
in large distorting rnio@xmath0 such as ynio@xmath0 , the charge disproportionation 2ni@xmath86ni@xmath2ni@xmath3 occurs . the charge ordering mechanism
can explain the stabilization of the asymmetric alignment of the local magnetic moments around each nickel site in both systems .
we may add the final comment about effects of electron - electron correlation in rnio@xmath0 .
the widths of the calculated e@xmath28 bands @xmath87 by the lda are @xmath88(ynio@xmath0 ) , @xmath89(ndnio@xmath0 ) , and @xmath90(lanio@xmath0 ) . then , the ratio of @xmath91 may be estimated as @xmath92 , assuming the value of the coulomb repulsion @xmath16 is common for all , and one can see a large reduction of @xmath91 in lanio@xmath0 , which may be the key parameter for the difference of the ground states of these perovskite nickelates .
ndnio@xmath0 shows the anomalous m - i transition .
@xcite lanio@xmath0 is presumably an anomalous metal of strongly correlated electrons @xcite and could not be treated within the framework of the lsda+u method . |
one may wonder whether the two - time correlations @xmath158 reflect time - dependent measurements after the preparation of some initial state .
we show that this is the case for the simple , but important example of a spin correlation for @xmath18 , i.e. , for @xmath73 .
then we write @xmath159 where @xmath160 projects onto the states with @xmath161 .
if @xmath7 denotes the density matrix of the total system before any state preparation we calculate where we assumed that the hamiltonian @xmath4 and the density matrix @xmath7 are invariant under total inversion @xmath163 so that the second term in equals the first one .
finally , in we define the initial density matrix @xmath164 which results from @xmath7 by projecting it to the states with @xmath165 and its proper normalization .
this clearly shows that in the studied case @xmath14 equals the time - dependent expectation value for a suitably prepared initial state .
the above procedure can be modified to other observables .
generally , we can consider @xmath166 to focus on the time - dependent expectation value @xmath167 starting from the initial density matrix @xmath168 .
however , do not claim that a suitable operator @xmath169 is easy to find .
this route remains to be explored in future work .
with these matrix and vector elements we can compute @xmath66 in for various sets of conserved quantities . note that @xmath185 is linearly dependent on the @xmath102 quantities
@xmath157 with @xmath186 due to @xmath187 similarly , @xmath188 depends linearly on them due to @xmath189 hence , one may either consider @xmath87 together with the @xmath102 quantities @xmath157 with @xmath186 _ or _ the three quantities @xmath190 .
the first choice exploits all the known conserved quantities on the considered level of at most trilinear spin combinations .
this is what is called ` all quantities ' in fig . 1 in the letter
. no explicit formula can be given , but the required matrix inversion is easily performed for up to @xmath191 spins with any computer algebra program and up to @xmath192 spins by any subroutine package for linear algebra . the second choice of @xmath190 yields @xmath193 matrices and can be analysed analytically .
inserting the elements in and in and those in into yields @xmath194 furthermore , these three quantities are conserved for any isotropic spin model so that we may also consider the system with the additional bond @xmath195 , see fig . 1 .
thus we extend the above formulae by passing from @xmath88 to @xmath4 and hence from @xmath185 to @xmath196 .
the modified scalar products are they lead to a bound @xmath198 as depicted in fig . 1 .
the explicit formula is similar to the one in , but lengthy so that we do not present it here .
it can be easily computed by computer algebra programs .
. relates the non - decaying fraction @xmath26 to the relative bound for the overhauser field @xmath199 where @xmath144 is arbitrary if the central spin has @xmath18 .
we stress , however , that the derivation yielding in ref
. only holds for the csm so that we do not consider extensions to finite @xmath109 in this case .
we use the freedom to choose @xmath144 to maximize the resulting lower bound for @xmath200 .
we reuse all matrix elements of the norm matrix @xmath56 in and in .
since uses the relative correlation we have to compute @xmath201 as well .
furthermore , the vector elements of @xmath202 must be determined anew these elements allow us to determine the ratio @xmath204 for the three quantities @xmath190 or for all quantities , i.e. , @xmath87 and @xmath157 with @xmath205 .
the ensuing lower bounds can be optimized by varying @xmath144 in such a way that the ratios become maximum yielding the best bounds .
the latter step is easy to perform since the non - linear equation in @xmath144 to be solved to determine the maximum is just a quadratic one . in this way ,
the triangle and square symbols in fig . 1 are computed . the comparison to the bethe ansatz data for up to @xmath206 spins in ref .
@xcite yields an excellent agreement within the accuracy with which we can read off @xmath26 from the numerically evaluated bethe ansatz correlation @xmath14 .
this concludes the section on the required input of matrix and vector elements . | mazur s inequality renders statements about persistent correlations possible
. we generalize it in a convenient form applicable to any set of linearly independent constants of motion .
this approach is used to show rigorously that a fraction of the initial spin correlations persists indefinitely in the isotropic central spin model unless the average coupling vanishes .
the central spin model describes a major mechanism of decoherence in a large class of potential realizations of quantum bits .
thus the derived results contribute significantly to the understanding of the preservation of coherence .
we will show that persisting quantum correlations are not linked to the integrability of the model , but caused by a finite operator overlap with a finite set of constants of motion .
[ [ introduction . ] ] introduction .
+ + + + + + + + + + + + + the two - time correlation function of two observables reveals important information about the dynamics of a system in and out of equilibrium : the noise spectra are obtained from symmetric combinations of correlation functions , while the causal , antisymmetric combination determines the susceptibilities required for the theory of linear response .
the two - time correlation function only depends on the time difference if at @xmath0 the system of interest is prepared in a stationary state whose density operator commutes with the time - independent hamiltonian .
this is what will be considered in this work .
since correlations generically decay for @xmath1 , important information about the system dynamics is gained if a non - decaying fraction of correlations prevails at infinite times .
such non - decaying correlations are clearly connected to a limited dynamics in certain subspaces of the hilbert space .
the question arises if such a restricted dynamics is always linked to the integrability of the hamiltonian . here
integrability means that the hamiltonian can be diagonalized by bethe ansatz which implies that there is an extensive number of constants of motion . identifying and understanding
those non - decaying correlations can be potentially exploited in applications for persistent storage of ( quantum ) information . in this letter
we first prove that persisting correlations are not restricted to integrable systems by using a generalized form of mazur s inequality @xcite .
this is in contrast to the behavior of the drude weight in the frequency - dependent conductivity of one - dimensional systems which appears to vanish abruptly once the integrability is lost , even if only by including an arbitrarily small perturbation .
so far , the drude weight has been the most common application of mazur s inequality , see for instance refs . and references therein .
second , we apply this approach to the central spin model ( csm ) @xcite describing the interaction of a single spin , e.g. , an electronic spin in a quantum dot @xcite , an effective two - level model in a nv center in diamond @xcite , or a @xmath2c nuclear spin @xcite , coupled to a bath of surrounding nuclear spins inducing decoherence .
persisting spin correlations have been found in the csm by averaging the central spin dynamics over a bath of random classical spins @xcite or in markov approximation @xcite .
finite - size calculations @xcite of the full quantum problem and stochastic evaluation @xcite of the exact bethe ansatz equations @xcite for small system sizes @xmath3 have also provided evidence for a non - decaying fraction of the central spin correlation , predicting a non - universal , system dependent value .
its origin has remained obscure , and it has been speculated that the lack of spin decay might be linked to bose - einstein condensate - like physics @xcite . while it is fascinating to identify such non - decaying correlations , it is technically very difficult to rigorously establish them .
approximate methods often miss precisely those intricate aspects allowing correlations to persist , especially when they explicitly exploit the assumption that the system relaxes towards a statistical mixture .
numerical approaches are either restricted in system size @xcite , or they are limited in the maximum time which can reliably be captured @xcite . even analytical solutions @xcite can often only be evaluated in small systems @xcite .
thus , a rigorous result establishing the existence of non - decaying correlations is highly desirable and we resort to mazur s inequality for this purpose .
[ [ general - derivation . ] ] general derivation . + + + + + + + + + + + + + + + + + + + to establish the key idea and to fix the notation we present the following modified derivation related to suzuki s derivation in ref . .
we consider the time - independent hamiltonian @xmath4 and the operator @xmath5 with a vanishing expectation value @xmath6 with respect to a stationary density operator @xmath7 , i.e. @xmath8=0 $ ] so that two - time correlation functions only depend on the time difference .
note that @xmath7 does not need to be the equilibrium density operator .
then , @xmath7 and @xmath4 have a complete common eigenbasis @xmath9 in a finite - dimensional hilbert space , and their spectra are @xmath10 and @xmath11 , respectively .
we define the correlation function of @xmath5 as @xmath12 \\ \label{eq : lehmann } & = & \sum_{j , m } \rho_j |a_{jm}|^2 \exp(i(e_j - e_m)t),\end{aligned}\ ] ] so that eq .
is its lehmann representation , and @xmath13 denotes the matrix element of @xmath5 .
physically , @xmath14 stands for a measurement of @xmath15 at time @xmath16 after the evolution from the initial state prepared by applying @xmath5 at @xmath0 .
especially , for @xmath17 of a spin @xmath18 in a disordered environment , @xmath14 is proportional to @xmath19 if @xmath20 , see supplement a for details . if @xmath21 exists , it is given by @xmath22 if @xmath23 does not exist , and @xmath24 , the long - time average @xmath25 is projecting out the time - independent part @xmath26 and uniquely defines the non - decaying fraction of the correlation . in practice
, the lehmann representation requires the complete diagonalization of @xmath4 which is not feasible for large systems .
hence one resorts to constants of motion . to this end , we define the scalar product for two operators @xmath27 and @xmath28 as @xmath29\ ] ] in the super - hilbert space of the operators .
if a set of @xmath30 conserved linearly independent operators @xmath31 with @xmath32=0 $ ] is known , one may assume their orthonormality @xmath33 provided by a gram - schmidt process .
then , we expand the operator of interest @xmath5 @xmath34 in this incomplete operator basis where @xmath35 and @xmath36 is the remaining rest with @xmath37 @xmath38 . substituting into the definition yields @xmath39 with @xmath40 .
this relies on the constancy of ( i ) @xmath41 , of ( ii ) @xmath42 , and of ( iii ) @xmath43 all stemming from @xmath44=0 $ ] . for the last relation we have used the cyclic invariance of the trace and @xmath45=0
$ ] .
if we knew @xmath46 , we would deduce @xmath47 .
but in general this does not hold because @xmath36 may still contain a non - decaying part . but implies mazur s inequality @xmath48 for a given @xmath4 , the complete set of conserved operators @xmath49 is spanned by all pairs of energy - degenerate eigenstates @xmath50 the elements of @xmath49 are orthonormal with respect to the scalar product .
the coefficent @xmath51 of @xmath52 takes the value @xmath53 so that the right hand side of equals @xmath26 as given by the lehmann representation .
thus , the inequality is tight because it becomes exact for the _ complete _ set @xmath49 of conserved operators .
the physical interpretation of eq .
is straightforward in the heisenberg picture if we view the time - dependent observable @xmath54 as super vector .
its components parallel to conserved quantities ( super vector directions ) are constant in time because these quantities commute with the hamiltonian .
but all other components , which are perpendicular to the conserved super subspace , finally decay .
if not all conserved operators are considered , the r.h.s . of decreases and
only the inequality holds .
generally , if _ any _ subspace of the space spanned by @xmath49 is considered mazur s inequality holds .
one does not need to know the complete set of eigenstates of @xmath4 in order to calculate a lower bound : any finite ( sub)set of conserved operators is sufficient .
now we proceed to generalize mazur s inequality for easy - to - use application .
usually , some conserved operators @xmath55 are known but they are not necessarily orthonormal in general .
rather their overlaps yield a hermitian , positive norm matrix @xmath56 with matrix elements @xmath57 .
each operator @xmath55 can be represented as a linear superposition of the complete set of orthonormal @xmath31 .
these superpositions can be summarized in a matrix @xmath58 so that @xmath59 where the vectors @xmath60 and @xmath61 contain the operators @xmath31 and @xmath55 as coefficients ; @xmath62 is the complex ( not hermitian ! ) conjugate of @xmath58 .
a short calculation shows that @xmath63 .
if we define the vector @xmath64 with complex components @xmath65 , the bound @xmath66 can be expressed by @xmath67 . in analogy , we compute @xmath68 with complex components @xmath69 .
obviously , @xmath70 holds and the lower bound is computed by @xmath71 without resorting to orthonormalized operators , relying only on the scalar products of @xmath55 and @xmath5 .
we have successfully eliminated the construction of a subset of orthogonal operators @xmath31 and related the lower bound to some known set of linear independent unnormalized conserved operators @xmath55 .
the general lower bound is our first key result .
a possible route to generalizations to various initial states is sketched in the supplement .
[ [ central - spin - model . ] ] central spin model .
+ + + + + + + + + + + + + + + + + + + the hamiltonian of the csm reads @xmath72 where we assume all spins to be @xmath18 for simplicity .
it is a generic model to study the interaction between a two - level system and a bath of spins or more generally a set of subsystems with finite number of levels .
currently , it is intensively investigated for understanding the decoherence and dephasing in possible realizations of quantum bits @xcite .
theoretical tools comprise chebyshev polynomial technique @xcite , perturbative approaches @xcite , generalized master equations @xcite , equations of motion @xcite various cluster expansions @xcite , bethe ansatz @xcite , density - matrix renormalization @xcite , and studies of the classical analogue @xcite . by focusing on @xmath73 , the correlation function defined in reveals important information on the decay of the central spin .
due to isotropy no other components of the central spin need to be considered .
given the smallness of the hyperfine couplings ( @xmath74 is in the range of @xmath75ev corresponding to percents of a kelvin @xcite ) the experimentally relevant temperature can be considered as infinite , and we take the spin system to be completely disordered , i.e. , @xmath76 , prior to the preparation of an initial state of the central spin , cf . supplement .
for classical spins @xmath77 , there are strong analytical arguments that a fraction of central spin correlations persists unless there is a diverging number of arbitrarily weakly coupled spins in the bath @xcite . in the quantum case
smaller systems have been studied and evidence for a non - decaying fraction of spin polarization @xcite has only be compiled in fairly small ( @xmath78 ) systems or up to fairly short times @xcite . based on the generalized mazur s inequality , we are able to address the nature and the lower bound of these non - decaying correlations for arbitrary system sizes . the total spin @xmath79 could serve as a first guess for a useful conserved quantity .
only the @xmath80-component @xmath81 has an overlap @xmath82 ( we omit the subscript @xmath83 for brevity ) .
the norm @xmath84 takes the value @xmath85 so that provides @xmath86 .
irrespective of the considered distribution of the couplings @xmath74 , using only @xmath87 as single conserved operator does not provide a meaningful lower bound for thermodynamically large , or infinite baths .
the next important conserved quantity is the energy @xmath88 itself .
but , of course , @xmath89 because @xmath88 is a scalar and @xmath90 a vector component .
the @xmath80-component of the product @xmath91 , @xmath92 , clearly fulfills @xmath93=0 $ ] and defines a conserved composite vector operator .
we find @xmath94 where @xmath95 and @xmath96 . with this input eq .
yields @xmath97 this bound remains finite for @xmath98 if the @xmath74 are drawn from a probability distribution @xmath99 with average @xmath100 and variance @xmath101 . for large @xmath102 one
has @xmath103 and @xmath104 so that @xmath105 $ ] ensues for @xmath98 .
this is a finite lower bound unless the average values @xmath100 vanishes .
this rigorous bound is our second key result . for @xmath106 bath spins with @xmath107 ,
but normalized such that @xmath108 is the unit of energy , and various @xmath109 defined in .
the inset compares @xmath26 from the average of the numerical data with @xmath110 $ ] to @xmath66 obtained from for the 3 quantities ( @xmath111 ) or for all quantities ( @xmath112 with @xmath113 ) .
the estimates from the overhauser correlations @xmath114 are also shown .
[ fig : ss ] ] for any finite system with non - vanishing sum @xmath115 , eq . provides a rigorous finite lower bound which is very easy to compute for any given set of couplings .
it can serve to check the validity of numerical results such as provided in refs .
@xcite .
generically , distributions of the @xmath74 have finite values @xmath100 and @xmath116 .
this is the case for nuclear spins in molecules @xcite or nv centers in diamond @xcite because the spin baths are finite . in quantum dots ,
the convergence and existence @xmath115 and @xmath117 is ensured even for arbitrary number of spins because the couplings are bounded from above , but become arbitrarily small due to exponential tails of the electron wave function @xcite .
this leads to vanishing @xmath100 implying complete decay for infinite times .
for large , but finite times , however , our results include the possibility of slow decays @xmath118 previously advocated for infinitely large spin baths @xcite . assuming exponential scaling for the couplings @xmath119 , where @xmath120 is inversely proportional to the number of relevant bath spins , to @xmath121 .
it is not the total number of nuclear spins which is of the order of avogadro s constant . ]
it is clear that @xmath115 and @xmath122 converge quickly for @xmath98 so that eq
. implies @xmath123 .
chen et al .
@xcite have argued that at any given _ finite _
time @xmath16 , only those spins @xmath124 with couplings @xmath125 significantly influence the real - time dynamics of the central spin .
hence , only an effective number @xmath126 of spins contribute to the correlation function implying @xmath127 for such a distribution function .
the lower bound can be improved by considering the three conserved observables @xmath87 , @xmath128 , and @xmath129 .
the required vector and matrix elements are given in the supplemental material .
still the bound does not exhaust the numerically found value as depicted in the inset of fig .
[ fig : ss ] for @xmath130 ( @xmath109 makes the system non - integrable , it will be defined in ) . even resorting to the integrability of the csm @xcite which implies @xmath131 $ ] with @xmath132 and @xmath133
does not account for the full non - decaying fraction obtained in finite size calculations @xcite , see circle in the inset of fig.[fig : ss ] .
the bound has been computed considering @xmath87 and @xmath134 for @xmath113 ( for matrix elements see supplement ) .
the above results suggest that the integrability is not the key ingredient for a finite non - decaying fraction .
to support this claim we extend the hamiltonian by adding one extra coupling @xmath135 @xmath136 between the most weakly and the most strongly coupled bath spin , defined to be at @xmath137 and @xmath102 , respectively .
its value @xmath109 is chosen to be @xmath138 so that it constitutes a sizable perturbation even for large spin baths .
the modified time - dependence of @xmath14 is depicted for various @xmath109 in fig .
[ fig : ss ] .
a finite @xmath109 spoils the integrability completely @xcite , but leaves the quantities @xmath139 conserved .
these three constants of motion generic for isotropic spin models are used to obtain the lower bound ( red curve ) in the inset of fig .
[ fig : ss ] .
obviously , @xmath66 is decreased smoothly and only moderately upon increasing @xmath109 in line with the numerically determined @xmath26 .
there is no abrupt jump to zero , in contrast to what is known for the drude weight .
the conclusion that integrability is only secondary for the non - decaying spin correlation is our third key result . at present
it remains an open question which conserved quantities one has to include to yield a tight lower bound .
we presume that higher powers of @xmath4 , for instance @xmath140 , have to be considered .
such studies are more tedious and left for future research .
instead , we take a mathematically less rigorous route based on the estimate by merkulov et al.@xcite @xmath141 where @xmath142 is the correlation of the overhauser field operator @xmath143 .
note that an arbitrary @xmath144 can be included because @xmath145 differs from @xmath88 in only by an irrelevant constant for spin @xmath146 .
this estimate was derived for a classical , large overhauser field @xcite and prevails in the thermodynamic limit of the quantum case : the overhauser field becomes a classical variable upon @xmath98 as shown in ref .
@xcite .
thus we now apply the general approach to @xmath147 . considering only @xmath148 as conserved operator already yields a meaningful lower bound for the overhauser field correlation function for @xmath98 @xmath149 recall @xmath150 and @xmath151 if the couplings are drawn from a normalized distribution function @xmath99 .
this lower bound can be optimized by choosing the arbitrary value @xmath144 such that the bound becomes maximal . with the matrix elements given in the supplement @xmath152
can be improved considering the three constants @xmath139 or all integrals @xmath87 and @xmath153 .
the results are also included in fig .
[ fig : ss ] ( triangle and square symbols ) .
they hold only for @xmath130 because the estimate applies only in this case .
remarkably , the resulting estimates for @xmath26 seem to be tight .
in particular , the easily evaluated estimate based on all integrals reproduces the numerically found @xmath26 to its accuracy .
we applied the same estimate to the case @xmath119 studied by stochastically evaluating the bethe ansatz equations and found excellent agreement with the published data with @xmath154 in ref.@xcite as well .
thus we conjecture that the non - decaying fraction @xmath26 in the central spin model is quantitatively described by @xmath155 if @xmath152 is determined from the @xmath156 integrals @xmath87 and @xmath157 .
this constitutes our fourth key result .
the small difference , however , between triangle ( from three constants of motion ) and square ( from @xmath156 constants of motion ) in fig .
[ fig : ss ] indicates again that the significance of the integrability is limited . in summary ,
four key results are obtained : ( i ) an easy - to - use version of mazur s inequality to prove persisting correlations ; ( ii ) a rigorous finite lower bound for the infinite - time spin correlation in the csm , valid for the infinite system if the average coupling is finite ; ( iii ) only a small part of the persisting correlation is due to the integrability ; ( iv ) a quantitative estimate for the persisting correlation is conjectured , based on the overhauser field . clearly ,
the generalized inequality calls for application to other problems @xcite .
the approach is easy to evaluate and can be used for very large systems and large numbers of constants of motion .
thus it can prove fruitful in the intensely studied field of integrable systems , for instance in estimating drude weights . in the context of coherence in particular , various extensions of the csm , e.g. , by magnetic fields , anisotropies , or more intra - bath couplings suggest themselves to be investigated in the presented manner .
we gratefully acknowledge helpful discussions with m. brockmann , a. faribault , a. greilich , and d. schuricht .
financial support was given by the mercator stiftung under pr-2011 - 0003 ( gsu ) , by the studienstiftung des deutschen volkes ( ds ) and by the deutsche forschungsgemeinschaft under an 275/7 - 1 ( fba ) and uh 90/9 - 1 ( gsu ) .
43ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ]
+ 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop _ _ ( , ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1103/physrevb.89.045317 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) |
in the following , we formulate a one - electron microcanonical distribution for triatomic molecules . we denote the positions of the nuclei by @xmath1 , @xmath2 and @xmath3 and the inter - nuclear distances by @xmath4 , @xmath5 and @xmath6 , see fig .
one can show that the coordinates of the nucleus c are expressed in terms of the inter - nuclear distances as follows : we denote the position vector of the electron by @xmath8 and the distances of the electron from nuclei a , b and c by @xmath9 , @xmath10 and @xmath11 , respectively .
we then define the confocal elliptical coordinates @xmath12 and @xmath13 using the nuclei a and b as the foci of the ellipse , that is , where @xmath15 and @xmath16}$ ] .
the third coordinate @xmath17}$ ] is the angle between the projection of the position vector @xmath8 on the xy plane and the positive x axis ; it thus defines the rotation angle around the axis that passes through nuclei a and b. the potential of the electron in the presence of the nuclei a , b and c , which have charges @xmath18 , @xmath19 and @xmath20 , respectively , is given by @xmath21 this potential is expressed in terms of the confocal elliptical coordinates as follows the one - electron microcanonical distribution is given by @xmath23 where @xmath24 is the ionization energy of the one - electron triatomic molecule .
note that the energy is given by @xmath25 . the electron momentum in terms of the confocal elliptical coordinates
is expressed as follows the @xmath36 distribution goes to zero and is thus well - behaved when the electron is placed on top of either nucleus a or b. however , when @xmath37 , i.e. , the electron is placed on top of nucleus c , @xmath38 .
we eliminate this singularity by introducing an additional transformation . setting @xmath39 , @xmath40 and expanding @xmath41 around @xmath42
we find @xmath43 where @xmath44 and @xmath45 are the values of @xmath12 and @xmath13 , respectively , when the electron is placed on top of the nucleus c. to eliminate the singularity in eq .
( [ eq : sing ] ) , we introduce a new variable @xmath46 , such that @xmath47 .
the new distribution takes the form since @xmath16}$ ] , @xmath49 and @xmath46 take both negative and positive values and therefore , if we choose one @xmath50 for all values of @xmath13 , @xmath50 must be odd .
moreover , to avoid the singularity when the electron is placed on top of nucleus c , @xmath50 must be such that @xmath51 , i.e. , @xmath52 . combining the above two conditions , yields @xmath53 .
the new distribution @xmath54 goes to zero when the electron is placed on top of the nucleus c , i.e. , when @xmath55 , @xmath56 and @xmath57 . to set up the initial conditions we find @xmath58 so that @xmath59 and equivalently @xmath60
we then find the maximum value @xmath61 of the distribution @xmath54 , for the allowed values of the parameters @xmath12 , @xmath46 and @xmath62 .
we next generate the uniform random numbers @xmath63}$ ] , @xmath64}$ ] , @xmath65}$ ] and @xmath66}$ ] , with @xmath67 and @xmath68 .
if @xmath69 then the generated values of @xmath12 , @xmath46 and @xmath62 are accepted as initial conditions , otherwise , they are rejected and the sampling process starts again . following the above described formulation , we obtain the initial conditions of the electron with respect to the origin of the coordinate system . to obtain the initial conditions for the position of the electron with respect to the center of mass of the triatomic molecule , @xmath70 , in terms of the ones with respect to the origin , @xmath8
, we shift the coordinates by @xmath71 , where @xmath72 is given by @xmath73 with @xmath74 with @xmath75 , @xmath76 and @xmath77 the masses of the nuclei . as an example , we next obtain the probability densities of the position and the momentum of the electron that is initially bound in @xmath78 when the molecule is driven by an intense infrared laser field . we assume the other electron tunnel - ionizes in the initial state .
we consider the @xmath78 triatomic molecule in its ground state , where the distance of the nuclei in the equilateral triangle arrangement is 1.65 a.u . and
the first and second ionization energies are @xmath79 a.u . and @xmath80 a.u .
, respectively .
we find the ionization potentials and equilibrium distances of the initial state using molpro , which is a quantum chemistry package @xcite .
for the microcanonical distribution the relevant ionization energy is @xmath81 , since @xmath82 is associated with the electron that tunnel - ionizes in the initial state . in fig .
[ position ] ( b ) we plot the probability density of the position of the electron on the x - z plane for @xmath83 using the above described microcanonical distribution . to compare , in fig .
[ position ] ( a ) we plot the quantum mechanical probability density of the position of the electron on the x - z plane .
that is , we plot @xmath84 , where @xmath85 is the quantum mechanical wavefunction for the @xmath86 molecule , which we obtain using molpro .
the two plots , fig .
[ position ] ( a ) and ( b ) , show that the two probability densities for the electron position compare well .
however , the microcanonical probability density underestimates the electron probability density between the nuclei and overestimates the electron probability density around the nuclei .
[ ht ! ] plane .
the middle panel shows the microcanonical probability density of the electron momentum plotted on the @xmath87 plane for all values of @xmath88 .
the right panel shows the projections on the @xmath89 axis of the probability densities plotted in fig
. [ momentum ] ( a ) and ( b ) .
, title="fig:",scaledwidth=50.0% ] in addition , in fig
. [ momentum ] ( b ) for all values of the electron momentum component along the y - axis , @xmath88 , we plot the probability density of the electron momentum on the @xmath90 plane using the microcanonical distribution . to compare , in fig .
[ momentum ] ( a ) we plot @xmath91 , which we obtain by first computing the quantum mechanical wavefunction in momentum space using the quantum mechanical wavefunction @xmath85 computed from molpro and then by integrating over @xmath88 @xmath93 the two plots , fig .
[ momentum ] ( a ) and ( b ) , show that the two probability densities for the electron momentum compare well . however , the microcanonical probability density overestimates the higher values of the electron momentum .
this can be seen more clearly in fig .
[ momentum ] ( c ) where we plot the probability density of the electron momentum along the @xmath89 axis both quantum mechanically and using our microcanonical distribution . to obtain the plots in fig .
[ momentum ] ( c ) we project the probability densities of the electron momentum in fig . [ momentum ] ( a ) and ( b ) on the @xmath89 axis .
[ momentum ] ( c ) clearly shows that the probability density of the electron momentum obtained from the microcanonical distribution overestimates the higher values of the momentum component @xmath89 .
this is consistent with our previous finding that the microcanonical distribution overestimates values of the electron position around the nuclei resulting to higher values of the momentum . in conclusion , in the current work we have formulated a microcanonical distribution for a general one - electron triatomic molecule .
this distribution can be used to describe the initial state of the bound electron in semiclassical models of strongly - driven two - electron triatomic molecules .
10 meckel m , comtois d , zeidler d , staudte a , pavii d , bandulet h c , ppin h , kieffer j c , drner r , villeneuve d m and corkum p b 2008 _ science _ * 320 * 1478 lefebvre c , lu h z , chelkowski s and bandrauk a d 2014 _ phys . rev . a _ * 89 * 023403 liu j , ye d f , chen j and liu x 2007 _ phys .
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rev . a _ * 90 * 053419 landau l d and lifshitz e m 1977 _ quantum mechanics _ ( pergamon press , new york ) ; delone n b and krainov v p 1991 _ j. opt .
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a _ * 40 * , 3637 werner h j. knowles p j , knizia g , manby f , schtz r m , et al .
2012 _ molpro , version 2012.1 , a package of ab initio programs _
, see http://www.molpro.net | we formulate a microcanonical distribution for an arbitrary one - electron triatomic molecule .
this distribution can be used to describe the initial state in strongly - driven two - electron triatomic molecules .
namely , in many semiclassical models that describe ionization of two - electron molecules driven by intense infrared laser fields in the tunneling regime initially one electron tunnels while the other electron is bound . the microcanonical distribution presented in this work can be used to describe the initial state of this bound electron .
the nonlinear response of multi - center molecules to intense laser fields is a fundamental problem .
for instance , understanding the break - up dynamics of strongly - driven molecules paves the way for controlling and imaging molecular processes @xcite .
semi - classical models are essential in understanding the dynamics during the fragmentation of multi - center molecules driven by intense infrared laser pulses .
one reason is that treating the dynamics of electrons and nuclei at the same time poses an immense challenge for fully ab - initio quantum mechanical calculations .
currently quantum mechanical techniques can only address one electron in triatomic molecules in two - dimensions @xcite .
semi - classical models have provided significant insights , for example , in double ionization of strongly - driven @xmath0 with fixed nuclei " @xcite and in frustrated " double ionization during the fragmentation of strongly - driven @xmath0 @xcite , where one electron eventually stays bound in a highly excited state of the h atom .
the initial state that is commonly employed by semi - classical models for strongly - driven two - electron atoms and molecules , for intensities in the tunneling regime , involves one electron that tunnel - ionizes in the field - lowered coulomb potential and another electron that remains bound .
the electron that tunnel - ionizes emerges from the barrier with a zero velocity along the direction of the laser field , while its velocity perpendicular to the laser field is given by a gaussian distribution @xcite .
the tunneling rate can be obtained using semi - classical treatments , for instance see @xcite for atoms and @xcite for molecules .
the electron that is initially bound is commonly described in semi - classical models by a microcanonical distribution . to our knowledge , in the literature ,
a microcanonical distribution is available only for diatomic molecules @xcite . in this work
, we formulate a microcanonical distribution for any one - electron triatomic molecule which can also describe the initial state of the bound electron in the above described semi - classical models . |
one of the most important questions to be clarified in the hydrodynamical approach to the relativistic heavy ion physics is the effect of dissipative processes .
the second order theory , first proposed by muller and developed by israel and stewart , has been considered standard approach for this problem @xcite .
but it is quite complex and involves many unknown parameters from the point of qcd dynamics so that its complete application to practical problems such as relativistic heavy ion reactions has not been done yet @xcite . in this work ,
we propose an alternative approach to this question @xcite .
we show that the physical origin of the second order theories can easily be understood in terms of memory effects .
the irreversible current modified by the memory effects becomes consistently with causality and sum rules @xcite .
based on this idea , we introduced the memory effect to the relativistic dissipative hydrodynamic of landau @xcite , where we introduce only one extra parameter , the relaxation time @xmath0 in addition to the usual viscosity coefficients of the navier - stokes equation .
the resulting equation becomes hyperbolic @xcite .
the effect of viscosity is also important when we discuss the possible generation and propagation of shock waves in the qcd medium created in the process of relativistic heavy ion collisions .
as discussed extensively in this conference@xcite , it has been suggested that a high energy jet propagating in the qgp may generate a mach cone and observables associated with such phenomena may bring important information of the genuine hydrodynamical properties of the matter @xcite .
the dynamical simulation of shock wave generation is very difficult even for the non - relativistic regime .
a full 3d simulation of shock wave dynamics has never been done for the heavy ion collisions . in this work
, we apply our formulation to the calculation of full 3d relativistic ( causal ) shock wave problem .
the implementation of our method to the existing ideal hydro - codes is straightforward , particularly to those based on the local lagrangian coordinate system such as spherio @xcite .
we organize the present work as follows . in the next section ,
we briefly introduce our formalism and discuss its application to the generation of shock waves . in section 3 , we present some results of 3d calculation of shock wave propagation within the causal formulation of the dissipative hydrodynamics . in section 4 , we discuss the result and perspectives .
the fundamental problem of the first order theory like the navier - stokes theory comes from the fact that the diffusion equation is parabolic . the physical origin of this problem can be followed up to the fact that the irreversible current @xmath1 is assumed to be proportional to a thermodynamic force @xmath2 as @xmath3where the onsager coefficient @xmath4 is , in general , a function of thermodynamic quantities .
usually @xmath2 is related to the inhomogeneity in the density .
when the microscopic rearrangement time scale is not negligible compared to the time scale of the change in the irreversible current , then the above should be replaced by the equation of motion for the current , @xmath5where @xmath6 is the relaxation time .
for very small @xmath7 we recover eq.([curr ] ) . thus eq.([curr ] ) can be understood as the large viscous limit of the damped motion , where the velocity ( current ) is proportional to the force ( aristotelian vision ) .
it can be shown that the above modification is enough to convert the parabolic nature of a diffusion equation to hyperbolic one @xcite .
for the relativistic hydrodynamics , we have to consider several different kind of thermodynamical forces related to the velocity and density inhomogeneity .
they are @xmath8 and@xmath9where @xmath10 is the four - velocity of the fluid , @xmath11 with @xmath12 the chemical potential . these inhomgeneities generate the corresponding irreversible currents and the analogous equations to eq.(irrev ) for them should be @xmath13where @xmath14 and @xmath15 @xmath16 and @xmath17 are bulk viscosity , shear viscosity and thermal conductivity coefficients , respectively .
the energy - momentum tensor is expressed with these currents as @xmath18 where @xmath19 and @xmath20 is the double symmetric traceless projection , @xmath21 whereas the conserved baryon number current is given by @xmath22 the hydrodynamic equations are @xmath23
although eqs.([heat],[hydro ] ) together with the equation of state give the complete description of the hydrodynamical motion of the system , in practice , some additional care to be taken , especially for the simulation of the shock wave dynamics . whenever there exists a shock wave , always occurs an entropy production through the shock front . in an idealized hydrodynamical approach ,
the shock front is a discontinuity in thermodynamical quantities in a hydrodynamic solution .
mathematically speaking , it should be treated as the boundary condition to connect two distinct hydrodynamic solutions .
physically , it is not a real discontinuity , but a quick change of the density in the region where the local equilibrium is not satisfied .
thus it has a finite thickness at least a few times of the mean - free path ( typical microscopic scale of distance ) for a stationary shock . under a dynamical condition such as relativistic heavy ion collisions ,
the compression shock may have much more larger thickness due to the many complicated local transient properties . to reproduce true shock wave phenomena ,
the full degrees of freedom of the hydrodynamics , together with a proper boundary condition correctly connecting to regions through the non - equilibrated domain of the shock , are required .
the usual numerical approach of hydrodynamics excludes such a possibility from the beginning . since there exist no short wavelength excitation modes due to the finite discretization , the energy and momentum conservation required by the hydrodynamics result in a very rapidly oscillations of the variables near the shock region .
these quick oscillations are somewhat compensating the thermal energy associated to the entropy production throughout the shock front . in order to avoid these oscillations ,
von neumann and richtmeyer@xcite introduced the method of pseudo - viscosity .
the idea is to put the bulk viscosity in the shock region to replace the entropy production through the shock front .
the form of the pseudo - viscosity is chosen so that asymptotic values of thermodynamic quantities connects smoothly from one side to the other through the shock , satisfying the huguniot - rankine boundary condition .
for the relativistic extension , we have to transform this formalism in the causal form .
thus , we introduce the causal pseudo - viscosity by using the bulk viscosity coefficient @xmath24 in eq.([heat ] ) as @xmath25 $ ] for @xmath26 and @xmath27 otherwise where @xmath28 and @xmath29 and @xmath30 are constants proportional to the space resolution scale of the numerical solution . from the condition of causality ,
the relaxation time associated to this pseudo - viscosity should satisfy @xmath31this means , the larger the viscosity , the larger the relaxation time . in fig.1
, we show the example of creation and propagation of shock wave induced by a small qgp drop injected into the homogeneous qgp fluid at a relativistic energy ( @xmath32 ) . here , we take a massless ideal gas equation of state , and the incident drop has half the temperature of the background in the local rest frame . the relaxation time necessary to maintain the causality in this calculation
is found to be @xmath33 .
this seems to be large , but the effect of shock wave requires a large viscosity so that a large relaxation time is necessary .
we can see the generation of mach cone and also the turbulent structure after the shock cone .
we found that the cone angle depends on the viscosity and also the related relaxation time @xmath34 for a finite @xmath6 the mach cone opens more than the usual estimate for ideal fluid case .
we presented the first full 3d relativistic viscous hydrodynamic calculation which preserve the causality correctly . in the case of shock wave simulation ,
it is fundamental to include the bulk viscosity to take account for the entropy generation through the shock front . to satisfy the causal propagation of the signal
, the presence of viscosity requires a finite relaxation time .
it is found that the mach cone angle depends on the viscosity and the relaxation time .
it is also observed that a very turbulent structure after the shock .
more quantitative and systematic study of the shock wave generation and its propagation in an expanding qgp is in progress .
chaudhuri , nucl - th/0604014 , u. heinz , h. song and a.k .
chaudhuri , phys.rev.c73:034904 ( 2006 ) , a. muronga and d.h .
rischke , nucl - th/0407114 , a. muronga , phys.rev.c69:034903,2004 , phys.rev.lett.88:062302,2002 , r. baier , p. romatschke , u. a. wiedemann , hep - ph/0602249 , nucl - th/0604006 . | the first 3d calculation of shock wave propagation in a homogeneous qgp has been performed within the new formulation of relativistic dissipative hydrodynamics which preserves the causality .
we found that the relaxation time plays an important role and also affects the angle of mach cone . |
i thank the cern and desy theory groups for their hospitality during this work , and w. buchmller and m. lscher for fruitful discussions . this work was supported in part by the united states department of energy under contract no .
de fg02 90er40560 .
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c * # 1 * ( # 3 ) # 2 | when a heavy quark and the corresponding antiquark are separated by more than @xmath0 fm , it becomes energetically favorable for a light quark - antiquark pair to be produced , leading to fragmentation into a pair of flavored mesons .
the relation of this critical quark separation to other dimensional constants of the strong interactions ( such as the pion decay constant , the qcd scale , and the light - quark constituent mass ) is discussed .
5.8 in -0.8 in -0.2 in * critical spacing for heavy quarkonium dissociation * + + + + + _ university of chicago , chicago , il 60637 usa _
+ the dimensional nature of quantum chromodynamics is manifested in a number of different ways , all of which are plausibly equivalent to one another .
for example : ( 1 ) the scale of low - energy pion - pion interactions is set by the ratios @xmath1 , where @xmath2 are pion 4-momenta and @xmath3 mev is the pion decay constant .
( 2 ) a qcd scale @xmath4 mev whose specific value depends on renormalization scheme is necessary in order to define the strong - coupling constant @xmath5 at a suitable momentum scale . ( 3 ) the masses of @xmath6 and @xmath7 quarks as manifested in hadrons can be regarded as `` constituent - quark '' values @xmath8 of order 300 400 mev .
the scale of @xmath8 , while not as precisely defined as @xmath9 or @xmath10 , must be related to these two quantities if , as expected , the limit of zero bare mass for @xmath6 and @xmath7 quarks makes sense . in the present note
we add a quantity to this list .
there appears to be a critical separation between a heavy quark and a heavy antiquark for which it is energetically favorable to produce a pair of flavored mesons [ as , for example , in @xmath11 .
this feature was noted in early studies of the @xmath12 system @xcite .
however , the explicit magnitude of the interquark separation leading to heavy quarkonium dissociation was not presented .
we find that it is of order @xmath0 fm .
this number is of current interest for several reasons .
\(1 ) lattice gauge theories are approaching a stage where the dimensional quantities just mentioned ( as well as others ) can be related to one another .
the study of light - quark production between color centers represented by a heavy quark and antiquark is becoming feasible @xcite as one learns to cope with the `` unquenched '' version of qcd in which light quark - antiquark pairs are properly treated .
\(2 ) the quarkonium systems to which the critical dissociation distance applies include @xmath13 and @xmath14 systems , for which there remain prospects for discovering a few more p - wave and d - wave states , and @xmath15 states , for which there are extensive theoretical studies of the spectroscopy @xcite and a hint of the ground state @xcite .
the top quark is too heavy to have a quarkonium spectroscopy ( since its decay width will be greater than the expected level spacing ) , but the critical - separation parameter should still apply to @xmath16 pairs or their products @xmath17 , @xmath18 , or @xmath19 @xcite .
\(3 ) one might expect the critical separation of a pair of static color centers for dissociation into a pair of flavored mesons to be a fundamental parameter in theories @xcite linking heavy - quark physics and chiral perturbation theory .
we assume that a flavor - independent potential @xmath20 describes all bound states @xmath21 of a heavy quark @xmath22 and its antiquark as well as flavored mesons @xmath23 and @xmath24 involving the heavy quark @xmath22 and a light quark @xmath25 . in the notation of ref .
@xcite , we define @xmath26 .
this quantity should tend to a finite limit @xmath27 as @xmath28 .
the quantity @xmath29 is the same as the parameter @xmath30 of heavy quark effective theory @xcite .
we seek the value of the critical threshold @xmath21 separation @xmath31 for which @xmath32 .
a trivial modification permits the description of bound states such as @xmath15 involving unlike - mass quarks
. the value of @xmath33 will be universal to the extent that ( a ) @xmath27 is well - defined ( as expected in heavy quark effective theory ) , and ( b ) a flavor - independent potential @xmath20 actually provides a good description of the @xmath21 interaction near flavor threshold .
the parameters @xmath29 and the light - quark constituent mass @xmath8 are closely related ; neither parameter can be chosen arbitrarily in a theory with given @xmath9 or @xmath10 .
the assumption of a flavor - independent potential has been reasonably well borne out @xcite by comparison of @xmath13 and @xmath14 systems , and will be tested further in studies of @xmath15 states @xcite .
we calculate the critical separation using a simple phenomenological potential @xcite .
we then compare it with values obtained in a more model - independent manner , and discuss its relation to other dimensional constants in qcd .
a satisfactory interpolation between charmonium ( @xmath13 ) and upsilon ( @xmath34 ) states is provided by a potential of the form @xmath35 , with @xmath36 gev and @xmath37 depending upon the specific choice of @xmath38 and @xmath39 quark masses @xcite .
the schrdinger equation for the reduced radial wave function @xmath40 of s - wave bound states is [ eqn : schr ] - + c ( ) u = e u , where @xmath41 is the reduced mass : @xmath42 for a @xmath21 bound state , and @xmath43 . in terms of dimensionless variables @xmath44 and @xmath45 , ( [ eqn : schr ] ) becomes - + u = [ + ( r_0 ) ] u .
the lowest eigenvalue of this equation is @xmath46 , based on a numerical solution @xcite .
consequently , one may eliminate the parameter @xmath37 in favor of the ground state mass , the parameter @xmath47 , and the reduced mass .
recalling the definition of the radius @xmath31 and setting @xmath48 , we finally have /c + 1.0443 = ( ) .
we begin by neglecting spin - dependent effects in both @xmath21 and @xmath49 systems , and reduced - mass effects in the @xmath49 system .
this approximation is most reliable for the @xmath12 levels .
consequently , taking @xmath50 gev , @xmath51 = 9.460 $ ] gev , @xmath52 gev , and a range of @xmath53 between 4.5 and 5 gev , we find the values of @xmath31 shown as the dashed line in fig . 1 . to account for the hyperfine splittings in the @xmath21 and @xmath49 systems and the reduced - mass effect in the @xmath49 system
, we assume that the @xmath54 level is 10 mev above the spin - averaged @xmath55 mass @xcite .
furthermore , we apply the corrections @xcite ( m_q)_hfs = ( m_b^ * - m_b ) = 69 mev ( ) and ( m_q)_red .
mass = - c c m_q ( - ) to estimate - ( m_b ) 10 mev + 69 mev - 46 mev = 33 mev , where the first term is our estimate of the @xmath56 hyperfine term , the second is the contribution of the hyperfine term in @xmath57 , and the third is the reduced - mass effect , estimated for the logarithmic potential .
one is thus assuming such a potential to hold not only for @xmath21 but also for @xmath58 states . we have used a light - quark constituent mass @xcite @xmath59 mev .
with the above corrections , we now estimate the range of @xmath31 shown as the solid line in fig . 1 . the corrected values of @xmath31 range between about 7.6 and 7.2 gev@xmath60 ( 1.5 1.42 fm ) for @xmath61 gev . for comparison , the dot - dashed line in fig
.
1 depicts the values of @xmath31 obtained from an inverse - scattering construction of the interquark potential @xcite using the @xmath12 levels .
these values have not been corrected for hyperfine or reduced - mass effects , so they should be compared with the uncorrected values obtained above .
a power - law potential @xcite fitting charmonium and @xmath12 spectra with @xmath62 gev gives @xmath63 gev@xmath60 ( uncorrected ) and 7.6 gev@xmath60 ( corrected ) .
the agreement of the various estimates is fairly good , indicating that model - dependent effects are unlikely to affect the estimate significantly .
as shown in inverse - scattering @xcite and explicit potential @xcite calculations , the shape of any smooth potential which reproduces a given set of energy levels is fairly well specified for the range of energies corresponding to the known levels . once a potential
is required to reproduce the @xmath64 levels and their leptonic widths , that potential s shape is specified between roughly 0.1 fm = 0.5 gev@xmath60 and the interquark separation corresponding to @xmath65 - 2 m_b$ ] , which is just above flavor threshold .
lattice gauge theories are able to estimate the distance at which a string of chromoelectric flux breaks by the deviation from a linear behavior of the field energy as a function of interquark separation .
it is not clear that such a distance corresponds to flavor threshold , since discrete @xmath14 resonances ( and indeed , series of light - quark resonances ) persist well above flavor threshold .
nonetheless , our estimate of @xmath31 is in accord with an upper bound of @xmath66 fm @xcite ( quoted in ref .
@xcite as 1.7 fm on the basis of a calculation in ref .
@xcite ) for the breaking of a qcd string obtained using a quenched approximation in lattice gauge theory . in a quenched lattice of size ( 1.5 fm)@xmath67 ,
no breaking of a qcd string has been observed ; the linear behavior persists out to the maximum accessible interquark separation
. it would be interesting to see whether at slightly larger distances a linear behavior could actually _ coexist _ with production of light quark - antiquark pairs . how might the critical spacing parameter @xmath31 be related to other dimensionful quantities in qcd ?
it is clearly related to the constituent - quark mass since a certain amount of chromoelectric energy is required to create the @xmath68 pair . in turn , the constituent - quark mass scale is set @xcite by the need to agree with such quantities as @xmath69 and @xmath70 , whose values are related to the qcd scale @xmath10 .
it has been argued @xcite ( cf .
, however , refs .
@xcite ) that the mass scale of resonances like the @xmath71 meson can be regarded as a number of order @xmath72 in a chirally symmetric theory involving massless pions . in any event
a direct relation between @xmath9 and @xmath73 in a theory of massless pions is highly likely .
further dimensionful quantities in the strong interactions which might bear a relation to those mentioned include the universal string tension describing the long - distance interquark interaction @xmath74 , @xmath75 gev@xmath76 , and the universal slope @xmath77 of regge trajectories for light - quark systems , @xmath78 gev@xmath79 @xcite .
the production of light quark - antiquark pairs in a linear potential has been considered some time ago @xcite . to conclude , we have argued that once a heavy color triplet and antitriplet become separated by more than 1.4 1.5 fm , the chromoelectric flux lines joining them contain sufficient energy to produce a light quark - antiquark pair , leading to the decay of the heavy quarkonium system into a pair of flavored mesons .
it would be interesting to see whether current lattice gauge and chiral theories of non - perturbative qcd could relate this quantity to others which set the qcd scale . |
un rsultat classique d brouwer nonce que tout homomorphisme du plan @xmath3 qui prserve lorientation et possde une orbite priodique , possde galement un point fixe . dans le mme ordre dides , on peut montrer @xcite quun tel homomorphisme @xmath0 possde un point fixe li cette orbite priodique , en ce sens quil nexiste pas de courbe de jordan @xmath4 , bordant un disque @xmath5 contenant lorbite priodique mais ne contenant pas le point fixe , et telle que @xmath6 soit homotope @xmath4 dans le complmentaire de lorbite priodique et du point fixe .
une question pose par john franks dans @xcite demeure toujours sans rponse : tant donn un homomorphisme @xmath7 prservant lorientation , existe - t - il pour toute orbite priodique de @xmath0 un point fixe ayant un nombre denlacement non nul avec cette
orbite priodique ? on sait
que la rponse cette question est positive pour les orbites de priode @xmath8 ( voir @xcite ) ou de priode @xmath9 @xcite .
dautre part , dans une prpublication rcente , franks @xcite utilise la rponse affirmative cette question comme tant un thorme de handel ( sans rfrence ) : on peut donc supposer que cette question est , soit rsolue , soit en passe de ltre .
nous montrons ici quun raisonnement trs simple et trs rapide permet de rpondre par laffirmative la question de franks pour les orbites de toutes les priodes des homomorphismes @xmath0 de @xmath3 pour lesquels @xmath1 vrifie un condition de lipschitz . plus
prcisment : soit @xmath7 un homomorphisme qui prserve lorientation et tel que @xmath1 soit lipschitzienne de rapport @xmath10 $ ] .
alors , pour toute orbite priodique @xmath11 de @xmath0 , il existe un point fixe de @xmath0 , @xmath12 , ayant un nombre denlacement non nul avec @xmath2 . outre lintrt du rsultat , la simplicit de la preuve met en valeur lavantage quil y a tester sur cette classe ( pas trop petite ) dhomomorphismes , les conjectures concernant les homomorphismes des surfaces .
soit @xmath7 un homomorphisme . on note @xmath13 lensemble de ses points fixes .
un point @xmath14 est priodique de priode @xmath15 si @xmath16 mais @xmath17 pour @xmath18 . on note @xmath19
lorbite de @xmath20 sous @xmath0 .
soit @xmath21 , @xmath20 un point priodique de priode @xmath15 et @xmath22 un arc joignant @xmath20 et @xmath23 dans @xmath24 , on note @xmath25 la courbe ferme obtenue en joignant bout bout les arcs , @xmath26 . on note
@xmath27 le nombre denroulement de @xmath25 autour de @xmath12 cest dire le nombre dintersection algbrique dune demi - droite gnrique issue de @xmath12 avec @xmath25 ( ce nombre est souvent appel indice de @xmath12 par rapport @xmath25 ) .
[ lem1 ] soient @xmath22 et @xmath28 deux arcs quelconques joignant @xmath20 et @xmath23 dans @xmath29 .
si @xmath0 prserve lorientation , alors @xmath30 . on a @xmath31 or si @xmath0 prserve lorientation @xmath32 do @xmath33 . on peut montrer galement
que la valeur de @xmath34 ( mod @xmath15 ) ne dpend pas du choix du point @xmath20 de @xmath2 choisi pour le construire .
avec les notations ci - dessus , on note @xmath35 lunique entier @xmath36 tel que @xmath37 pour un choix quelconque de @xmath22 et on lappelle le _ nombre denlacement _ ( ou _ linking number _ ) du point fixe @xmath12 avec lorbite priodique @xmath2 .
lappellation nombre denlacement est justifie par la remarque suivante : @xmath38 est aussi le nombre denlacement des deux orbites fermes @xmath39 et @xmath40 du champ de vecteurs canonique induit dans la suspension @xmath41 de @xmath0 .
le point fixe de la rotation dangle @xmath42 a pour nombre denlacement @xmath43 avec lune quelconque de ses orbites priodiques .
soit @xmath44 une application continue .
si lensemble @xmath45 est non vide , on note @xmath46 sa borne infrieure .
sinon , on pose @xmath47 .
soient @xmath20 et @xmath48 deux points de @xmath3 , on note @xmath49 $ ] le segment de droite joignant @xmath20 et @xmath48 .
[ lem2 ] soit @xmath7 un homomorphisme tel que @xmath50 et @xmath51 .
alors @xmath52=\emptyset$ ] .
par labsurde , supposons quil existe @xmath53 . on a alors : @xmath54 dautre part @xmath55 car @xmath0 est injective ,
ce qui conclut .
[ lem3 ] soit @xmath56 un homomorphisme tel que @xmath57 et @xmath51 .
alors , @xmath58)$ ] et @xmath59 $ ] sont homotopes relativement @xmath23 , @xmath60 dans @xmath61 .
soit @xmath62^{2}\rightarrow { \mathbb r}^{2}$ ] dfinie par : @xmath63 limage de @xmath64 est la runion des segments de droite @xmath65(y\in[x , f(x)])$ ] .
daprs le lemme [ lem2 ] @xmath66 $ ] nest pas un point fixe de @xmath0 , donc @xmath65\subset { \mathbb r}^{2}\setminus fix(f)$ ] .
do @xmath67 .
dautre part , @xmath68 .
on obtient donc une application du disque : @xmath69^{2}/(s , 0)\sim(0 ,
s)-{\mathbb r}^{2}\setminus fix(f)\ ] ] telle que @xmath70\cup f([x , f(x)])$ ] . on a ainsi ralis lhomotopie .
soient @xmath71 , @xmath72 deux vecteurs de @xmath3 . on note
@xmath73 $ ] langle non orient des vecteurs @xmath71 et @xmath72 .
[ lem4 ] soit @xmath7 un homomorphisme tel que @xmath50 et @xmath51 .
alors pour tout @xmath66 $ ] : @xmath74 on a : @xmath75 et par suite : @xmath76 .
si langle est @xmath77 , cela implique @xmath78 ce qui est impossible en vertu du lemme [ lem2 ] .
soit @xmath79 lorbite dun point priodique de priode @xmath15 dun homomorphisme de @xmath3 qui prserve lorientation et tel que @xmath50 .
soit @xmath80 la courbe polygonale obtenue en joignant bout bout les segments @xmath81 $ ] , @xmath59 $ ] , @xmath82 , @xmath83 $ ] ( voir figure [ fig1 ] ) et soit @xmath84 $ ] .
lassertion ( 1 ) rsulte du lemme [ lem2 ] .
en raisonnant par rcurrence et en utilisant le lemme [ lem3 ] , on tablit que @xmath80 est homotope @xmath25 dans @xmath24 , do lgalit @xmath87 .
par ailleurs , le nombre denroulement de @xmath80 par rapport @xmath12 est aussi le nombre algbrique de croisements dune demi - droite issue de @xmath12 avec @xmath80 .
ce nombre est donc ncessairement infrieur @xmath88 en valeur absolue .
soient @xmath89 les composantes connexes bornes de @xmath90 ( remarquer quil en existe au moins une , sinon @xmath80 serait rduit un segment de droite ce qui est exclu en vertu du lemme [ lem4 ] ) et @xmath91 la composante connexe non borne .
si @xmath92 on dfinit lindice de @xmath93 en posant : @xmath94 o @xmath95 dsigne une dtermination continue de langle du vecteur @xmath96 avec une direction fixe et o @xmath97 est le bord orient de @xmath93 .
dans chaque composante dindice non nul il existe au moins un point fixe de @xmath0 .
soient @xmath98 les sommets de @xmath97 et @xmath99 ses arrtes munies de lorientation induite par celle de @xmath80 .
en un sommet @xmath100 , il y a deux configurations possibles quant lorientation des artes adjacentes @xmath100 : ou bien ces deux arrtes ont des orientations compatibles , ou bien il y a un changement dorientation ( voir figure [ fig2 ] ) . on a : @xmath103 o @xmath104 et @xmath105 sont les
valeurs respectives en @xmath100 et @xmath106 ( @xmath107 ) dune dtermination continue @xmath108 de langle @xmath109 ( @xmath110 ) avec la tangente oriente @xmath111 .
il rsulte alors du lemme [ lem4 ] que @xmath112 $ ] ( autrement dit le vecteur @xmath109 ne dcrit pas de tour complet lorsque @xmath48 parcourt @xmath111 ) . en
dsignant alors par @xmath113 $ ] langle intrieur @xmath93 en @xmath100 , on a ( voir figure [ fig3 ] ) : @xmath114 par suite : @xmath115\\ & = \frac{1}{2\pi}\left[\sum_{i=0}^{m-1}(\varphi_{i-1}^{1}-\varphi_{i}^{0})\right]\\ & = \frac{1}{2\pi}\left[\sum_{i=0}^{m-1}(\pi-\beta_{i})-2p\pi\right]\\ & = 1-p.\end{aligned}\ ] ] nous pouvons maintenant tablir le thorme .
le nombre denroulement @xmath116 dun point @xmath117 ne dpendant que de la composante @xmath93 laquelle il appartient , on notera @xmath118 cette valeur commune .
il nous reste donc tablir lexistence dune composante @xmath119 de @xmath90 telle que : @xmath120 remarquons dabord que @xmath124 et que @xmath125 pour toute composante @xmath119 adjacente @xmath91 .
il existe donc bien @xmath126 tel que : @xmath127 par labsurde , supposons que @xmath128 .
daprs le lemme [ lem6 ] , il existe alors au moins un changement dorientation en un des sommets @xmath129 de @xmath130 . alors lune des composantes @xmath131 adjacente @xmath132 en @xmath129 vrifie @xmath133 et lautre @xmath134 vrifie @xmath135 ( voir figure [ fig4 ] ) . en effet ,
les valeurs de @xmath136 et @xmath137 ne dpendent que de lorientation avec laquelle on franchit @xmath80 pour passer de @xmath132 @xmath131 et @xmath134 .
il existe donc @xmath138 ( @xmath139 ) tel que : @xmath140 ce qui contredit lhypothse faite sur @xmath141 . | soit @xmath0 un homomorphisme du plan qui prserve lorientation et tel que @xmath1 soit une contraction .
sous ces hypothses , on tablit lexistence , pour toute orbite priodique @xmath2 , dun point fixe ayant un nombre denlacement non nul avec @xmath2 . |
super - massive black holes ( smbhs ) are ubiquitous in galactic nuclei ( @xcite ) , and binaries of these massive objects are a likely product of the hierarchical evolution of structures in the universe . after a galaxy merger , where both progenitors host a smbh , different mechanisms are responsible for the evolution of the binary orbit depending on its separation ( see review by @xcite ) . dynamical interaction with stars appears to be efficient to bring the smbhs down to parsec scales only , what is known as the `` last parsec problem '' ( @xcite ) . a possible way to overcome this barrier and merge the smbhs within a hubble time is interaction with gas .
many theoretical and numerical studies have focused on the orbital evolution of a sub - parsec binary surrounded by a circumbinary disc ( e.g. @xcite ) . however , the exact mechanism that would produce such discs is still unclear ; it is necessary an efficient transport of gas from thousands or hundreds of parsecs to the central parsec .
turbulence and gravitational instabilities in the interstellar medium , through the formation of clumps , allow portions of gas to travel almost unaffected by its surrounding , enhancing the probability of reaching the galactic nuclei ( @xcite ) .
a possible manifestation of these events is the putative molecular cloud that resulted in the unusual distribution of young stars orbiting our galaxy s smbh . in particular , the simulation of ( * ? ? ?
* bonnell & rice ( 2008 ) ) shows a spherical , turbulent cloud falling with a very low impact parameter ( @xmath20.1 pc ) onto a one million solar masses smbh . assuming that these accretion events are common in galactic nuclei , the goal of our work is to model such an event onto a binary instead of a single smbh .
in particular , we are interested on the properties of the discs that will form given different relative orientations between the orbital angular momenta of the cloud and the binary . notice
that this study is complementary to that shown in @xcite , as we are modeling clouds with very low orbital angular momentum .
we model the interaction between the binaries and clouds using a modified version of the sph code gadget-3 ( @xcite ) .
the cloud is represented using over @xmath3 gas particles with a total mass of @xmath4 , an initial turbulent velocity field and uniform density .
the smbhs are modelled as two equally - massive sink particles that interact only through gravity and can accrete sph particles .
the total mass of the binary is @xmath5 , and its initial orbit is keplerian and circular .
the physical setup of the simulation is shown in figure [ initial ] .
the initial velocity of the cloud yields a highly eccentric ( @xmath6 ) , bound orbit where the pericenter distance is @xmath7 pc , which is less than the binary radius , making the interaction between the gas and smbhs very strong . as we expect clouds approaching the binary from different directions , we model systems with three different inclinations between the cloud and binary orbits : aligned , perpendicular and counter - aligned .
in this section we present the main results of the simulations with the different inclinations , in particular the discs that form around the binary and each smbhs . on the left panel of figure [ bhbxy ]
we show the column density map of the simulation at different times , where we can see how the interaction develops .
as the gas falls almost radially onto the binary , around 80% of the cloud is accreted by the smbhs .
most of the remaining gas is pushed away due to an efficient slingshot .
the bound material forms a tail that get stretched and diluted over time , feeding mini - discs " that form around each smbh . to measure the alignment between the binary orbit and the mini - discs , we compute its angular momentum on the corresponding black hole reference frame . we show the time evolution of the direction of both discs on the hammer projection of figure [ bhbxy ] . here
we observe that they tend to align with the orbit of the binary , as expected , although one disc is slightly tilted with respect to the aligned position and also precesses around that position .
this behavior could have distinctive electromagnetic signatures .
for example , the misalignment could affect the variability of spectral lines , or each disc have different polarisation .
the precession could be observed if jets are launched from the smbhs and align with the mini - discs . with this inclination ,
as in the previous case , around 80% of the cloud mass is added to the smbhs .
however , the interaction between the gas and the binary , that we can see in figure [ bhbxz ] , is completely different respect to the aligned case . due to a less efficient slingshot
, most of the remaining material stays bound to the system and it retains its original angular momentum , forming an unstable structure around the binary .
the gas that reaches the smbhs also produce mini - discs , but they are less massive and more intermittent than in the aligned case .
the direction of the mini - discs , shown on the right panel of figure [ bhbxz ] , shows that they tend to follow the original direction of the cloud , which makes them completely misaligned respect to the binary orbit . as well as the previous case
, this could have distinctive signatures on the variability of lines or the direction of possible jets . , but for the model with perpendicular orbits .
in this case the cloud moves on the x - y plane while the binary is on the x - z plane.,title="fig:",scaledwidth=60.0% ] , but for the model with perpendicular orbits .
in this case the cloud moves on the x - y plane while the binary is on the x - z plane.,title="fig:",scaledwidth=40.0% ] in this case we have that the interaction of the binary with the gas produces shocks that cancel angular momentum , allowing the smbhs to accrete even more material than in the previous cases ; around 90% of the cloud is swallowed .
the remaining material forms a tail that , due to the gravitational torques , produces a circumbinary ring . in this case
we do not observe mini - discs during the entire length of the simulation . finally , we compute the eccentricity distribution of the gas on three different stages , as shown on the right panel of figure [ bhb - xy ] .
it is interesting that , if there is star formation in the ring , the stars would have very different orbits around the binary depending on the formation time - scale . for a very rapid star formation we could have highly eccentric orbits ( solid line ) , while for a slow process the stars could be distributed on a narrow ring with nearly circular orbits ( dashed line ) . , but for the model with the counter - aligned orbits . in this case , the cloud and the binary move on the x - y plane , but the latter is rotating clockwise .
right : eccentricity distribution of the gas for three different times in the simulation.,title="fig:",scaledwidth=60.0% ] , but for the model with the counter - aligned orbits .
in this case , the cloud and the binary move on the x - y plane , but the latter is rotating clockwise .
right : eccentricity distribution of the gas for three different times in the simulation.,title="fig:",scaledwidth=42.0% ]
the preliminary results presented here show that accretion events onto binaries result in very different disc morphologies , depending on the relative inclination between the cloud and the binary orbits .
our work in progress is extending this study to larger impact parameters , showing lower accretion rates , and exploring the effect of the interaction on the black holes orbit and spin evolution .
these results are likely to have important implications on the multi - messenger future studies of smbh binaries and on the long - term evolution of these systems .
column density maps were created with splash by @xcite .
we acknowledge support from conicyt - chile through pcha / doctorado nacional , fondecyt ( 1141175 ) , basal ( pfb0609 ) , anillo ( act1101 ) , redes ( 120021 ) and exchange ( pcci130064 ) grants . | we model numerically the evolution of @xmath0 turbulent molecular clouds in near - radial infall onto @xmath1 , equal - mass super - massive black hole binaries , using a modified version of the sph code gadget-3 .
we investigate the different gas structures formed depending on the relative inclination between the binary and the cloud orbits .
our first results indicate that an aligned orbit produces mini - discs around each black hole , almost aligned with the binary ; a perpendicular orbit produces misaligned mini - discs ; and a counter - aligned orbit produces a circumbinary , counter - rotating ring . |
the large hadron collider ( lhc ) machine will enter the collision mode at centre - of - mass energy of 10 tev in 2008 and eventually will operate at 14 tev from 2009 onwards gradually improving upon the luminosity .
two general - purpose detectors , cms ( compact muon solenoid ) and atlas ( a toroidal apparatus ) , are ready for the data - taking phase with intense detector commisioning works underway .
the much awaited discoveries at the lhc have to be preceeded by the _ rediscovery _ of the standard model ( sm ) , and early discovery , though possible , will be challenging . on the other hand , from early phase on , _
ie _ , starting from an integrated luminosity of mere 1 pb@xmath0 , various sm processes can be studied ; in particular , heavy quarkonia peaks of @xmath1 and @xmath2 will shine well above background in the low mass range of the invariant mass distribution of dileptons .
electroweak ( ew ) processes of w and z productions , having very large rates combined with clean leptonic decay mode signatures ( @xmath3 ) , are not only the _ first physics _ at the lhc , they will be studied at all luminosities
. these will be the _ standard candles _ for a large variety of lhc measurements .
the w , z physics will enable , as a function of accumulated data , detector and physics - analysis tools commissioning of the experiments , precision determination of electroweak variables as well as measurements in as yet unexplored kinematic regions . these programmes constitute both the confirmation as well as the consistency checks of sm at the highest energies lhc offer .
the breakthrough discoveries at the lhc will be interpreted by critically studying sm processes with experimental accuracy matched by theoretical understanding at the same level . since the production cross section and dynamics are largely controlled by qcd , events with inclusive jets , photons , dileptons , heavy quarks will be produced copiously at the lhc , as exemplified in table [ evtrate ] , providing complementary datasets which will eventually probe many aspects of strong and ew interactions with high precision .
the large samples will also be useful for search of rare processes which potentially hint at as yet unknown _
new physics_. .expected triggered event yield in atlas with 1 pb@xmath0 data at 14 tev . [ cols="<,^",options="header " , ] [ wzsyst2 ]
to establish the anticipated discoveries at the lhc , the standard model processes must be well understood .
various aspects of z - boson production and subsequent decays will be utilised by experiments for precision determination of electroweak parameters .
an early , competitive w mass measurement from the lhc is improbable .
some of the di - boson productions are likely to be etsablished during the early phase of the lhc .
the author wishes to thank the organisers for the kind support and local hospitality without which the participation would not have been possible .
the author also gratefully acknowledges many collaborators in cms experiment for overall support in presenting the talk and preparing this report . 9 the cms collaboration , cms physics analysis summary , cms pas 2007/002 .
the cms collaboration , cms physics analysis summary , cms pas ewk-08 - 005 .
d.bourlikov , contribution to these proceedings .
g. quast et.al . , cms note 2006/061 .
m. boonekamp , acta physica olonica b , vol.38 ( 2007 ) .
n. besson , m. boonekamp , atl - phys - pub-2006 - 007 , a. tricoli et.al .
, hera - lhc workshop proceedings , arxiv : hep - ex/05090021 . the cms collaboration , cms physics analysis summary , cms pas ewk-08 - 003 . | the large hadron collider , lhc , though meant for discovery , will provide enough data from early phase to also perform various studies of standard model processes in as yet unexplored kinematic regions .
precision measurements of the electroweak variables will be possible due to the large rates of w and z boson productions combined with clean leptonic signatures .
examples of simulation results from cms and atlas collaboration studies are presented to show the wide variety of measurements possible and how various issues like background estimation , determination of systematic effects will be taken care of by the experiments . |
in this paper , we study the problem of discrete polynomial blending , a discretization of the problem of curve blending . in curve blending ,
one approximates a bivariate function by interpolating to a network of curves extracted from the graph of the function .
discrete blending involves a second level of discretization , whereby the blended curves are interpolated at finite sets of points .
this is illustrated in fig .
[ fblend1 ] . in the figure ,
the blended interpolant would interpolate to the 9 curves ( 4 horizontal and 5 vertical ) in the network , while the discrete blended surface interpolates at @xmath0 grid points . in our work
, the term `` interpolation '' can be taken loosely to mean interpolation with respect to a given set of functionals , and may not necessarily imply point evaluation . the grid in fig .
[ fblend1 ] is not uniform due to gaps between some grid points .
if we filled in these holes we would have a uniform grid with @xmath1 points that can be interpolated using tensor product polynomials .
hence , we can interpolate at just @xmath0 points rather than @xmath2 , and in some cases do so with the same ( or nearly the same ) rate of approximation , as we shall show in this paper . in discrete polynomial blending ,
the approximating spaces are not generally tensor product polynomial spaces ( although that is a special case ) .
as it turns out , our approximating spaces are the `` sum of tensor product polynomial spaces '' .
hence , our study is one of approximation from the sum of tensor product polynomial spaces .
what is known about discrete blending comes mainly from the literature on boolean sum interpolation , sparse grid methods , lower set interpolation and finite elements .
the topic was perhaps first studied by biermann @xcite who constructed polynomial interpolants using the bivariate lagrange basis .
the book @xcite is an excellent summary of boolean sum methods , including an analysis of biermann interpolation . in @xcite
, a construction was given that generalized biermann interpolation to interpolation with respect to more general sequences of functionals , much like we will do in this paper .
biermann interpolation was generalized to higher dimensions in @xcite , under the title `` d - variate boolean interpolation '' , and more recently to arbitrary `` lower sets '' in @xcite ( which reduces to the results in @xcite for total degree interpolation ) . in this paper
we construct a new discrete blended quasi - interpolant based on the bernstein basis .
to do so , we will bring in some techniques on `` dual basis in subspaces '' that the author has studied in @xcite . from this
we construct dual bases for the space of discrete blending , and compute approximation estimates .
one of the main contributions is to show our quasi - interpolants achieve rates of approximation comparable or the same as that of tensor product interpolation on a larger grid , but with much fewer data points .
this leads us to the construction of a quasi - interpolant analogous to the serendipity elements in the finite element method .
the results presented in this paper originate from a talk by the author at the conference on curves and surfaces in oslo , norway , in 2012 .
the remainder of the paper is organized as follows . * the approximating space .
* quasi - uniform grids . * the bernstein basis and univariate quasi - interpolant .
* discretely blended bernstein - bzier quasi - interpolants .
* order of approximation .
* serendipity elements .
* examples .
in discrete polynomial blending , the approximating space is the algebraic sum of tensor product polynomial spaces .
let @xmath3 $ ] and @xmath4 $ ] be sequences in @xmath5 , the space of @xmath6-tuples of non - negative integers .
let @xmath7 be the tensor product of the spaces @xmath8 and @xmath9 of polynomials of degrees at most @xmath10 and @xmath11 , respectively .
then , we define our approximating spaces as @xmath12 we assume that both @xmath13 and @xmath14 are strictly increasing sequences , an assumption that we justify by the following lemma .
let @xmath15 be defined as in ( [ e1 ] ) for some @xmath13 and @xmath14 in @xmath5
. there exists strictly increasing sequences @xmath16 and @xmath17 in @xmath18 for some @xmath19 such that @xmath20 . to begin , let @xmath21 and let @xmath22 and @xmath23 .
to prove this result , we will rearrange and truncate @xmath16 and @xmath17 until they are strictly increasing .
suppose @xmath24 for some @xmath25 and @xmath26 . then either @xmath27 or @xmath28 . in the former case
, @xmath29 can be removed from the representation in ( [ e1 ] ) without changing @xmath30 , and so we remove @xmath31 and @xmath32 from the sequences @xmath33 and @xmath34 . in the latter case ,
we remove @xmath35 and @xmath36 . after removing these unnecessary terms ,
the terms left in the revised sequence @xmath33 are distinct .
that is , @xmath37 for all @xmath25 and @xmath26 .
further , since @xmath38 is not affected by the ordering of the tensor product terms , we can rearrange the pairs @xmath39 in @xmath40 so that @xmath16 is strictly increasing .
thus , assume that @xmath16 is strictly increasing .
now , if @xmath34 is not strictly increasing , then there exists an index @xmath25 such that @xmath41 and @xmath42 , in which case @xmath43 , and so @xmath29 can be removed from the sum without changing @xmath30 . after trimming away all such terms in the sequence ,
we are left with @xmath34 strictly increasing .
hence , we are left with strictly increasing sequences @xmath33 and @xmath34 in @xmath44 for some @xmath45 such that @xmath46 .
further , since we are not adding new terms , @xmath19 . a polynomial @xmath47 can be represented @xmath48 with @xmath49 .
each @xmath50 can be expressed @xmath51 for some coefficients @xmath52 .
therefore , the power basis for the space @xmath15 is the union @xmath53 however , this union is not disjoint .
this basis can visualized by the dots in a _ lower grid _ , which is defined to be the graph of the _ lower set _
\times [ 0 , \ldots , n_{r - k}].\ ] ] the power basis for @xmath15 is therefore @xmath55 , and the dimension of @xmath15 is the number of dots in the lower grid . by counting the distinct dots in the lower grid , we arrive at the following : [ prop0 ] the space @xmath15 is a vector space of dimension @xmath56 with @xmath57 . in tbl .
[ f1a ] , the dimension of the approximating space is given for a few choices of @xmath13 and @xmath14 . in fig .
[ f1b ] , the corresponding lower grids are plotted . .
approximating spaces for : @xmath58 $ ] , @xmath59 $ ] , @xmath60 $ ] and @xmath61 $ ] . [ cols="<,<,<,<",options="header " , ] [ 6b ]
in this paper we have constructed a new quasi - interpolant for discrete blended surface approximation based on dual basis functions in the bernstein basis , and we have established error estimates comparable to approximation on full tensor product grids , much like the serendipity elements in the finite element literature . throughout this paper we assumed @xmath62 and @xmath63 .
if we do not have this , we can still apply our construction by first using degree elevation .
for example , if @xmath64 $ ] we would degree elevation to get @xmath65 $ ] , and then proceed as before .
the framework for this originates from the talk `` dual bases on subspaces and the approximation from sums of polynomial and spline spaces '' , given by the author at the conference `` mathematical methods for curves and surfaces '' , held in oslo norway , june , 2012 .
the talk included constructions for hermite and spline blended elements similar to the construction in this paper .
our plan is to publish the details of these results in forthcoming papers . | in this paper we study `` discrete polynomial blending , '' a term used to define a certain discretized version of curve blending whereby one approximates from the `` sum of tensor product polynomial spaces '' over certain grids .
our strategy is to combine the theory of boolean sum methods with dual bases connected to the bernstein basis to construct a new quasi - interpolant for discrete blending .
our blended element has geometric properties similar to that of the bernstein - bzier tensor product surface patch , and rates of approximation that are comparable with those obtained in tensor product polynomial approximation .
[ multiblock footnote omitted ] |
the one - dimensional poisson equation , @xmath0 with dirichlet boundary conditions , @xmath1 plays an important role in many branches of science .
particularly , the poisson equation is essential in self - consistent calculations in solid state physics @xcite . in general
, we have to solve it numerically many times .
therefore , is vital to have the fastest and the most accurate numerical scheme to solve it . in this article
, we present a very efficient direct method , based on a numerov @xcite sixth order numerical scheme , to solve the poisson equation numerically . because of its efficiency and simplicity
, this new method can be used as a canonical numerical scheme to accurately solve the one - dimensional poisson equation .
this article is organized as follows .
our numerical scheme is presented in section [ sec : numerov ] .
its linearization , together with a few discussions , are presented in section [ sec : discus ] .
our conclusions are presented in section [ sec : conclus ] .
let @xmath2 represents the solution of at the @xmath3-th point , @xmath4 , of an equally spaced net of step @xmath5 and dimension @xmath6 .
let also @xmath7 represents the @xmath8-th derivative evaluated at the same point @xmath9 .
then we can evaluate the solution @xmath10 at the nearest neighborhood points @xmath11 of @xmath9 using taylor series @xcite , @xmath12 the basic idea in the numerov approach is to eliminate the fourth order derivative in the expression @xmath13 where @xmath14 to obtain the sixth order three - point numerical scheme @xmath15 where we chose @xmath16 and , consequently , @xmath17 . in a similar way
, we can eliminate the third order derivative from @xmath18 where @xmath19 to obtain the fifth order three - point numerical scheme @xmath20 for the first derivative of @xmath10 , where we chose @xmath21 and , consequently , @xmath22 .
so far , the three - point numerical scheme is an iterative method , i.e. , given two informations , @xmath23 and @xmath24 , we can calculate @xmath25 .
one difficulty of this iterative method is related with the dirichlet boundary conditions : they are known only at end - points @xmath26 and @xmath27 .
thus , we can not initiate our iterative scheme .
fortunately , the recurrence relation in is linear with constant coefficients .
these two features imply we can find an unique solution to it , @xmath28 where @xmath29 and @xmath30 must be expressed in terms of @xmath31 ( the dirichlet boundary conditions ) , @xmath32 now we have an analytical sixth order numerical scheme to solve accurately the poisson equation with the dirichlet boundary conditions .
it should be mentioned that the analytical third order numerical scheme presented by hu and oconnell @xcite , making use of tridiagonal matrices , can also be derived by the present approach restricted to the third order , @xmath33 where @xmath34
although we have found a very accurate analytical direct method to solve the one - dimensional poisson equation with dirichlet boundary conditions , namely , the sixth order numerov scheme , it has one undesirable feature : its execution time is proportional to the square of the grid dimension
. fortunately it can be linearized .
first , we create a vector @xmath35 , whose components are the partial sums @xmath36 ( @xmath37 ) .
next , we create a second vector @xmath38 with @xmath39 and @xmath40 . we also need a third vector @xmath41 with @xmath42 and a fourth vector @xmath43 with the complete sums @xmath44 . using these new vectors ,
our sixth order numerov scheme can be rewritten as follows , @xmath45.\ ] ] this numerical scheme has now a linear execution time proportional to five times the grid dimension @xmath6 .
let us use a gaussian density , @xmath46 to verify the accuracy and the efficiency of the non - linear numerical scheme , as well as the linear numerical scheme .
the solution for the poisson equation , along with the boundary conditions @xmath47 and @xmath48 , is @xmath49 where @xmath50 is the error function , @xmath51 figure [ f1 ] shows the execution time as a function of the grid dimension @xmath6 for three cases . in one case ( the dotted line ) ,
the numerical solution was computed by the non - linear third order numerical scheme . in the second case ( the dashed line ) , the numerical solution was computed by the non - linear sixth order numerical scheme . in the last case ( the solid line ) , the numerical solution was computed by the linear sixth order numerical scheme . at @xmath52 , the execution time of the non - linear third ( sixth )
order numerical scheme is approximately 145 ( 51 ) times the execution time of the linear sixth order numerical scheme .
clearly , we can see that the linearization process described above plays an essential role in the present numerov scheme . in order to measure the accuracy of the present numerov scheme
, we can compute the euclidean norm @xmath53^{2}}\ ] ] where @xmath54 stands for the exact solution and @xmath55 stands for the numerical solution .
figure [ f2 ] shows ( right vertical axis ) a comparasion between two euclidean norms : one ( dashed line ) using the third - order numerical scheme and the other ( solid line ) using the sixth - order numerical scheme .
note that , at @xmath56 , the exact euclidean norm of the third - order scheme is approximately four orders of magnitude above the exact euclidean norm of the sixth - order scheme .
naturally , we can see that the sixth - order numerical scheme is much more accurate and efficient than the third - order numerical scheme . of course
, we do nt know the exact solution in practical applications .
in that case , the best we can do is to compute the mean euclidean norm of the numerical solution @xmath55 , @xmath57 this mean euclidean norm can be used as a convergency criterion , as shown in figure [ f2 ] ( left vertical axis ) .
we have applied the numerov method to derive a sixth - order numerical scheme to solve the one - dimensional poisson equation with dirichlet boundary conditions .
the resulting recurrence relations were exactly solved and the corresponding execution time was linearized [ see ] in such way to avoid the handling of a dense matrix .
therefore , the numerical scheme is both accurate and efficient as illustrated in figure [ fig : tempos ] .
moreover , it is extremely ease to implement in any numerical or algebraic computer language .
as pointed by j. m. blatt @xcite , the numerov method is both a three - point method , which implies it is stable , and of highest order , which implies it is accurate .
all these features make the numerical scheme the canonical method of choice for the integration of the poisson equation .
the author wish to thank rafael casalverini for useful discussions and fapesp for financial supports . | in this article , we present an analytical direct method , based on a numerov three - point scheme , which is sixth order accurate and has a linear execution time on the grid dimension , to solve the discrete one - dimensional poisson equation with dirichlet boundary conditions .
our results should improve numerical codes used mainly in self - consistent calculations in solid state physics . |
with the launch of nasa s stereo mission in october 2006 , a new dimension of solar coronal observations has been opened . for the first time , objects above the solar surface can be perceived in three dimensions by analysing the stereo image pairs observed with the secchi instruments onboard the stereo spacecraft and without making a - priori assumptions about their shape .
the two stereo spacecraft orbit the sun at approximately 1 au near the ecliptic plane with a slowly increasing angle of about 45 degrees / year between stereo a and stereo b. each spacecraft is equipped with , among other instruments , an euv telescope ( secchi / euvi ) . for the objectives of the mission and
more details about the euvi telescopes see @xcite and @xcite .
the major building blocks of the solar corona are loops of magnetic flux which are outlined by emissions at , e.g. , euv wavelengths . in principle , the magnetic field in the lower corona can be derived from surface magnetograms by way of extrapolations ( e.g. * ? ? ?
. however , missing boundary values and measurement errors may introduce considerable uncertainties in the extrapolation results so that there is an obvious need for an alternative three - dimensional determination of the coronal magnetic field geometry . among other goals of the mission ,
this requirement has been one of the drivers for stereo .
attempts for a three - dimensional reconstruction of the coronal magnetic field from euv observations have started long before stereo data was available and date back more than a decade @xcite . here ,
we for the first time use two simultaneously observed euvi images observed by the two stereo probes and rigourously reconstruct loop shapes without any further assumption about their temporal or spatial behaviour from which earlier reconstructions employing consecutive images from a single spacecraft suffered @xcite .
we compare the reconstruction results with field lines derived from linear force - free magnetic field models with variable @xmath0 , the ratio of field - aligned current density to field strength @xcite .
.stereo spacecraft coordinates at the time of the observations .
spacecraft longitude and latitude are given in the heliocentric earth ecliptic ( hee ) coordinate system . [ cols="<,>,>",options="header " , ] the loop reconstruction is also prone to errors , however .
these may occur whenever a projected loop section in the images are directed tangentially to an epipolar line @xcite . for the viewing geometry of our observations , epipolar lines are nearly horizontal in the images and
the critical part for closed , e - w orientated loops therefore lies more or less near their apex .
also the open loop structures 16 - 19 in image b and 17 - 20 in image a ( see figure [ fig : loopab ] ) suffer from this problem as they are orientated almost entirely horizontally in the images .
we have therefore not attempted to reconstruct them even though a correspondence could well be identified . in figure [ fig:3dloop5a3b_e ]
we display the reconstruction of loop ( 5,3 ) ( yellow curve ) which shows by far the largest deviation to its best fit linear force - free field line ( red curve ) . for most other loops ,
this discrepancy is much less although the agreement is rarely perfect .
for some points along the loop ( 5,3 ) , we also show error bars which represent the geometrical reconstruction error when the uncertainty for the loop projection in the images is assumed to be 1.5 pixels . in this case
, the height of the loop top turns out to be @xmath1 1.5 times above that of the corresponding field line .
this field line ( the first entry in table [ tab : loopparam ] ) again shows a relatively small value @xmath2 .
since this @xmath0 value gave the best fit of linear force - free field lines to the loop projection in the images , we conclude that the linear force - free assumption is often not adequate ( cf .
we demonstrated that euv data from the new stereo spacecraft allows for the first time to make a reliable stereoscopic reconstruction of the spatial distribution of hot , magnetically confined coronal plasma and , by inference , provide a full three dimensional view of the arrangement of coronal field lines .
we found that linear force - free field models are helpful to establish correspondences between the loops observed in the stereo image pairs .
the field lines from these linear force - free models need not be physical but only serve as a first order approximation to the final loops .
realistic magnetic field models of the corona will have to be judged by their capability to yield field lines in agreement with the stereoscopically reconstructed loops .
our scheme to determine correspondences will become even more valuable when the stereo base angle grows and loop structures become more difficult to be identified in the image pairs .
the reconstructions will also allow more precise analyses of emissions from loops .
the observed brightness of euv loops is , e.g. , strongly modified by the inverse cosine of the angle between the line of sight and the loop s local tangent .
this may , besides other effects , contribute to the enhanced euv brightness of the lower loop segments commonly observed on the solar disk : these loop segments close to the loop s foot points are more aligned with the radial direction and they make a small angle with the view direction .
this may cause them to appear brighter than the loop top which is viewed at more or less right angles .
other applications have been proposed @xcite .
e.g. , the amount of twist of a reconstructed loop indicates how close the flux tube is to a kink instability .
@xcite found a threshold of about @xmath3 in numerical simulations for the twist @xmath4 . here
@xmath5 is the length of the flux tube , @xmath6 the toroidal field along its axis and @xmath7 the poloidal field at a radius @xmath8 from the flux tube centre . in some cases it may be possible to resolve the number of turns @xmath9 which a field line makes about the flux tube centre from stereoscopic reconstruction and thus to determine the twist from @xmath10
likewise , the twist is also related to @xmath0 and @xmath5 by @xmath11 . for the active region
observed here , table [ tab : loopparam ] gives values of @xmath12 well below the kink instability threshold .
another perspective for stereoscopic loop reconstruction is the analysis of loop oscillations from a series of image pairs .
the reconstructed loops will allow us to determine the transverse polarisation of these oscillations @xcite . since the coronal magnetic field has a complicated geometry without symmetries , the frequency of these oscillations will significantly depend on this polarisation .
note that these phenomena are invisible in the magnetic surface data and therefore can not be retrieved from field extrapolations , which in addition require a stationary magnetic field .
the authors thank the mdi / soho and the secchi / stereo consortia for the supply of their data .
stereo is a project of nasa , soho a joint esa / nasa project .
the secchi data used here were produced by an international consortium of the naval research laboratory ( usa ) , lockheed martin solar and astrophysics lab ( usa ) , nasa goddard space flight center ( usa ) , rutherford appleton laboratory ( uk ) , university of birmingham ( uk ) , max - planck - institut for solar system research ( germany ) , centre spatiale de lige ( belgium ) , institut doptique thorique et applique ( france ) , institut dastrophysique spatiale ( france ) . | we present the first reconstruction of the three - dimensional shape of magnetic loops in an active region from two different vantage points based on simultaneously recorded images .
the images were taken by the two euvi telescopes of the secchi instrument onboard the recently launched stereo spacecraft when the heliocentric separation of the two space probes was 12 degrees .
we demostrate that these data allow to obtain a reliable three - dimensional reconstruction of sufficiently bright loops .
the result is compared with field lines derived from a coronal magnetic field model extrapolated from a photospheric magnetogram recorded nearly simultaneously by soho / mdi .
we attribute discrepancies between reconstructed loops and extrapolated field lines to the inadequacy of the linear force - free field model used for the extrapolation . |
high quality measurements of anisotropies in the cosmic microwave background ( cmb ) probe the cosmic fluctuations generated during an inflationary epoch in the very early universe @xcite . recently ,
boomerang @xcite and maxima @xcite teams announced the clear detection of a first acoustic peak at an angular scale @xmath0 , which confirms the most important prediction of inflation : the universe seems to be spatially flat @xcite .
another generic prediction of inflation is that the primordial spectra of density perturbations and gravitational waves are _ almost _ scale - invariant .
more cmb precision measurements will be available soon .
we argue @xcite that cmb predictions on the basis of the simplest inflationary model , slow - roll inflation @xcite , are not as precise as could be believed from the accuracy of the power spectra @xcite .
we compare the predictions from the slow - roll approximation @xcite with the exact solutions from the model of power - law inflation @xcite .
we find unacceptable large errors in the predictions of multipole moments .
the reason is as follows : the primordial spectrum is best approximated at some pivot scale @xmath1 .
a small error in the spectral index gives rise to a large error at wavenumbers that differ significantly from @xmath1 , due to a large lever arm .
a natural choice for the pivot scale is the present hubble scale , but leads to extremely large errors for high multipole moments . a shift of the pivot scale to the scale of the first acoustic peak decreases these errors
dramatically ( see figure [ fig1 ] ) . in @xcite
we compare the improved ( optimal pivot scale ) slow - roll predictions with recent cmb data ( see figure 2 ) .
most data analysis so far @xcite was based on a power - law shape of the primordial spectra .
this shape is _ not _ predicted by the slow - roll approximation , only the first two terms in a taylor expansion with respect to the wavenumber coincide .
slow - roll inflation is very simple and is an attractor for many inflationary models .
inflation driven by a single field @xmath2 , may be characterized at a given moment of time @xmath3 by the parameters @xmath4_*$ ] , @xmath5_*$ ] , @xmath6_*$ ] , , where @xmath7 is the hubble rate .
the condition for inflation is @xmath8 , whereas slow - roll inflation is characterized by @xmath9 , and negligible higher derivatives .
based on these approximations the power spectrum of the bardeen potential @xmath10 and of the amplitude of gravitational waves @xmath11 reads @xcite @xmath12 , \\
\label{specsrgw } k^3p_h & = & \frac{16 h_*^2 l_{\rm pl}^2}{\pi } \biggl[1 - 2\epsilon \biggl(c+1+\ln \frac{k}{k_*}\biggr)\biggr],\end{aligned}\ ] ] where @xmath13 , @xmath14 being the euler constant .
the pivot scale is defined as @xmath15 .
fixing @xmath1 corresponds to a choice of the time @xmath3 during inflation .
the spectral indices can be obtained from @xmath16 and @xmath17 .
we call this the next - to - leading order of the slow - roll approximation ( at the leading order strictly scale - invariant spectra are predicted ) .
( 2,0.6 ) ( 0.5,0.05)(0,0)@xmath18 ( 0.22,0.535)(0,0)@xmath19 ( 0.405,0.46)(0,0)@xmath20 ( 0.575,0.36)(0,0)@xmath21 ( 0.63,0.28)(0,0)@xmath22 ( 0.74,0.185)(0,0)@xmath23 ( 0.71,0.53)(0,0)error in % ( 0.45,0.33)(0,0 ) ( 1.4,0.05)(0,0)@xmath18 ( 1.13,0.40)(0,0)@xmath19 ( 1.08,0.325)(0,0)@xmath24 ( 1.08,0.255)(0,0)@xmath25 ( 1.08,0.19)(0,0)@xmath26 ( 1.06,0.14)(3,1)0.3 ( 1.47,0.245)(0,0)@xmath23 ( 1.61,0.53)(0,0)error in % ( 1.35,0.33 ) ( 0,0 ) on the other hand , the power spectra may be calculated exactly for power - law inflation , which is characterized by a power - law behavior of the scale factor , i.e. , @xmath27 . for power - law inflation
we have @xmath28 and @xmath29 during inflation .
we use @xmath30 to parametrize the spectra , i.e. @xmath31 .
the corresponding power spectra then read @xcite @xmath32 where @xmath33^{2/(1-\epsilon ) } \gamma[1/(1-\epsilon ) + 1/2]^2/\pi$ ] , with @xmath34 . for power - law inflation
the spectral indices read : @xmath35 . in the limit
@xmath36 the power spectra ( [ specpl ] ) go to ( [ specsrd ] ) with @xmath28 and to ( [ specsrgw ] ) , respectively .
we can now calculate the multipole moments @xmath37 for the power - law and slow - roll spectra for @xmath28 .
we define the error from the slow - roll approximation as @xmath38 for similar spectra the error ( [ deferr ] ) depends only weakly on the transfer function .
this allows us to neglect the evolution of the transfer function for this purpose and to obtain an analytic result , which is plotted in figure [ fig1 ] .
the values of @xmath39 refer to the exact power - law solution . in the left figure @xmath40
gives the smallest error for the quadrupole and unacceptably large errors at high multipoles . in the right figure
the pivot scale has been chosen to minimize the error around the first acoustic peak , @xmath41 .
the corresponding condition is @xmath42 , where @xmath43 is the comoving distance to the last scattering surface and @xmath44 $ ] with @xmath45 . for @xmath46
this gives @xmath47 , where @xmath48 for @xmath49cdm .
let us now compare @xcite the predictions of slow - roll inflation with recent data from boomerang @xcite and maxima-1 @xcite , supplemented with the cobe / dmr dataset @xcite .
instead of fitting ten cosmological parameters we fix the values of otherwise measured parameters and assume that slow - roll inflation is the correct theory .
in figure [ fig2 ] we present the sum of scalar and tensor cmb band power for a @xmath49cdm model with @xmath50 and @xmath51 .
the boltzmann code used here was developed by one of us ( a.r . ) .
we see without a @xmath52 analysis that qualitatively different inflationary models are consistent with the observations : both models with @xmath53 give reasonable fits , one of these models has a flat scalar spectrum ( with @xmath54 ) , the other one has a negative tilt ( with @xmath55 ) .
both models have an important contribution of gravitational waves ( @xmath56 ) .
we emphasize that the generic slow - roll predictions ( [ specsrd ] ) and ( [ specsrgw ] ) do not have a power - law shape .
this fact induces large differences to multipole moments that are predicted under the assumption that the power - law shape ( [ specpl ] ) is the generic inflationary prediction . besides using the correct primordial spectrum
a clever choice of the pivot scale can hide unavoidable uncertainties of the multipole moments in the cosmic variance on one side and in the instrumental noise on the other side of the spectrum .
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j. _ * 464 * , l1 ( 1996 ) . | inflationary predictions of the cosmic microwave background anisotropy are often based on the slow - roll approximation .
we study the precision of these predictions and compare them with the recent data from boomerang and maxima-1 . |
ls i + 61 303 is a high mass x - ray binary ( hmxb ) that consists of an optical star with spectral type b0 ve and an unknown compact companion in a highly eccentric , 26.5 day orbit @xcite . while the system has a relatively low x - ray luminosity for a hmxb , ls i + 61 303 is the 15th brightest @xmath0-ray source included in the _ fermi _ lat 1-year point source catalogue ( @xcite ) . the be disk interacts with the compact companion , producing emission that has been observed to vary with orbital phase at every wavelength across the electromagnetic spectrum , from radio to tev ( eg . @xcite , @xcite ) .
@xcite found periodic radio outbursts that peak near @xmath2 , and they defined the arbitrary reference for zero phase at hjd 2,443,366.775 that remains the conventional definition for ls i + 61 303 .
periastron occurs at @xmath3 @xcite .
during 2008 october and november , we performed an intense multiwavelength observing campaign on ls i + 61 303 supported by a _
cycle 1 program .
we obtained optical h@xmath1 spectra of ls i + 61 303 at the kpno coud feed telescope over 35 consecutive nights to study the evolution of the emission during a complete orbit @xcite , @xcite .
the h@xmath1 line profile exhibits a dramatic emission burst near @xmath4 , observed as a redshifted shoulder in the line profile ( see fig .
[ gray ] ) as the compact source moves almost directly away from the observer .
smaller temporal changes in the red spectra suggest additional h@xmath1 emission variability , so we subtracted the mean emission line profile to investigate the residuals carefully ( see fig .
[ diff ] ) .
during about half of the orbit , @xmath5 , the difference spectra reveal a partial s - shaped pattern similar to a spiral density wave that is commonly observed in be star disks @xcite .
@xcite also observed a strong blue peak near @xmath6 , which supports the development of a spiral density wave near periastron .
after this phase , the peculiar red shoulder develops .
we measured the equivalent width of h@xmath1 , @xmath7 , for each spectrum by directly integrating over the line profile .
( we use the convention that @xmath7 is negative for an emission line . )
the errors in @xmath7 are typically about 10% due to noise and placement of the continuum .
figure [ eqwidth ] shows that during our coud feed run , @xmath7 decreased slightly just before periastron .
since @xmath7 is correlated to the radius of a be star s circumstellar disk @xcite , we interpret the decline in emission as a slight decrease in disk radius as gas is stripped away by the compact companion .
@xmath7 then rises dramatically with the onset of the red shoulder emission component near @xmath4 .
figure [ eqwidth ] also compares our recent @xmath7 with those measured by @xcite .
their data were accumulated over six different observing runs over 19982000 , and the long term differences in emission strength are substantial .
also during 2008 october and november , g. pooley obtained nearly simultaneous radio flux coverage with the arcminute microkelvin imager ( ami ) array .
the 15 ghz ami light curve ( fig .
[ radio ] ) reveals emission that peaks at the same time as the h@xmath1 `` red shoulder '' outburst .
contemporaneous _ rxte _
light curves from @xciteand _ fermi _ light curves ( @xcite ) also reveal orbitally modulated emission that peaks just before the h@xmath1 red shoulder , although their wide phase bins may mask a true correlation .
the h@xmath1 emission clearly traces the high energy emission region in this system .
the unusual broadness of the h@xmath1 red shoulder emission is consistent with a balmer - dominated shock ( bds ; @xcite ) .
bds are traditionally observed around supernova remnants but are also sometimes produced within pulsar wind nebulae and other evolved stellar systems .
they form when high velocity ( 2009000 km s@xmath8 ) shocks collide with the interstellar medium , manifesting themselves as optically emitting filaments .
energetic particles and/or photons may be generated in the post - shock region of the collisionless , non - radiative shock .
direct collisional excitation of the pre - shock atoms produces a narrow emission line component that reflects thermal conditions within the pre - shock gas .
if the energetic particles exceed the shock velocity , the pre - shock hydrogen atoms also exchange electrons with post - shock protons , manifesting themselves as broad neutral hydrogen lines ( widths @xmath9 km s@xmath8 ) .
the h@xmath1 line structure in ls i + 61 303 is complicated by the superposition of emission from the circumstellar disk ; however , the broad red shoulder is consistent with such a bds .
the temporary nature of the red shoulder , as well as the correlated gev
radio emission , suggests that the bds only forms when a high density tidal mass stream interacts with a pulsar wind in ls i + 61 303 .
we thank di harmer and the staff at kpno for their hard work to schedule and support the coud feed observations .
guy pooley , christina aragona , tabetha boyajian , amber marsh , and rachael roettenbacher helped collect the data presented here and should be cheered for their heroic efforts .
this work is supported by nasa dpr numbers nnx08av70 g , nng08e1671 , nnx09at67 g , and an institutional grant from lehigh university . | the @xmath0-ray binary ls i + 61 303 is one of the brightest fermi sources , with orbitally modulated emission across the electromagnetic spectrum .
here we present h@xmath1 spectra of ls i + 61 303 that exhibit a dramatic emission burst shortly before apastron , observed as a redshifted shoulder in the line profile . a correlated burst in radio , x - ray , and gev emission
is observed at the same orbital phase .
we interpret the source of the emission as a compact pulsar wind nebula that forms when a tidal mass stream from the be circumstellar disk interacts with the relativistic pulsar wind .
the h@xmath1 emission offers an important probe of the high energy emission morphology in this system . |
giant pulses ( gps ) have been reported in four pulsars ( b0531 + 21 , b1937 + 21 , b1821@xmath124 and b0540@xmath169 ) todate ( staelin & reifenstein 1968 ; lundgren et al . 1995 ; cognard et al .
1996 ; romani & johnston 2001 ; johnston & romani 2003 ) .
three of these pulsars are millisecond pulsars ( msps ) and also show strongly pulsed hard x - ray profiles ( takahashi et al .
the radio gps occur in a narrow phase window close to the high energy non - thermal pulse indicating a common magnetospheric origin .
all these pulsars have a high value of @xmath0 .
we have used gmrt to search for gps in candidate msps with a non - thermal high energy emission and a range of @xmath0 and report detection of such pulses in two more pulsars , psr j0218 + 4232 and b1957 + 20 .
we obtained about 3600 s of data on each pulsar using 20 to 22 gmrt antennae in an incoherent mode at 610 mhz with 16 mhz bandwidth .
the expected rms noise in the above configuration of gmrt for a sampling time of 258 @xmath2 is about 1 jy . the data in two subbands ( 8 mhz each ) were dedispersed to a common sky frequency ( 610 mhz ) .
the periods with a peak greater than 3.5 times rms in both bands at the same sample were identified as large amplitude pulses ( laps ) .
this procedure disperses any narrow interference spike discriminating against interference .
a number of marginal laps , i.e. pulses with a peak between 3.0 to 3.5 times rms , were also identified .
we searched 2.2 million periods for psr j0218 + 4232 ( @xmath3 3.2 @xmath4 g ) and found three significant laps .
figure 1a shows the integrated profile for this pulsar and the detected laps are marked with filled circles .
the largest of these had an intensity 51 times the mean intensity ( intensity of lap , @xmath5 jy-@xmath6s ) .
our data also consisted of 9 marginal laps , 7 of which occur between phase 0.89 - 1.2 , which is the phase interval corresponding to one of the high energy peaks .
we searched about 1 million periods for psr b1957 + 20 ( @xmath3 3.8 @xmath4 g ) and found one significant lap , shown in figure 1b , with an intensity 129 times the mean intensity ( @xmath7 jy-@xmath6s ) .
in addition , we also detected 5 marginal laps .
psrs b1957 + 20 and j0218 + 4232 have the fourth and sixth highest values of @xmath0 respectively of known radio pulsars .
hence , these new detections support a connection between the magnitude of @xmath0 and the existence of gps and laps .
the data for pulsars with @xmath0 marginally below @xmath8 g are being analyzed currently . , i. et al .
1996 , apj , 457 , 81 johnston , s. , & romani , r. w. 2003 , private communication lundgren , s. c. et al .
1995 , apj , 453 , 433 romani , r. w. , & johnston , s. 2001 , apj , 557 , l93 staelin , d. h. , & reifenstein , e. c. 1968 , science , 162 , 1481 , m. et al .
2001 , apj , 554 , 316 | giant pulses ( gps ) , occasional individual pulses with an intensity 100 times the average intensity , have been detected in four pulsars todate .
their origin is not well understood , but studies suggest a connection between the strength of magnetic field at the light cylinder @xmath0 and the existence of gps . here , we report on detection of significant large amplitude pulses ( laps ) in two more pulsars with high values of @xmath0 , psrs j0218 + 4232 and b1957 + 20 , observed using giant meterwave radio telescope ( gmrt ) .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
the specific curve pairs are the most popular subjects in curve and surface theory and involute - evolute pair is one of them .
we can see in most textbooks various applications not only in curve theory but also in surface theory and mechanic . in this study ,
the spherical indicatrices of involute of a space curve are given . in order to make a involute of a space curve and its evolute curve slant helix , the feature that spherical indicatrices curve s need to have
are examined .
let @xmath0 be a curve with @xmath1 , where @xmath2 @xmath3 .
the arc - lenght @xmath4 of a curve @xmath5 is determined such that @xmath6 let us denote @xmath7 and we call @xmath8 a tangent vector of @xmath9 at @xmath10 .
we define the curvature of @xmath11 by @xmath12 . if @xmath13 then the unit principal normal vector @xmath14 of the curve at @xmath10 is given by @xmath15 .
the unit vector @xmath16 is called the unit binormal vector of @xmath11 at @xmath17 .
then we have the frenet - serret formulae @xmath18where @xmath19 is the torsion of @xmath11 at @xmath10 @xcite . the curve @xmath11 is called evolute of @xmath20 if the tangent vectors are orthogonal at the corresponding points for each @xmath21 in this case , @xmath20 is called involute of the curve @xmath11 and there exists a relationship between the position vectors as@xmath22where @xmath23 is the distance between the curves @xmath11 and @xmath24 at the corresponding points for each @xmath25 the pair of ( @xmath24 , @xmath11 ) is called a involute - evolute pair .
@xmath26 is not a constant for involute - evolute pairs@xcite . on the other hand , izumiya and takeuchi
have introduced the concept of slant helix by saying that the normal lines make a constant angle with a fixed straight line .
they characterize a slant helix if and only if the geodesic curvature of the principal image of the principal normal indicatrix@xmath27is a constant function , where @xmath28@xcite . in this study , we denote @xmath29 , @xmath30 , @xmath31 @xmath32 , @xmath33 and @xmath34 , @xmath35 , @xmath36 @xmath37 , @xmath38 are the frenet equipments of @xmath11 and @xmath39 respectively .
tangent , principal normal and binormal vectors are described for the spherical curves which are called tangent , principal normal and binormal indicatrices both the curves @xmath11 and @xmath39 respectively . throughout this study ,
both involute and evolute curves are regular .
in this section , we introduced the spherical indicatrices of involute curve of a curve in euclidean 3-space and gave considerable results by using the properties of the curves , similar to the previous section .
let @xmath11 be a curve with its involute curve @xmath20 then @xmath40where @xmath41and @xmath42 is definitely positive .
let @xmath43 be the sign of @xmath42 such that if @xmath44 , @xmath45 and if @xmath46 , @xmath47 we differentiate the equation ( [ 2 ] ) with respect to @xmath4 , we get@xmath48since @xmath29 and @xmath49 are orthogonal , there is no any component of @xmath50 on @xmath29 .
thus @xmath43 has to be @xmath51 .
[ t1]let @xmath20 be involute of a space curve , then we have frenet formula:@xmath52where @xmath53with the parametrization @xmath54@xmath55and the curvature and torsion of @xmath56 are @xmath57the geodesic curvature of the the principal image of the principal normal indicatrix of involute curve is@xmath58 from ( [ 5 ] ) , it is obvious that involute of @xmath11 is a planar curve if and only if @xmath11 is a generalized helix . for further usage
we denote @xmath59 as @xmath60 . by using ( [ 1 ] ) and
( [ 5 ] ) we obtained the relation@xmath61and so we have @xmath62thus we have the following theorem .
[ t2]if the frenet frame of the tangent indicatrix @xmath68 of involute of @xmath10 is @xmath69 , we have frenet formula:@xmath70where@xmath71with the parametrization@xmath72and the curvature and torsion of @xmath73 are@xmath74the geodesic curvature of the principal image of the principal normal indicatrix of @xmath73 is@xmath75 let @xmath20 be involute of a space curve @xmath11 then spherical image of the tangent indicatrix of @xmath20 is a spherical helix if and only if involute of @xmath11 is a slant helix . in this case ,
spherical image of the tangent indicatrix of @xmath20 is a slant helix on unit sphere too . if the frenet frame of the principal normal indicatrix @xmath82 of involute of the curve @xmath10 is @xmath83 , we have frenet formula:@xmath84where@xmath85with the parametrization@xmath86and the curvature and torsion of @xmath87 are@xmath88 + \left [ \left ( \tfrac{-% \widetilde{f}^{^{\prime } } \left ( 1+\widetilde{f}^{2}\right ) ^{\frac{3}{2}}}{% \rho } \right ) \left ( \tfrac{\widetilde{\kappa } ^{2}\left ( 1+\widetilde{f}% ^{2}\right ) ^{\frac{5}{2}}}{\rho } \right ) ^{^{\prime } } \right ] + \left [ \left ( \tfrac{\widetilde{\kappa } \widetilde{f}^{^{\prime } } \left ( 1+% \widetilde{f}^{2}\right ) ^{\frac{3}{2}}}{\rho } \right ) ^{^{\prime } } \left ( \tfrac{\widetilde{\kappa } \left ( 1+\widetilde{f}^{2}\right ) ^{\frac{5}{2}}}{% \rho } \right ) \right ] \right\ } \notag\end{aligned}\ ] ] where @xmath89@xmath90the geodesic curvature of the principal image of the principal normal indicatrix of @xmath87 is@xmath91where if the frenet frame of the binormal indicatrix @xmath96 of involute of the curve @xmath10 is @xmath97 , we have frenet formula:@xmath98where @xmath99with the parametrization @xmath100and the curvature and torsion of @xmath101 are@xmath102the geodesic curvature of the principal image of the principal normal indicatrix of @xmath101 is@xmath103 let @xmath11 be a space curve and @xmath20 be its involute with nonzero torsion then spherical image of binormal indicatrix of @xmath24 is a circle on unit sphere if and only if @xmath104 is a generalized helix .
let @xmath112 and @xmath113be two regular curves in @xmath114then @xmath115 and @xmath116 are similar curves with variable transformation if and only if the principal normal vectors are the same for all curves @xmath117 under the particular variable transformation @xmath118@xmath119of the arc - lengths .
let @xmath120 and @xmath121be two regular curves in @xmath114then @xmath73 and @xmath122 are similar curves with variable transformation if and only if the principal normal vectors are the same for all curves @xmath123 under the particular variable transformation @xmath118@xmath124of the arc - lengths . in @xcite , the general equation of spherical helix family
is obtained by monterde which is , @xmath125where @xmath126 @xmath127 in 4b , kula et al .
obtained the general equation of a slant helix family similar to following@xmath128where @xmath129}{% 2w\left ( w+1\right ) } + \frac{\left ( w+1\right ) \sin [ \left ( w-1\right ) t]}{% 2w\left ( w-1\right ) } \\ \gamma _ { \mu } ^{2}(s ) & = & \frac{\left ( w+1\right ) \cos [ \left ( w-1\right ) t]}{% 2w\left ( w-1\right ) } + \frac{\left ( w-1\right ) \cos [ \left ( w+1\right ) t]}{% 2w\left ( w+1\right ) } \\ \gamma _ { \mu } ^{3}(s ) & = & -\frac{\cos \left ( s\right ) } { \mu w}.\end{aligned}\]]and @xmath130 @xmath131 by using the theorem [ c5 ] , we can obtained the general equation of general helix family in euclidean 3-space according to the non - zero constant @xmath132 as follows@xmath133where@xmath134+\left ( w-1\right ) \cos [ \left ( w+1\right ) t]\right\ } \\ & & + \frac{1}{2w\left ( w^{2}-1\right ) } \left\ { \left ( w+1\right ) ^{2}\sin [ \left ( w-1\right ) t]+\left ( w-1\right ) ^{2}\sin [ \left ( w+1\right ) t]\right\ } \\ \widetilde{\gamma } _ { \mu } ^{2}(s ) & = & \frac{-\left ( c - s\right ) } { 2w}\left\ { \left ( w+1\right ) \sin [ \left ( w-1\right ) t]+\left ( w-1\right ) \sin [ \left ( w+1\right ) t]\right\ } \\ & & + \frac{1}{2w\left ( w^{2}-1\right ) } \left\ { \left ( w+1\right ) ^{2}\cos [ \left ( w-1\right ) t]+\left ( w-1\right ) ^{2}\cos [ \left ( w+1\right ) t]\right\ } \\ \widetilde{\gamma } _ { \mu }
^{3}(s ) & = & \frac{\left ( c - s\right ) \sin \left ( s\right ) -\cos \left ( s\right ) } { \mu w}\end{aligned}\]]and @xmath130 @xmath135 with the parametrization@xmath136and the curvature and torsion of curve @xmath137 is @xmath138 | in this work , we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices , spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices . |
in paper i , by comparing the fbs ( markarian et al . 1989 ) and bqs ( green et al .
1986 ) surveys in their area in common , we derived a completeness of @xmath170% for the bqs .
a number of bright agns have since been discovered in the area which , together with our new spectroscopic observations , allowed us to refine our previous estimate of the bqs completeness .
we have obtained new spectra for 11 fbs objects .
the observations were carried out on november 25 , 1998 and january 1415 , 1999 at the byurakan astrophysical observatory ( bao ) and at the observatoire de haute - provence ( ohp ) , respectively .
the journal of observations is given in table 1 , together with relevant data .
+ .[spectra]new spectra .
1 gives the name , col .
2 the fbs number , col .
3 the original fbs classification , col .
4 the magnitude , cols . 5 and 6 the place and date of observation , col .
7 the galactic latitude , col .
8 the classification and col .
9 the redshift [ cols="<,>,<,<,<,<,>,<,<",options="header " , ] in the case of rxsj12110@xmath57005 for which the aps magnitude is not available , schwope et al . ( 2000 ) give @xmath0 17.0 , while the usno @xmath6 magnitude is 14.3 ; but this object has a moderate redshift ( @xmath7 0.127 ) ; moreover its apm @xmath6 magnitude ( irwin et al . 1994 ) is 17.66 ; we therefore adopted the schwope et al .
mag and excluded it from the complete " sample . the first bright quasar survey ( fbqs ) was built by matching the vla first survey with the cambridge automated plate measuring machine ( apm ) catalog of poss - i objects ( irwin et al .
1994 ) ; it covers an area of 2682 deg@xmath2 in the north galactic cap ; it contains 1238 objects brighter than 17.8 mag on the poss - i @xmath8 plates ( white et al .
about 1180 square degrees are within the fbs area ; they contain 38 first radio sources identified with an agn brighter than @xmath0 17.0 at @xmath9 30 ; nine are bright qsos ( @xmath10 16.0 ) , three ( cso 900 , firstj1306@xmath53915 and rxsj17102@xmath53344 ) being new .
although the numbers are small , this suggests that the complete " sample we built in paper i is only 67@xmath415% complete .
according to white et al .
( 2000 ) , qsos with radio emission above the first 1 mjy limit constitute about 25% of all qsos brighter than @xmath11 17.6 , but for qsos brighter than @xmath0 16.4 , the fbqs qso density is indistinguishable from the density of optically selected qsos .
nevertheless , of the 15 bright qsos known prior to the first survey in the area common to the first and fbs surveys , only six ( 40% ) have been detected as first radio sources ; therefore the complete identification of the first sources with bright starlike objects could not yield a complete survey of bright qsos .
+ a number of recent papers are devoted to the optical identification of rass sources ( beuermann et al .
1999 ; cao et al . 1999 ; grazian et al . 2000 ; schwope et al .
2000 ; wei et al . 1999 ; xu et al .
one of the new identifications is rxsj12043@xmath54330 , a qso at @xmath7 0.663 ( xu et al .
1999 ) ; it is also fbs1201@xmath5437 ( fbs#302 ) or pg1201@xmath5436 , which had been classified as a dc white dwarf by green et al .
its aps @xmath6 magnitude is 16.23 ; it is therefore not bright enough to be included in our complete " sample .
+ nineteen rass sources are now identified with a bright qso in the area discussed in this paper ( including the three new first qsos ) ; of the 17 fbs or bqs bright qsos in our sample ( table [ brightqso ] ) , 12 ( 70% ) are rosat all sky survey ( rass ) x - ray sources , suggesting that the total number of bright qsos is equal to 19/0.70 @xmath12 27 ( if all optically bright , x - ray sources have been discovered ) .
our complete " sample of bright qsos ( table [ brightqso ] ) contains 29 objects brighter than @xmath0 16.16 ( @xmath10 16.00 ) , three of them ( indicated by a
n " in the last column of table [ brightqso ] ) are not within the pg area .
the area common to the pg and fbs surveys at @xmath9 30 ( @xmath12250 deg@xmath2 ) contains 26 bright qsos ( 13 pg qsos and 13 others ) ( but there are 17 pg qsos with @xmath13 16.16 in the area ; this larger number is probably due to the eddington ( 1940 ) effect , the pg magnitudes being affected by relatively large errors , @xmath14 0.37 mag ) . from these data ,
we derive a surface density of 0.012 deg@xmath3 , which is to be compared with the original value of the pg survey : 0.0064 deg@xmath3 , implying a maximum completeness of 53@xmath410% for the pg survey . + grazian et al .
( 2000 ) have cross - correlated the rass with photometric databases in an 8164 deg@xmath2 area of the northern sky at @xmath15 30 , selecting all coincidences brighter than @xmath16 15.4 ; from this , they derive a surface density of bright ( @xmath17 15.5 ) qsos ( defined as agns with @xmath1823.0 ) of 10@xmath42 10@xmath19 deg@xmath3 and conclude that the true surface density of such objects is about three times larger than that derived from the pg survey .
however , they do not specify how the @xmath20 magnitude of their objects was derived .
their sample contains 46 qsos ; 15 of them have @xmath21 0.20 ; we have extracted from the aps catalogue the @xmath6 magnitudes for 12 of them ( for the three others , these magnitudes are unavailable ) ; it turns out that only one ( j172320.5@xmath5341756 ) has @xmath22 15.34 , corresponding to @xmath17 15.5 , suggesting that the @xmath6 magnitudes used by grazian et al . are underestimated and , consequently , the surface density overestimated . + lamontagne et al .
( 2000 ) claim that they found a surface density of bright qsos three times larger than the pg value .
they have searched for uv - excess stellar - like objects with @xmath17 16.5 and @xmath23 @xmath240.6 in a 840 deg@xmath2 area covering the south galactic cap ; the errors in the @xmath20 magnitudes are estimated to be 0.30 mag _ rms_.
they have found 228 such objects which have all been spectroscopically identified ; 32 are agns , out of which only eleven are brighter than @xmath0 16.16 and @xmath2524.0 ( including 0117@xmath262837 which , according to grupe et al .
( 1999 ) , has a redshift of 0.349 rather than 0.055 ) .
we derive a surface density or 0.013 deg@xmath3 , in agreement with our value and only twice the pg value .
in paper i , we compared the surface density of qsos in the bright quasar survey and in the first byurakan survey and concluded that the completeness of the bqs is of the order of 70% ; wisotzki et al .
( 2000 ) have found that the bqs is 68% complete from a comparison with the hamburg / eso survey , in agreement with our previoys estimate .
based on a number of recently published data , as well as on our own new observations , we redetermined the surface density of qsos brighter than @xmath0 16.16 in the bqs area to be @xmath10.012 deg@xmath3 , implying that the completeness of the bqs is 53@xmath410% .
it should be stressed however that the numbers involved are quite small , and that larger areas should be investigated before a definitive value of the surface density of bright qsos could be determined .
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1999 , a&as 134 , 365 | in paper i ( mickaelian et al .
1999 ) , we compared the surface density of qsos in the bright quasar survey ( bqs ) and in the first byurakan survey ( fbs ) and concluded that the completeness of the bqs is of the order of 70% rather than 3050% as suggested by several authors .
a number of new observations recently became available , allowing a re - evaluation of this completeness .
we now obtain a surface density of qsos brighter than @xmath0 16.16 in a subarea of the fbs covering @xmath12250 deg@xmath2 , equal to 0.012 deg@xmath3 ( 26 qsos ) , implying a completeness of 53@xmath410% . |
we thank richard friend , ayelet vilan and dassia egorova , as well as the reviewers , for useful discussions , and johannes zimmermann and tobias glaser for the angle - dependent ir spectra .
this work was supported by the netherlands organization for scientific research onderzoek ( nwo ) through the `` stichting voor fundamenteel onderzoek der materie '' ( fom ) research program .
also acknowledges a veni grant from the nwo .
is currently a royal society university research fellow .
r.l . acknowledges a marie curie ie fellowship from the eu , held at the weizmann institute .
thanks the council for higher education ( israel ) for a pbc program postdoctoral research fellowship . v.c . and j.l.b .
thank support from the office of naval research and muri center on advanced molecular photovoltaics , award no .
n00014 - 14 - 1 - 0580 .
thanks the israel science foundation centre of excellence program , the grand centre for sensors and security and the schmidt minerva centre for supramolecular architecture for partial support .
d.c . holds the sylvia and rowland schaefer chair in energy research .
50ifxundefined [ 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 10.1021/ar00118a005 [ * * , ( ) ] link:\doibase 10.1126/science.1146556 [ * * , ( ) ] link:\doibase 10.1038/nature09346 [ * * , ( ) ] link:\doibase 10.1371/journal.pone.0055780 [ * * , ( ) ] link:\doibase 10.1126/science.1249771 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.109.056801 [ * * , ( ) ] link:\doibase 10.1038/nphys2515 [ * * , ( ) ] link:\doibase 10.1038/nature01649 [ * * , ( ) ] link:\doibase 10.1038/ncomms2708 [ * * , ( ) ] link:\doibase 10.1038/nmat3710 [ * * , ( ) ] link:\doibase 10.1038/nnano.2010.240 [ * * , ( ) ] link:\doibase 10.1038/nnano.2012.37 [ * * , ( ) ] link:\doibase 10.1021/jp403005q [ * * , ( ) ] link:\doibase 10.1021/ja1040732 [ * * , ( ) ] link:\doibase 10.1038/ncomms1164 [ * * , ( ) ] link:\doibase 10.1016/j.chemphys.2010.05.021 [ , * * , ( ) ] link:\doibase 10.1038/nature06262 [ * * , ( ) ] link:\doibase 10.1146/annurev.physchem.58.032806.104456 [ * * , ( ) ] link:\doibase 10.1039/c3cp50871d [ * * , ( ) ] link:\doibase 10.1021/ja074657x [ * * , ( ) ] link:\doibase 10.1038/nature06119 [ * * , ( ) ] link:\doibase 10.1038/srep03823 [ * * ( ) , 10.1038/srep03823 ] link:\doibase 10.1038/nature03429 [ * * , ( ) ] link:\doibase 10.1038/nchem.1881 [ * * , ( ) ] link:\doibase 10.1038/nature08811 [ * * , ( ) ] link:\doibase 10.1364/josab.28.000171 [ * * , ( ) ] link:\doibase 10.1126/science.1217745 [ * * , ( ) ] link:\doibase 10.1016/0009 - 2614(81)80471-x [ * * , ( ) ] link:\doibase 10.1103/physrevb.62.2505 [ * * , ( ) ] link:\doibase 10.1103/physrevb.72.195208 [ * * , ( ) ] link:\doibase 10.1364/oe.21.028617 [ * * , ( ) ] link:\doibase 10.1038/nphoton.2013.151 [ * * , ( ) ] link:\doibase 10.1016/j.chemphys.2012.08.019 [ , * * , ( ) ] link:\doibase 10.1021/ar300345h [ * * , ( ) ] link:\doibase 10.1002/adma.201000376 [ * * , ( ) ] link:\doibase 10.1063/1.2403241 [ * * , ( ) ] link:\doibase 10.1002/adma.201403556 [ * * , ( ) ] link:\doibase 10.1126/science.287.5454.839 [ * * , ( ) ] link:\doibase 10.1016/0301 - 0104(95)00290 - 1 [ * * , ( ) ] link:\doibase 10.1021/jp048343x [ * * , ( ) ] link:\doibase 10.1103/physrevb.70.081309 [ * * , ( ) ] link:\doibase 10.1038/990058 [ * * , ( ) ] link:\doibase 10.1103/physrev.120.745 [ * * , ( ) ] link:\doibase 10.1073/pnas.092143399 [ * * , ( ) ] link:\doibase 10.1016/s0379 - 6779(99)00050 - 8 [ * * , ( ) ] link:\doibase 10.1107/s0365110x62000699 [ * * , ( ) ] link:\doibase 10.1016/j.apsusc.2004.10.131 [ , * * , ( ) ] link:\doibase 10.1103/physrevb.75.174108 [ * * , ( ) ] link:\doibase 10.1021/jp900157p [ * * , ( ) ] `` , '' in link:\doibase 10.1002/9781119953678.rad046 [ _ _ ] ( , ) | * a.a.b . , r.l . , and y.x . contributed equally .
+ + the soft character of organic materials leads to strong coupling between molecular nuclear and electronic dynamics .
this coupling opens the way to control charge transport in organic electronic devices by exciting molecular vibrational motions . however , despite encouraging theoretical predictions , experimental realization of such control has remained elusive .
here we demonstrate experimentally that photoconductivity in a model organic optoelectronic device can be controlled by the selective excitation of molecular vibrations . using an ultrafast infrared laser source to create a coherent superposition of vibrational motions in a pentacene / c60 photoresistor
, we observe that excitation of certain modes in the @xmath0{cm^{-1}}$ ] region leads to photocurrent enhancement .
excited vibrations affect predominantly trapped carriers .
the effect depends on the nature of the vibration and its mode - specific character can be well described by the vibrational modulation of intermolecular electronic couplings .
vibrational control thus presents a new tool for studying electron - phonon coupling and charge dynamics in ( bio)molecular materials .
+ * submitted * : nov .
11 , 2014 + * revised * : feb . 3 , 2015 the soft character of organic materials strongly influences their electronic functionality .
@xcite in these systems charge hopping and electronic delocalization are determined by the overlap of the molecular orbitals and , therefore , is highly sensitive to minor changes in molecular geometry .
hence , the electronic properties of organic materials are largely determined by the interplay between the electronic and nuclear dynamics of the molecules , referred to as vibronic coupling phenomena .
a growing number of interdisciplinary studies show that vibronic effects lie at the heart of a diverse class of effects in physics , chemistry and biology - from non - linear behavior of molecular junctions @xcite to photophysics of vision @xcite and even olfactory reception .
@xcite vibrational motions have been postulated to regulate the interaction between different molecular electronic states by modulating inter- and intra - molecular couplings , by donating or accepting extra energy quanta @xcite , and by suppressing @xcite or promoting @xcite quantum interference phenomena .
vibronic effects were also shown to be fundamentally important for the conductivity of organic materials .
vibrational motions influence intermolecular electron tunneling probabilities @xcite and govern a variety of non - equilibrium phenomena such as local heating @xcite , switching @xcite , hysteresis , and electronic decoherence @xcite .
this makes vibrational excitation a promising tool for spectroscopy of molecular junctions @xcite , tracking charge transfer processes in organic- and bio - electronic systems , and , more generally , for the development of electronic devices . for example , remarkable opportunities for organic electronics would arise from the possibility to control charge transport , and , thus , affect device performance by coherently driving nuclear motions along a pre - selected reaction coordinate trajectory .
however , despite many encouraging theoretical predictions @xcite the experimental realization of vibrationally controlled electronics is still elusive due to the complexity of selective control of nuclear motions in an actual electronic junction . until now
, vibration - associated charge dynamics in organic electronic devices have been only controlled with approaches that do not include mode selectivity .
for example , the density and the equilibrium population of vibrational states have been varied via chemical synthesis of molecules with different bond structures @xcite and via thermal population of low - frequency vibrations .
@xcite however , in principle , it should be possible to access particular non - equilibrium nuclear or vibronic states by using instrumentation of optical time - resolved techniques , like visible pump - probe @xcite , time - resolved stimulated / impulsive raman @xcite , or transient ir absorption @xcite .
for example , for inorganic perovskite materials @xcite and molecular mott insulators @xcite it has been reported that selective ir excitation can lead to strong modulation of the electronic properties by inducing a lattice phase transition .
sophisticated all - optical two - dimensional ( 2d ) photon echo techniques are even capable of guiding a molecular system through a desired quantum superposition of vibronic / vibrational states @xcite .
although such spectroscopic methods provide a comprehensive approach for probing and controlling molecular motions and have been applied to model systems such as molecular thin films or solutions , they have not yet been employed to control functional electronic ( nano)devices . in this work ,
we combine device characterization and ultrafast - spectroscopy methods to experimentally demonstrate that the performance of an organic optoelectronic system can be controlled by selectively exciting vibrational modes of the molecules involved in charge transport . as model system we use pentacene / c60 bi - layer photoresistors .
our experimental approach is based on the interferometric extension of the pump - push photocurrent ( ppp ) technique .
@xcite in a ppp experiment , an optoelectronic device is illuminated by a sequence of laser pulses interacting with the active material in the device .
the result of these interactions is detected by observing the variations in the current flow through the device as a function of time delay @xmath1 between the pump and push pulses and their spectra .
thus , ppp combines the sensitivity and device relevance of electronic methods with the excitation selectivity and ultrafast time resolution of optical methods . since its introduction @xcite ,
ppp has been applied and discussed in the context of photovoltaics @xcite , nanoelectronics , spectroscopy @xcite , microscopy @xcite , and molecular junction research @xcite . in this work ,
we extend the ppp method , using the recent progress in ultrafast interferometry @xcite that allows for a precise control over the time / frequency - domain structure of the ir optical pulses .
we apply a sequence of ultrafast mid - ir laser pulses to create a coherent superposition of molecular vibrational motions inside the active layer of a device and correlate this excitation with the device performance .
the molecular electronic device characterisation : ( a ) molecular arrangement of molecules in the pentacene crystal and c60 fullerene structure .
( b - c ) layout and microscope image of the device .
( d ) ir absorption in the vibrational fingerprint region and optical absorption spectra of pentacene and c60 .
the yellow shaded contour shows a typical laser spectrum used for ir push .
( e ) photocurrent from the device as a function of visible light modulation frequency ; the line is a cole - cole fit with a @xmath2{ms}$ ] lifetime constant and @xmath3 dispersion parameter . ]
figure [ fig1 ] a)-c ) describes the organic bilayer photoresistor model system .
the active layer of the device consists of polycrystalline pentacene ( @xmath4{nm}$ ] ) and fullerene c60 ( @xmath5{nm}$ ] ) films ( fig .
[ fig1 ] a ) ) , thermally evaporated on top of 3- , 5- or @xmath6{\upmu m}$ ] spaced electrodes arranged in a comb - like geometry on a sio@xmath7 substrate ( fig .
[ fig1 ] b ) ) .
we chose this geometry rather than a sandwich - like structure , typical for photodiodes or solar cells , to improve the access of mid - ir pump - pulses to the active layer . adding the c60 layer was critical to enhance the photocarrier generation in the film .
@xcite figure [ fig1 ] d ) compares the absorption spectra of pentacene and c60 in the ir vibrational fingerprint region and in the region of the optical electronic transitions .
c60 shows several distinct vibrational modes at @xmath8{cm^{-1}}$ ] , @xmath9{cm^{-1}}$ ] , and @xmath10{cm^{-1}}$ ] and has a comparably low optical density in the visible .
pentacene has a rich spectrum of vibrational lines in the ir and also shows strong excitonic absorption features at frequencies above @xmath11{cm^{-1}}$ ] ( @xmath12{nm}$ ] ) .
according to density functional theory calculations , the strong ir peaks at 1300 and @xmath13{cm^{-1}}$ ] are mostly associated with @xmath14 stretching vibrations along the short axis of pentacene , while the weaker high - frequency vibrations correspond to atomic motions mostly aligned with the long axis of the molecule ( see si ) .
the dark i - v curves of the devices are symmetric and roughly linear , indicating good hole injection from the gold electrodes to the pentacene layer ( see si ) .
upon exposure to visible light , the current flow through the devices strongly increases ( @xmath15 times under @xmath6{mw / cm^2}$ ] illumination ) .
devices without a c60 layer demonstrated only negligible photoconductivity , which indicates that singlet ( and triplet ) @xcite excitons generated after pentacene excitation are dissociating at the pentacene / c60 interface and that the charge generation proceeds through the interfacial charge transfer states @xcite .
due to the large electron injection barrier at the pentacene / au interface , the dark current is mostly provided by holes , while under illumination both holes and electrons contribute to the photocurrent . unlike in a typical solar cell , both electrodes are placed below the pentacene films .
therefore , electrons and holes have to pass through the pentacene , which is known to lead to extremely long ( up to seconds ) extraction times of electrons residing in low - lying trap states in pentacene .
@xcite this notion is confirmed by the dependence of the photocurrent on the light - modulation frequency ( fig .
[ fig1 ] e ) ) .
cole - cole analysis of this dependence shows a typical time constant @xmath16{ms}$ ] , which we interpret as the lifetime of long - lived electronic charge carriers .
figure [ fig2 ] a ) shows the layout of the experiment , designed to observe the effect of molecular vibrations on the charge transport through the device .
the setup combines a @xmath17{khz}$ ] visible - infrared ultrafast spectrometer and a lock - in current probe station wired to the device under @xmath18{v}$ ] external bias .
first , a visible ( @xmath19{cm^{-1}}$ ] ; @xmath20{nm}$ ] ; @xmath21{ev}$ ] ) pump pulse illuminates the device .
the absorption of the pump light in pentacene leads to the build - up of excitons and charge carriers in the active layer .
the generated carriers produce a sequence of @xmath17{ms}$]-spaced current pulses in the measurement circuit with an average photocurrent @xmath22{na}$ ] , detected by the lock - in amplifier at @xmath17{khz}$ ] .
we note that at such low current densities a charge - induced phase transition @xcite can be excluded .
the device is irradiated with a push pulse at certain delay times @xmath1 before or after the pump pulse .
the push pulse can promote @xmath23 of the molecules to the excited vibrational state and can also excite low - frequency charge - associated ir electronic transitions .
@xcite the effect of ir light on the charge separation and transport was detected via the variation of device photocurrent @xmath24 .
figure [ fig2 ] c ) presents a typical ppp transient , measured with a single - pulse push ( one interferometer arm blocked ) at @xmath25{cm^{-1}}$ ] .
when the pump was blocked we observed no signal due to the push only . at negative delay time @xmath1 ,
when the push pulse arrives before the pump , we already observe a substantial increase of the current due to ir excitation ( i.e. , @xmath26 ) .
we associate this response with the excitation of long - lived photocarriers that were generated by the preceding pump pulse that arrives @xmath27{ms}$ ] earlier .
this observation is in line with the long collection times of trapped carriers observed for electrons in pentacene .
@xcite at delay time @xmath28 , the ppp response promptly increases as the concentration of charges in the cell rises due to the arrival of the new pump pulse and the ir push influences their dynamics .
the rapid rise is followed by a @xmath29{ps}$ ] decay component that we assign to the geminate recombination of newly generated charge pairs , which are likely to form electrostatically bound charge - transfer excitons .
@xcite in a broadband experiment using a single - pulse push , it is not possible to distinguish the effects of low - frequency electronic excitations from the vibronic phenomena associated with the interference between the molecular vibrational motions and charge dynamics . to separate and address these phenomena individually ,
we performed push - frequency resolved measurements by exploiting the ultrafast interferometry approach .
@xcite using a mach - zehnder scheme ( fig .
[ fig2 ] a ) ) , the push beam is split into two pulses displaced in time by an interferometric delay @xmath30 .
this leads to the formation of a 1/@xmath30 periodic modulation in the total push spectrum ( fig .
2b ) which allows for selective excitation of different coherent superpositions of modes within the bandwidth of the ir light . in a typical experiment , for a certain pump - push delay
@xmath1 , the signal @xmath31 is detected as a function of interferometric delay @xmath30 ( fig .
[ fig2 ] d ) ) .
the obtained interferogram is fourier - transformed along the @xmath30 axis to yield the action spectrum of the push effect .
figure [ fig2 ] e ) shows a typical frequency - resolved ppp response of a pentacene / c60 device at negative and positive pump - push delay times @xmath1 , and with no pump ( dark ) . at both delays the response consists of a number of narrow peaks on top of a broad featureless response , roughly following the ir source spectrum .
we associate the broad feature with intraband electronic and polaronic absorption , which typically spreads between 1000 and @xmath32{cm^{-1}}$ ] .
@xcite the intraband excitation brings the associated charge carriers to a higher - lying delocalized state , thereby enhancing their mobility , decreasing their recombination , and thus increasing the current output .
@xcite the narrow features in the ppp signal match well with the absorption peaks of the vibrational modes of pentacene and c60 .
therefore these features in the frequency - resolved ppp response are assigned to the excitation of molecular vibrations that modulate the electronic dynamics .
interestingly , the broad electronic response dominates the ppp signal when the push arrives after the pump , while the vibrational features have similar amplitudes ( within the experimental accuracy ) at positive and negative @xmath1 delays .
this observation indicates that the ir electronic excitation substantially promotes charge separation at the pentacene / c60 interface , soon after exciton generation . at the same time , the effect of vibrational excitation is present for long - lived trapped charge carriers and , therefore , does not influence charge separation , but only carrier de - trapping dynamics .
@xcite
we now focus on the analysis of the vibrational features only .
the effect of broadband electronic ir excitation on charge dynamics in organic semiconductors has been investigated previously @xcite , and is outside the scope of this paper . to study the effect of vibrational excitation for a broader set of vibrational modes , we use a wide push spectral window of @xmath33{cm^{-1}}$ ] and long @xmath30-scanning to obtain high frequency resolution .
we also applied time - domain filtering ( see si ) to suppress broad features due to electronic excitation and non - linear field - induced tunneling currents .
experimental evaluation of vibrational control effect : ( a ) the vibrational part of the ppp response , measured at negative delay time ( @xmath34{ps}$ ] ) .
the signal amplitude is normalized to the spectral density of the ir push source .
the spectrum is obtained using two ppp spectra , each covering a different but overlapping wavenumber range ; these are scaled to match the amplitude of the @xmath9{cm^{-1}}$ ] mode that is present in both spectra . for comparison ,
the absorption spectrum of the pentacene / c60 layer is presented in red .
( b ) the influence of different vibrations on device photocurrent , estimated by normalizing the amplitude of the ppp signal to the absorbed ir intensity .
the change of photocurrent absolute value corresponds to a flat @xmath35{j / cm^2}$ ] per @xmath36 spectral density of exciting ir light , fully absorbed by the vibrations .
the error bars are calculated from standard deviations for measurements on different devices ; the number of measurements was 10 for @xmath37{cm^{-1}}$ ] modes and 4 for all other modes . ]
figure [ fig3 ] a ) presents the vibration - associated ppp spectrum covering most of the ir fingerprint frequency range .
the amplitude of the ppp response was normalized to the spectral density of the push pulse to allow for a direct comparison of the different vibrational lines .
the spectrum is the result of several measurements with different push frequencies spliced together to match the amplitude of the effect for the @xmath9{cm^{-1}}$ ] feature , which was present in all measurements . in the @xmath33{cm^{-1}}$ ] region , we observe twelve ppp peaks at frequencies that match well the ir - active vibrational modes of pentacene and c60 .
we note that , while the vibrations of charged pentacene may differ from those of the neutral molecules @xcite , these differences should not be observed in the ppp data .
firstly , the shift in frequency for most individual modes is small @xcite and , for most modes , below our frequency resolution ( @xmath38{cm^{-1}}$ ] ) .
this conclusion is also supported by dft calculations , see suppl .
information , tables s1 and s2 . secondly , the minor shifts of the vibrational levels lead to a highly efficient vibrational energy transfer @xcite between neutral and charged molecules , which allows the vibrational excitation of neutral pentacene to be delivered to the charge trapping sites .
thirdly , according to miller - abrahams formalism , when a carrier hops from a radical to a neutral state all vibrational modes coupled to these electronic states contribute to the transfer rate .
@xcite therefore , it is not surprising that the lattice vibrations , i.e. those of the neutral pentacene , are observed in the detrapping dynamics .
we observe that the amplitude of the ppp response does not follow the intensity of the ir absorption .
for example , the band at @xmath13{cm^{-1}}$ ] possesses a much stronger ir absorption than the @xmath39{cm^{-1}}$ ] vibration , but shows a weaker ppp response .
this result shows that the observed ppp response can not be explained by the equilibration of vibrational energy between modes and average heating of the device active layer , thus illustrating the mode - selective character of the ppp response .
this example illustrates that different atomic motions couple differently to the charge dynamics of the system . to exclude that the non - scaling of the ppp response with ir absorption is merely an effect of a different orientation of the vibration dipoles with respect to the exciting ir light
, we also performed angle - dependent ir absorption measurements .
these measurements showed that the modes exhibiting very different ppp effect , e.g. at @xmath13{cm^{-1}}$ ] and @xmath39{cm^{-1}}$ ] , have similar dipole orientations ( see si ) , which rules out orientation effects .
figure [ fig3 ] b ) compares the effect of vibrational excitation on the device photoconductivity for different vibrational modes , obtained by normalizing the ppp response to the number of photons absorbed by the vibrational mode . in accordance with figure 3a ,
the 1300 and @xmath13{cm^{-1}}$ ] modes show the weakest coupling .
the higher - frequency vibrations of pentacene show a 5 - 8 times higher effect on the photoconductivity . for two of the fullerene vibrations
the effect is similar to that of the high - frequency vibrational modes of pentacene .
these results can be rationalized in the framework of the phonon - assisted miller - abrahams ( ma ) theory .
@xcite according to this model , carrier hopping from a trapping state to higher - energy ( more conducting ) states takes place via absorption of a phonon with energy @xmath40 to compensate for the energy difference between initial and final electronic states ; the hopping rate @xmath41 is defined by the electron - vibrational coupling constant ( @xmath42 ) and the occupation number ( @xmath43 ) of the absorbed phonon , i.e. @xmath44 in thermal equilibrium , the occupation number of a high - energy molecular vibration is very small : @xmath45 for a comprehensive description of the ppp response the interaction with the ir photons should be included into the ma model .
however , at the conceptual level the effect can be understood by assuming that an ir excitation creates a non - equilibrium population of the molecular vibrational manifold ; therefore , an increase in the hopping probability is expected .
the mode - selective character of the ppp response is therefore defined by the electron - vibration coupling constants . to achieve mechanistic insight into the observed phenomena we performed a theoretical analysis of the coupling between the different molecular vibrations and the charge carriers ( holes ) in pentacene . in molecular systems
these couplings can be divided into two types , i.e. local ( holstein - type ) and non - local ( peierls - type ) .
@xcite the holstein electron - phonon interaction originates from the modulation of the site energies by the vibrations .
only totally symmetric molecular vibration modes can contribute to this interaction .
for centrosymmetric molecules like pentacene , the symmetric modes are not ir - active and will not absorb ir photons , so that we can rule out holstein electron - phonon coupling effects in the ppp response .
the peierls - type electron - phonon couplings are associated with the dependence of the transfer integrals on the distances between adjacent molecules and their relative orientations .
@xcite for this type of coupling , there are no symmetry restrictions .
based on previous studies @xcite , we used a triclinic polymorph @xcite to represent the pentacene layer structure in the calculations .
figure [ fig4 ] a ) shows the simulated ir spectra for a single pentacene molecule and for the crystal in comparison to the experimental ir absorption .
the agreement between the experimental and calculated vibrational frequencies ( with typical discrepancies @xmath46{cm^{-1}}$ ] ) allows the assignment of the vibrational modes observed in the frequency - resolved ppp experiment .
the 1300 and @xmath13{cm^{-1}}$ ] features in the experimental spectrum are associated ( fig .
[ fig4 ] c ) and si ) with in - plane ring stretching modes along the short axis of pentacene @xcite , while the ir peaks at @xmath10{cm^{-1}}$ ] and @xmath39{cm^{-1}}$ ] are associated with molecular deformations along the long axis of pentacene ( fig .
[ fig4 ] d ) and si ) .
the non - local hole - vibration couplings are defined as the derivatives of the charge transfer integrals with respect to the vibrational coordinates , @xmath47 , and can be computed numerically . @xcite
both the transfer integrals and electron - vibration couplings have been derived in a one - electron approximation ( see si for details ) .
our results indicate that there are two main transfer integrals contributing to charge transfer in the pentacene crystal : @xmath48{mev}$ ] and @xmath49{mev}$ ] ; both are associated with intermolecular interactions along the herringbone directions ( see the red and blue arrows in fig .
[ fig4 ] b ) .
the other two transfer integrals oriented along the a - axis are substantially smaller and do not demonstrate substantial modulation by ir - active modes .
( see si ) the derived coupling constants of the ir - active modes are shown in figure 4e .
the couplings in the @xmath50{cm^{-1}}$ ] range are about 2 to 5 times larger than in the @xmath51{cm^{-1}}$ ] range . to link the variations in coupling and the probability to de - trap a charge with a vibrational excitation , we estimated the rates of vibration - induced charge hopping . in the case of two pathways ,
the rate is defined within perturbation theory as : @xmath52 where @xmath53 and @xmath54 correspond to quasi - degenerate molecular vibrations of similar frequencies .
figure [ fig4 ] f ) presents these hopping rates together with the experimental observations from figure [ fig3 ] b ) .
the theoretical results are fully consistent with the experimental data . in particular , they capture well the mode - selective character of the phenomena , with the modes below @xmath9{cm^{-1}}$ ] calculated to have a much smaller impact on charge hopping than the higher - frequency ones . based on the calculations ,
the intermolecular electronic couplings and charge transport in pentacene crystals are seen to be most sensitive to stretching deformations along the long molecular axis , while the stretching deformations along the short molecular axis are less important . in conclusion
, we demonstrated that the vibrational coupling phenomena , which play an essential role in molecular - scale charge transport , can be explored and put to action by combining optical and electronic techniques .
both the experiment and theoretical calculations demonstrate that different non - equilibrium geometries and atomic motions have different effects on the charge dynamics .
specifically , our results show that vibrations along the long axis of pentacene molecules lead to a stronger increase of hopping transport via charge de - trapping than vibrations along the short axis .
the mode - selective vibrational control of charge dynamics introduced here opens up a plethora of opportunities for basic research , including the development of high - mobility organic semiconductors , and the utilization of vibronic phenomena for ultrafast switching of organic devices .
in addition , the mode - selective and local nature of our method might be particularly useful for the identification of charge transport mechanisms and pathways in ( bio)molecular junctions . |
the qcd - inspired light - front constituent quark model @xcite , with two components in the interaction , a contact term and a coulomb - like potential , was used previously to investigate the properties of mesons @xcite with reasonable success .
it was also applied to investigate the binding energy of the ground state of spin 1/2 @xmath0 baryons @xcite , where the coulomb - like interaction was left out . in that work
, a special regularization scheme was used in which the masses of the virtual two - body subsystems were constrained to be real , as a result the quark binding in the spin 1/2 low - lying states of the @xmath1 , @xmath4 and @xmath3 was qualitatively reproduced .
recently , the integral equation for a three - boson system interacting with pairwise contact interaction in the light - front @xcite was regularized with a sharp cut - off @xcite and applied in the study of the nucleon . in the infinite cut - off limit
it was previously shown that the three - boson system is stable for values of the two - boson bound state mass above a critical value @xcite .
this motivate us to study the effect of different cut - offs in the @xmath0 ground state masses , obtained by solving the light - front integral equations with a contact interaction .
our aim here is to check to which extend the qualitative properties of the quark binding is regularization independent .
we use only the flavor independent contact interaction between the constituent quarks , which brings the physical scale of the ground state of the nucleon and includes the minimal number of physical scales to describe @xmath0 systems . the spin is averaged out .
the model has as inputs the constituent quark masses and the nucleon mass is used to fix the interaction strength . in our previous work @xcite , where the masses of the virtual two - quark subsystems were constrained to be real with the nucleon mass fixed at the experimental value , there was no freedom left in the @xmath0 calculation
. here , even with the nucleon mass kept fixed still the cut - off has some freedom , which will be varied in our calculations . to obtain the @xmath0 masses ,
the mass of one of the constituent quark @xmath5 is varied while the strength of the effective contact interaction is supposed flavor independent .
this work is organized as follows . in sec.2
, we briefly discuss the coupled integral equations for the @xmath0 bound - state in the light - front and the regularization schemes . in sec . 3 , we present the numerical results for the binding energies of the @xmath6 , @xmath4 and @xmath7 and give a summary of the work with our conclusion .
with the assumption that the spin is averaged out , the @xmath0 system interacting through a contact pairwise force is represented by two spectator functions or faddeev components of the vertex , which satisfies the coupled bethe - salpeter type equations , derived elsewhere @xcite , and shown diagrammatically in fig . 1 . system . ,
title="fig:",width=264 ] system .
, title="fig:",width=340 ] the coupled integral equations for the fadeev components of the vertex function of the @xmath0 system , represented in fig . 1 , are given by @xcite : @xmath8 @xmath9 , \label{e26}\end{aligned}\ ] ] where @xmath10 and @xmath11 are the @xmath0 mass and four - momentum , respectively .
the masses of the virtual two - quark subsystems are @xmath12 and @xmath13 , and in the baryon rest frame are given by : @xmath14 with ( @xmath15,@xmath16)=@xmath17 or @xmath18 . in our previous work @xcite , we constrained the virtual two - body subsystem masses to real values and using eq .
( [ mass3a ] ) with @xmath19 and @xmath20 substituted by @xmath21 and @xmath22 , respectively , giving the lower bounds for the integration in @xmath22 and the maximum value for the transverse momentum , @xmath23 , for each vertex depending on @xmath22 , as well . in that case
, the theta functions bring to eqs .
( [ mass3 ] ) and ( [ e26 ] ) the discussed constraint .
the two - quark scattering amplitudes , @xmath24 , are the solutions of the bethe - salpeter equations in the ladder approximation for a contact interaction between the quarks . as a function of the baryon mass @xmath10 . attributed experimental binding energies for the spin 1/2 low - lying states of the nucleon , @xmath1 , @xmath2 and @xmath3 from @xcite ( full squares ) .
model results from ref .
@xcite ( solid curve ) .
present calculations with transverse momentum cut - off with the values of @xmath25 ( dashed curve ) , @xmath26 ( dotted curve ) and @xmath27 ( dot - dashed curve).,width=321 ] here , we use a different regularization scheme of eqs .
( [ mass3 ] ) and ( [ e26 ] ) , where @xmath28 and the theta functions in @xmath22 are dropped . the nucleon mass is fixed to its experimental value , therefore we have to adjust the renormalized coupling constant for each value of the transverse momentum cut - off @xmath29^{-1}\ , \label{tau}\end{aligned}\ ] ] where @xmath30 is the bare interaction strength . as its stands , eq .
( [ tau ] ) is ill - defined .
the renormalization condition is chosen at an arbitrary subtraction mass point @xmath31 where the value of @xmath32 is known and given by @xmath33 , the renormalized interaction strength , which is enough to remove the logarithmic divergence in eq .
( [ tau ] ) .
therefore , the bare strength is given as : @xmath34 which is supposed to be flavor independent . the strength of the effective interaction is determined by fitting the nucleon mass .
the physical inputs of the model defined by eqs .
( [ mass3 ] ) and ( [ e26 ] ) , are the renormalized interaction strength @xmath35 , the constituent quark masses @xmath36 gev and @xmath37 ( @xmath38 ) which were found in @xcite , where as well , it was attributed a binding energy to the spin 1/2 baryons ( nucleon , @xmath1 , @xmath4 and @xmath39 defined as @xmath40 . considering that the flavor - off - diagonal vector mesons are weakly bound systems of constituent quarks in the qcd - inspired model of ref .
@xcite , we obtained values of the constituent quark masses .
the attributed values to the binding energies were found @xcite using constituent quark masses and the experimental baryon masses from @xcite .
the attributed values for the constituent quark binding energies in the spin 1/2 low - lying states of the nucleon , @xmath41 , @xmath4 and @xmath3 are shown in fig . 2 by the full squares , from the left to the right , respectively .
in fig . 2 , we show results for the calculation of the binding energy of the baryon for different renormalization schemes and values of the transverse momentum cut - off compared to the attributed baryon binding energies . for the values of the cut - off , @xmath25 , @xmath26 and @xmath27
, we fit the renormalized strength of the interaction to reproduce the nucleon mass . by changing the mass of the heavy quark ,
while the strength of the interaction was kept unchanged , the coupled integral equations were solved to obtain the mass and binding energy of the baryons .
again , as observed in the work @xcite for the baryon mass above @xmath42 gev , the bound @xmath0 system goes to the diquark threshold .
our results show that the general behavior of the experimental data of masses and binding energies of the spin 1/2 low - lying states of @xmath43 , @xmath4 and @xmath3 are reproduced with different momentum cut - off s constrained by the value of the nucleon mass . in summary , in the present contribution
we have studied how different regularization schemes in the relativistic coupled @xmath0 homogeneous integral equation affects the qualitative properties of the quark binding in @xmath0 baryons .
our calculations indicate that the general features of the low - lying spin 1/2 baryon binding energy as a function of its mass , is model independent to a large extent ( small cut - off sensitivity ) as long as the relativistic @xmath0 model has a flavor independent effective short - range interaction . therefore , the conclusions drawn in our previous work @xcite does not qualitatively depend on the regularization scheme .
we would like to thank the brazilian funding agencies fapesp ( fundao de amparo a pesquisa do estado de so paulo ) and cnpq ( conselho nacional de desenvolvimento cientfico e tecnolgico ) .
efs thanks the organizing committee of the conference for the kindly invitation to present this work .
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* d66 * ( 2002 ) 010001 . | we study the mass of the ground state of @xmath0 systems using different regularization schemes of the relativistic integral equation obtained with a flavor independent contact interaction in a qcd - inspired light - front model .
we calculate the masses of the spin 1/2 low - lying states of the @xmath1 , @xmath2 and @xmath3 for different values of the regularization cut - off parameter with a fixed nucleon mass .
our results are in remarkable agreement with the experimental data . |
in heavy - ion ( ) as well as in proton - proton ( ) collisions , the measurements related to strange hadrons constitute unique tools to study the physics of the strong interaction . in this respect ,
given their strangeness content , the charged multi - strange baryons
( @xmath3 ) , ( @xmath4 ) , ( @xmath5 ) , ( @xmath6 ) are of certain importance . the interest in strangeness and specifically in and can be explained mainly by two reasons : * the initial system formed by the projectiles is free from strange valence quarks , thus the strange quarks that compose the strange hadrons of the final state have to be produced during the process of the collisions ; * due to the identification via weak - decay topology reconstruction , the multi - strange baryons can be studied over a large momentum range , typically from @xmath7 @xmath8 up to @xmath9 .
the resulting @xmath7 spectra then cover the region dominated by the soft processes and reach the energy scale where hard scattering mechanisms may prevail .
a significant part of the investigation in physics depends on our understanding of the production mechanisms ( soft and hard ) in the system , meaning as they occur in the benchmark system .
the measurement of multi - strange particle spectra in collisions is the topic of this report .
the data presented here are from a minimum bias ( mb ) sample of collisions at @xmath0 = 7 , collected at the lhc @xcite with the alice experiment @xcite during summer 2010 .
the entire statistics presently analysed stands for about @xmath10 mb interactions .
the study makes use of the two alice main tracking detectors placed at mid - rapidity , covering the full azimuth : the inner tracking system , composed of 6 cylindrical layers of high - resolution silicon detectors @xcite , and the cylindrical time projection chamber ( tpc ) @xcite .
the multi - strange hadron identification is performed using a combination of displaced - vertex finding , invariant mass analysis and particle identification ( pid ) method at the single track level ( in this analysis , compatibility selection based on the energy loss measurements from the tpc ) .
the reconstruction of the , , , particles hinges on their respective charged weak decays , the so - called _ cascade _ structures . for each species of interest ,
the main characteristics and utilized decay channels are listed in table [ tab : maire - cascdecaychannel ] .
the anti - baryons are similarly reconstructed via the decay channel involving the charge conjugates .
lccccc particles & mass ( @xmath11 ) & @xmath12 ( ) & charged decay channel & b.r .
+ @xmath13 ( @xmath14 ) & @xmath15 & @xmath16 & @xmath17 & 63.9% + @xmath18 ( @xmath3 ) & @xmath19 & @xmath20 & @xmath21 & 99.9% + @xmath22 ( @xmath5 ) & @xmath23 & @xmath24 & @xmath25 & 67.8% + the guidelines of the reconstruction algorithm , consisting of pairing a or baryon with an additional particle ( _ v0 _ structure combined with a so - called _ bachelor _ track ) , are sketched in @xcite and detailed in @xcite .
the protocol to extract the signal counts per @xmath7 interval ( bin ) is also presented in @xcite .
due to the large statistics available for the 7 data sample , and but also and can be studied distinctively . at central rapidity ( ) , the overall raw signal amounts to about @xmath26 counts for , as well as for , and about @xmath27 counts for as well as for its anti - particle .
the upper part of the figure [ fig : maire - fig1-correctedspectra ] shows the four corrected spectra .
they are normalised to the number of inelastic events ( inel ) .
both spectra range from @xmath7 = 0.6 to 8.5 , while the spectra are measured between 0.8 and 5.0 . in order to extract the integrated yields ,
the data points are fitted with a tsallis function @xcite .
the fits result in a good description of data ( @xmath28 close to unity ) and are further used to extrapolate the spectra in the non - measured low @xmath7 region ( @xmath29 of the total @xmath30 for or , @xmath31 for or ) . as a function of transverse momentum , for , , , measured at central rapidity ( @xmath32 ) in inelastic events at @xmath0 = 7 .
the upper panel shows the corrected spectra for the four different species together with their fits by a tsallis function .
the lower panel presents the ratio between the measured data and the predictions returned by the tune perugia 2011 ( p2011 ) of pythia . ] note that , provided the difference in the normalisation scheme chosen by alice ( inel ) and cms ( non - single diffractive , nsd ) @xcite , the ( ) spectra by both experiments are found to be in agreement within the limit of uncertainties .
a significant part of our understanding of collisions is based on description by the monte carlo models ( mc ) .
this is especially the case in the _ soft _ regime ( @xmath7@xmath33 2 - 3 ) .
the confrontation with experimental measurements is necessary , as it spurs further improvements of such phenomenological approaches .
the lower part of the figure [ fig : maire - fig1-correctedspectra ] shows the ratio between data and mc predictions .
the data are here compared to the tune perugia 2011 ( tune s350 @xcite ) of the pythia model @xcite .
although this specific tune provides an improved description of data with respect to earlier tunes ( tunes z2 and perugia 0 ) @xcite , it can still be seen that mc underestimates the measured spectra , up to a factor @xmath34 2 for the charged , @xmath34 5 for the
. however it should be noted for ( ) that there is an agreement between mc and data at @xmath7 @xmath35 6 , where the fragmentation regime may already be reached .
the figure [ fig : maire - fig2-ratioomegaoverxi - pt ] provides another viewpoint on the comparison of data to mc .
it computes the ratio of ( ) to ( ) as a function of @xmath7 . as before ,
it can be noted the model tends to underpredict the particle ratio , by a factor @xmath342 . regarding the data ratio itself
, it turns out the ratio first rises with @xmath7 , before seemingly saturating at a value of 0.15 , which could suggest that the hierarchy between and production becomes constant at high @xmath7 . between ( + ) and ( + ) as a function of transverse momentum , for collisions at @xmath0 = 7 .
the ratio is given for alice data as well as pythia perugia 2011 ( p2011 ) .
as a consistency check , the ratio of the tsallis functions fitted to the data or to the model predictions is also shown . ]
values ( @xmath36 ) for different species identified by the alice experiment in collisions , at @xmath0 = 0.9 @xcite and 7 .
these values are compared to the isr parametrisation ( performed from the @xmath37 , k , p species in collisions at ) and star measurements in central @xmath38 collisions at @xcite . ] the figure [ fig : maire - fig3-alicemeanpt - ppcollisions ] presents the alice preliminary values obtained for the mean @xmath7 ( @xmath36 ) of various identified particles , as measured in collisions at 7 . for comparison , the data are plotted together with results published by alice for data at @xmath0 = 0.9 @xcite as well as by star for the central @xmath38 collisions at @xmath39 = 0.2 @xcite . for a given particle studied in collisions
, it appears that the @xmath36 rises with @xmath0 . at ,
the data come to reach the values obtained in the most central collisions at rhic , raising the question of the physical similarities between these different systems at different energies .
with the results presented in this report , the alice experiment provides the first lhc measurement of and at central rapidity .
together with and results , it actually enables an extension of the excitation function in a system .
this is of importance to define the baseline necessary for the studies related to the so - called _ strangeness enhancement _
besides , although the tune perugia 2011 is a priori the current most suitable pythia tune for the description of hyperons in collisions at lhc energies , it is observed that it underestimates the data at intermediate @xmath7 . | in the perspective of comparisons between proton - proton and heavy - ion physics , understanding the production mechanisms ( soft and hard ) in that lead to strange particles is of importance .
measurements of charged multi - strange ( anti-)baryons ( and ) are presented for collisions at @xmath0 = 7 .
this report is based on results obtained by alice ( a large ion collider experiment ) from the 2010 data - taking .
+ taking advantage of the characteristic cascade - decay topology , the identification of , , and can be performed , over a wide range of momenta ( e.g. from 0.6 to 8.5 for , with the present statistics analysed ) .
the production at central rapidity ( @xmath1 ) as a function of transverse momentum , @xmath2 , is presented .
these results are compared to pythia perugia 2011 predictions . |
our data consists of 19 pointed observation of a2218 , taken with the 15 micron filter of the irc - l @xcite aboard _ akari _ @xcite .
the data was reduced using the standard irc pipeline , version 20070912 . the pipeline s median sky subtraction was utilized but resulted in dark areas , significantly around the brighter sources . to deal with this issue , and the remnants of scattered light persisting post - pipeline , a further median sky subtraction of the background areas was performed .
hot pixels were masked and removed , and the remaining bad pixels were addressed using an idl sigma filtering routine .
figure 1 shows four corresponding postage stamp sections taken from frame 19 illustrating the post - pipeline output , a median filtered mask , the median subtracted result and the sigma filtered result .
the resulting 19 images were aligned with aladin and idl s hastrom , and then average combined to give the final l15 image .
a 5@xmath0 source extraction was performed with daofind @xcite .
the resulting catalogue was eyeballed to eliminate any spurious detections , giving a final number of 565 sources .
a monte carlo completeness test was performed using an idl routine written to convolve a normalized empirical psf with the final l15 image , to create artificial sources at random positions .
the artificial sources were placed sufficiently apart from one another and known sources to avoid self - confusion .
the test was performed for 80 flux bins , covering the range of flux densities for detected sources within the l15 image . in order to reduce statistical errors
the test was repeated until an effective 18452 sources per bin was achieved .
the completeness test results show the l15 image is 50% complete to 30.7 @xmath1jy and 80% complete to 39.4 @xmath1jy .
aperture photometry was taken at random positions on the final image , excluding the edges and the brightest source , and the results were plotted as a histogram of flux density against number , see figure 2 .
the resulting distribution has an asymmetric tail that signifies the contributions from bright sources .
the combined confusion and detector noise can be represented by fitting a gaussian to the histogram , with a standard deviation of 8.33 @xmath1jy giving a 5@xmath0 sensitivity estimate of 41.67 @xmath1jy .
the mean rms per pixel of the l15 noise map is 2.20 @xmath1jy .
, scaledwidth=40.0% ]
multi waveband data of a2218 was used to identify counterparts of the l15 5@xmath0 source catalogue .
hst wfp2 f450 , f606 and f814 , palomar 200inch hale _ u , v , b , i _ and ingrid wfc _ ks _ and _ j _ images of a2218 were provided by ian smail .
spitzer irac ch 1 to 4 data was obtained via leopard and combined with mopex .
an _ akari _
s11 image was provided by myungshin i m and jongwan ko , and a spitzer mips 24 @xmath1 m image was provided by eiichi egami . the counterparting procedure identified an extra 368 sources and 3 spurious 5@xmath0 detections , giving a combined counterpart catalogue of 930 sources .
aperture photometry of the 5@xmath0 source catalogue was taken with phot @xcite using an aperture of 5.96@xmath2 and a sky annulus of radii 19.07@xmath2 and 31.0@xmath2 .
an aperture correction of 1.30 , derived using a growth curve correction method , was applied and the irc data user s manual version 1.4 @xcite conversion factor of 1.691 was used to convert from adu to @xmath1jy . for the hst images
, photometry was obtained from the published catalogue of @xcite via the ned database .
the remaining images were subject to a growth curve correction method to obtain corrected aperture photometry , using a routine written in idl . for each image one or two mean growth curves were empirically constructed .
these curves were used to calculate aperture radius and correction for each remaining source .
idl s aper was used to take the subsequent aperture photometry .
our _ ks _ band photometry was compared , where available , to previously published _
band photometry @xcite and showed a less than 2% difference .
we used eazy @xcite to gain photometric redshift estimates for our 5@xmath0 source catalogue .
eazy utilizes a minimum @xmath3@xmath4 sed fitting method , which is suitable for data sets with no available spectroscopic redshifts ( zspec ) or a biased set of zspec . in our case
the majority of the small zspec available are biased at the cluster distance .
the theoretical sed templates , used by eazy , are based on semi - analytical models , and a linear combination of templates can be fitted simultaneously .
eazy gives the option to apply priors , aimed at breaking the template colour degeneracies seen with increasing redshift .
a comparison of the resulting redshift estimates for our sources with known zspec shows that applying priors gives an improved correlation of approximately 10% .
our spectra were also fitted using the photometric redshift code illustrated in @xcite , photz from here on .
this code is uniquely optimised for fitting mid - to - far - infrared pah and silicate features seen in starburst seds .
starburst template @xcite and agn template @xcite components were simultaneously fitted by photz .
a comparison of the photz and eazy redshifts estimates for sources with prominent mid - to - far - infrared features shows a correlation of around 0.8 .
differential number counts ( dn / ds ) , corrected for incompleteness , were taken for our 5@xmath0 catalogue and normalized to a euclidean slope .
these counts were corrected for flux amplification by applying magnification factors obtained via lenstool @xcite .
figure 3 compares our corrected and uncorrected counts with previously published differential number counts .
our counts corrected for lensing show an upturn around 2 mjy and peak around 0.4 mjy , in agreement with previous counts ( e.g. , * ? ? ?
* ) and the @xcite model .
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2001 , mnras 323 , 839 stetson , p. b. , 1987 pasp , 99 , 191 takagi , t. , arimoto , n. , hanami , h. 2003 , mnras , 340 , 813 | we present photometry , photometric redshifts and extra galactic number counts for ultra deep 15 micron mapping of the gravitational lensing cluster abell 2218 ( a2218 ) , which is the deepest image taken by any facility at this wavelength .
this data resolves the cosmic infrared background ( cirb ) beyond the 80% that blank field
_ akari _
surveys aim to achieve . to gain an understanding of galaxy formation and evolution over the age of the universe a necessary step is to fully resolve the cirb , which represents the dust - shrouded cosmic star formation history .
observing through a2218 gives magnifications of up to a factor of 10 , thus allowing the sampling of a more representative spread of high redshift galaxies , which comprise the bulk of the cirb .
19 pointed observations were taken by _ akari _
s irc mir - l channel , and a final combined image with an area of 122.3 square arcminutes and effective integration time of 8460 seconds was achieved .
the 5@xmath0 sensitivity limit is estimated at 41.7 @xmath1jy .
an initial 5@xmath0 catalogue of 565 sources was extracted giving 39 beams per source , which shows the image is confusion limited .
our 15 micron number counts show strong evolution consistent with galaxy evolution models that incorporate downsizing in star formation . |
the issue of what happens to complexity in an evolving system is of great interest . in natural ( biological ) evolution
, the naive view is that life started simple , and evolved ever more complex life forms over time , leading to that pinnacle of complexity , _
homo sapiens_. the end points of that process are of course fixed . in the beginning , life must be simple . in our present era
, there must exist intelligent organisms ( namely us ) pondering over the mystery of how we came to be .
so the _ anthropic principle _ fixes the present day as having complex lifeforms .
there is nothing within the _ modern synthesis _ of darwinism that implies a steady interpolation between these two end points .
in fact it is even plausible that more complex organisms than us existed in the past , but have since vanished into obscurity .
however , examinations of the fossil record over the phanerozoic ( the last 550 million years of the earth s history ) indicate almost no growth in complexity by a number of different measures over that period , apart from an initial large jump at the cambrian explosion.@xcite the interesting thing is to ask what one might see if looking at another evolutionary system apart from the one in which we evolved
. would we see any growth in complexity at all ? since we do nt have an extra terrestrial biology to observe ( a few martian meteorites aside ) , the only other systems available are artificial life systems evolving within a digital computer such as tierra or avida .
the avida group has reported measuring the information content ( complexity ) of individual avidan organisms@xcite , or rather a lower bound of the organism s complexity .
their results are that this lower bound increases over time for the maximally fit organism , thus showing information accumulating as time progresses
. one important critique of this work , however , is that organisms do not interact directly with each other , and in order to prevent evolution stagnating , an externally imposed task ( eg computing a logical operation ) is added to the system .
organisms are given `` fitness points '' depending on how well they perform this task .
this heavily weights the system in favour for accruing information .
by contrast , in the tierra system , the organisms interact with each other , providing a rich array of possible ( intrinsic ) tasks for the organisms to exploit .
since this is an evolving ecology with no externally imposed task , the above critique does not apply .
however , the downside is that determining whether two genotypes are phenotypically equivalent is considerably more complex . in some work a couple of years ago@xcite , i studied the phenotypic properties of tierran organisms to build up a picture of the genotype to phenotype landscape .
a tierran organism s phenotype can be characterised by a couple of numbers for each possible pairwise interaction in the ecology .
multiway interactions are ignored in this study , as experience has shown them to be relatively rare .
the information content of a string is given by the difference between the maximal shannon entropy of that string ( i.e. considering the string to be random , or devoid of information ) , and the entropy given by assuming that the string codes for some phenotype @xmath0:@xcite @xmath1 where @xmath2 is the length of the genotype ( in instructions ) , and @xmath3 is the number of genotypes that give rise to the same phenotype @xmath0 .
the base , 32 , refers to the number of instructions in the tierra instruction set . if @xmath4 ( ie a completely random sequence ) , then @xmath5 .
similarly , if @xmath6 ( there is only one genetic sequence encoding a genotype , or no redundancy ) , then @xmath7 .
the most obvious way to compute @xmath3 is to search all @xmath8 genotypes for equivalent phenotypes .
however , this is an enormous number of strings to check , and computationally infeasible .
adami recognised this problem , and took the approach of counting the number of volatile sites @xmath9 ( sites that vary amongst phenotypic equivalents ) , and approximating @xmath10 . in one sense
this is an overestimate of @xmath3 , so they argue that this gives a lower bound to the information @xmath11 . in another sense , however , it is not strictly a lower bound . if it turns out that fixing one of the volatile sites to a particular value allows one of the fixed sites to vary without altering the phenotype , then this would be not be counted in the @xmath3 .
so what we have is really an overestimate of an underestimate .
the same criticism applies to this work .
we can estimate the above mentioned estimate fairly accurately , more precisely we can find the size of the neutral network@xcite connected by one - site neutral mutations to @xmath12 .
however , the possibility remains that there are other neutral networks of @xmath12 that are nt connected by single site mutations to @xmath12 .
probably the most efficient way of finding these is by using a genetic algorithm to explore genotype space , i.e. run tierra for a long time to see what it discovers ! the way we use this in our experiment is to keep a list of neutrally equivalent organisms that tierra discovers .
as we explore the neutral network connected to @xmath12 , we eliminate items from the list that we come across .
the remaining names on the list can then be used as seeds to start the process again . in this work ,
we use two different techniques to measure @xmath3 .
the first is a monte carlo random sampling technique to estimate the proportion of the @xmath13 strings found by varying the volatile sites .
the second technique , which we use in conjunction with the monte carlo approach mentioned above , is to walk the neutral net .
the monte carlo technique works well when the density of neutral variants is fairly high , whereas the latter technique is best on sparse networks . a decision on which technique to use for
which site is based on estimated densities of neutral variants .
equation ( 4 ) of @xcite presents the dynamical equations of two species of tierran organisms interacting .
the precise form of the dynamics is not important here , however the phenotype of the organism can be characterised by its interactions will all other possible tierran phenotypes .
since it is impossible to have the complete set of all possible tierran organisms , those organisms generated during a run of tierra are used . since tierran organisms coevolve , the most important organisms should be contemporaneous with the test organism .
the following characteristics are saved for each pair of organisms : 1 . the outcome of the tournament .
this may be one of the following : + infertile : : the test organism never calls the divide instruction , or does not produce any recognisable progeny ( essentially still born ) once : : the organism produces progeny once , but then never repeats the act .
repeat : : the organism continuous reproduces the same progeny . for this purpose
we ignore what is produced first time around , as this will be swamped by number latter progeny .
nonrepeat : : the organism continuously reproduces , but the progeny is either different each time , or the cpu is in a different state each time the divide instruction is called - thus ca nt be guaranteed to reproduce ad infinitum .
the name of the progeny organism .
this is usually identical to the parent , but may another type in the case of symbiosis or parasitism .
3 . the number of timesteps it takes to reach the first divide instruction ( @xmath14 ) , and the time it takes between successive divide steps after that ( @xmath15 ) .
4 . the number of template matching operations made to the opposing organism prior to the first divide ( @xmath16 ) and between successive divides ( @xmath17 ) .
two organisms are neutrally equivalent if they have identical characteristics against all tierran organisms . once all organisms are paired with each other , we can produce a list of phenotypically unique organisms , which provides a smaller test list to pit trial mutants against .
we may also eliminate some noninteractive pairings prior to simulation by trying to see if potential template matches could happen between organisms .
this still produces a fairly large list of test organisms , so it is still computationally expensive .
the high degree of parallelism in this problem allows it to be attacked in reasonable time on a parallel supercomputer . a further refinement may be possible by producing an archetypal list , perhaps by ignoring the ( @xmath18 and @xmath19 ) parameters
the idea being that the archetypes contain a representative organism from each niche of the ecology , and ignoring minor differences such as reproductive rate .
this would coarsen the approximation a little , but will probably give an acceptable result . at present this idea has not been tested .
due to the time constraints of producing this paper , the analysis of a reasonable length tierra run has not been completed . at the time of writing , a moderately large data set of 1660 organisms
was generated from a 24 hour tierra run .
tierra produces most of its diversity during the earliest stage of its running , so it becomes significantly more expensive to produce larger data sets .
this data set was halved by removing every second organism , and then a phenotypic analysis was carried out .
this set reduced to 103 distinct phenotypes , which formed the test list used for carrying out the complexity analysis .
each of these 103 organisms were then tested for phenotypic equivalence against their single site nearest neighbours .
the number of sites on which no mutation resulted in a phenotypically equivalent organism ( `` nonvolatile sites '' ) is plotted against the time of speciation in figure [ results ] . | recently , adami and coworkers have been able to measure the information content of digital organisms living in their _ avida _ artificial life system .
they show that over time , the organisms behave like maxwell s demon , accreting information ( or complexity ) as they evolve . in _ avida
_ the organisms do nt interact with each other , merely reproduce at a particular rate ( their fitness ) , and attempt to evaluate an externally given arithmetic function in order win bonus fitness points .
measuring the information content of a digital organism is essentially a process of counting the number of genotypes that give rise to the same phenotype .
whilst avidan organisms have a particularly simple phenotype , tierran organisms interact with each other , giving rise to an ecology of phenotypes . in this paper ,
i discuss techniques for comparing pairs of tierran organisms to determine if they are phenotypically equivalent .
i then discuss a method for computing an estimate of the number of phenotypically equivalent genotypes that is more accurate than the `` hot site '' estimate used by adami s group .
finally , i report on an experimental analysis of a tierra run . |
the synthetic field method ( sfm ) was developed by gonzlez et al .
( 1998 ) as a technique for determining the average opacity through the disk of a nearby spiral by counting more distant background galaxies .
this number is compared with those of `` synthetic fields '' , a known wfpc2 deep field , dimmed by a certain opacity , added to the foreground galaxy image .
gonzlez et al . ( 2003 ) examined the application of the method and concluded that the optimum results with hst / wfpc2 imaging would be obtained on fornax and virgo cluster galaxies , with the accuracy degrading for galaxies much closer or more distant .
our sample was drawn from the hst archives , in part from the cepheid distance scale hst key project sample .
we present preliminary results on ngc4535 , ngc4725 and ugc2302 . the numbers of real and simulated field galaxies were compared in annuli of deprojected radius .
ngc4535 is a face - on sabc with a half - light radius of 5.1 kpc at a distance of 16 mpc .
several spiral arms with bright hii regions are visible in the hst image .
ngc4725 is a sabab ringed galaxy at 12 mpc its half - light radius is 5.4 kpc .
the hst image shows much less structure .
the radial opacity profiles of both however are similar ( see figure 1 ) , showing 2.5 magnitudes of extinction in i at the half - light radius , dropping off to 0.5 magnitude .
ugc2302 is a lsb at 15 mpc is a much more compact object . at comparable radii
, it does not show as much absorption ; less then a magnitude at 5 kpc from the center .
the uncertainties in these individual profiles are large due to low numbers of field galaxies and an added uncertainty due to their clustering . by averaging a number of fields we will improve on these uncertainties for an average radial opacity model of spiral galaxies . for different hubble types , we intend to compare the radial dependence of opacity with the hi density profile to obtain cold dust - to - gas ratios .
gonz ' alez , r. a. , allen , r. j. , dirsch , b. , ferguson , h. c. , calzetti , d. , and panagia , n. 1998 , * 506 * , 152 gonz ' alez , r. a. , loinard , l. , allen , r. j. , and muller , s. 2003 , * 125 * , 1182 holwerda , b. w. , allen , r. j. , and van der kruit , p. c. : 2002 , asp conf .
ser . 273 : 337 | we have applied the `` synthetic field method '' on a sample of 20 nearby galaxies in order to determine the opacity of their disks .
we present preliminary results on the radial dependence of cold dust absorption for 3 examples .
the spirals ngc4535 and ngc4725 show significant absorption at a half - light radius . ugc2302 , a lsb galaxy , shows much less opacity . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
the primary mission of the batse instrument was to detect and locate @xmath0-ray bursts .
while the 8 detectors had no intrinsic positional sensitivity , burst positions were obtained by triangulation between detectors .
it was realised , prior to launch , that persistent sources of @xmath0-rays could also be observed by using the earth occultation technique @xcite .
this method calculates the source flux by measuring the step in the count rate of each batse detector as a source rises or sets below the earth s limb .
mass modelling is a technique to simulate the background radiation experienced by a space craft @xcite .
the batse mass model ( bamm ) is a geant3 monte - carlo simulation code developed at southampton @xcite .
bamm simulates the expected count rate from cosmic diffuse @xmath0-rays , atmospheric albedo @xmath0-rays and cosmic rays thoughout the orbit .
the position and orientation of the spacecraft relative to the earth are used to filter these results and generate the expected background .
bamm has been used to flat - field the entire 9 year batse data set .
it is thought that the origin of the exceptionally high luminosity of active galaxies is the accretion of matter onto a supermassive black hole located at the galaxy centre @xcite .
agn typically have highly variable x - ray and @xmath0-ray fluxes .
the very short timescale variability indicates that this emission originates from a small region very close to the central engine .
hence the variability of agn yields direct information about the central supermassive black hole .
the crab is one of the brightest @xmath0-ray sources in the sky and is well known for its lack of variability . as
such it is the ideal ` standard candle ' with which to test the flat - fielded data set and explore the capabilities of our methods .
[ fig : crab ] shows the 9 year light curve of the crab in the 30 - 230 kev energy band as measured on a daily basis and with a 53 day moving average fit ; 53 days is the precession period of cgro .
a histogram of this light curve is seen in fig .
[ fig : crabhist ] .
the crab appears relatively constant in the light curve , hence the histogram should have a gaussian profile . fitting a gaussian distribution to the histogram
yields a centroid of 1.005 @xmath1 0.002 crabs with a reduced @xmath2@xmath3 of @xmath43 .
examining the residuals of this fit indicates a number of spurious points in the 0.6 - 0.9 crab region which may be the result of an unknown low level systematic , removing these points renders a fit with a @xmath2@xmath3 of 1.3 .
rebinning the data into longer timescale averages , before generating the histogram , allows the estimation of the systematic component of any errors . as the time bins increase in size the standard deviation of the data set would ideally asymptotically approach 0 .
the inset graph of fig .
[ fig : crabhist ] shows that the curve approaches @xmath42.5% , indicating this level of systematic error .
this level is assumed in our studies of agn light curves .
agn are some of the most powerful persistent sources of @xmath0-rays in the observable universe .
however the low fluxes which arrive at earth make them a very challenging subject to observe in this waveband .
the three brightest agn seen in batse are : centaurus a , a radio galaxy ; ngc4151 , a seyfert galaxy ; 3c273 , a blazar . fig .
[ fig : lightcurves ] shows the light curves in the batse 20 - 50 kev and 50 - 160 kev band of these agn .
the data have been binned up to 30 day data points in order to minimise any errors .
additionally the rxte - asm 2 - 10 kev light curves are presented , scaled and offset from the batse curves to aid legibility .
[ fig : hard - soft ] is a hard flux - soft flux plot of the three agn showing the flux in the 30 - 50 kev band against that of the 50 - 160 kev band .
the hard and soft batse light curves seen in the upper panel of fig .
[ fig : lightcurves ] appear to be well correlated apart from a short , @xmath430 day outburst in the 20 - 50 kev band at tjd @xmath410800 which appears to coincide with a drop in the 50 - 160 kev flux .
however , the 20 - 50 kev flux continues to be correlated with the asm light curve during this period .
this appears to be corroborated by the hard - soft plot where the hard and soft fluxes indicate a positive correlation .
a spearman rank correlation coefficient of 0.56 with a probability of chance occurance of p@xmath50.0001 confirms this positive correlation .
the asm light curve follows the general trends exhibited by both of the batse light curves neglecting the outburst at tjd @xmath410800 .
the hard and soft light curves shown in the middle panel of fig . [ fig : lightcurves ] appear to be well correlated although there appears to be a potential time lag between them of @xmath430 days .
emission in the 50 - 160 kev band initially appears to precede that of the 20 - 50 kev band , however this is not obvious after tjd @xmath48800 . as this lag is on the same time scale as the data binning it is tenuous without a detailed statistical analysis .
the hard - soft plot looks flat as the hard flux appears independent of the soft flux , however , a positive correlation is indicated by a spearman rank correlation coefficient of 0.31 with a probability of chance occurance of p@xmath60.002 . both light curves seen in the lower panel of fig .
[ fig : lightcurves ] are synchronized and well correlated .
they both show the same general trends .
the hard - soft plot indicates a positive correlation with a spearman rank correlation coefficient of 0.45 with a probability of chance occurance of p@xmath50.0001 . ]
the 9 year batse data set has been flat - fielded using bamm to remove temporal variations in the instrument background .
we have then applied the standard earth occultation technique developed at marshall space flight centre @xcite on the flat - fielded data set and made measurements to the crab nebula and 3 agn : cen a ; ngc4151 ; 3c273 .
the crab light curve exhibits a constant flux of 1.005 @xmath1 0.002 crabs confirming that the flat - fielding had no adverse effect on the data .
additionally , the systematic error of the methods and analysis performed in the generation of the light curve is estimated to be limited to @xmath42.5% .
the agn light curves show that batse is sensitive to the variations in their @xmath0-ray fluxes .
work is in progress to re - optimise the standard earth occultation technique for use with the flat - fielded data with the intention of improving sensitivity and precision of measurements .
we are simultaneously using the flat - fielded data with new methods to generate all - sky images for the whole 9 years @xcite . , s. e. , bird , a. j. , dean , a. j. , et al .
, 2001 , in exploring the gamma - ray universe : proceedings of the 4th integral workshop , alicante , 2000 , ed
. a. gimenez , v. reglero , & c. winkler , vol .
esa sp-459 , 521524 | the burst and transient source experiment ( batse ) aboard cgro monitored the whole sky through 8 nai(tl ) crystal scintillators sensitive in the 20 kev - 2 mev energy band continuously from april 1991 until june 2000 .
results are presented on the long term variabilty observed in the brightest active galactic nuclei ( agn ) present in the batse data archive .
this was achieved through the application of the earth occultation technique to data flat - fielded using the batse mass model .
removal of the temporal background variations from the data should allow a more sensitive extraction of source parameters .
analysis of the general trends of the 9-year light curves are also presented .
[ 2004/02/13 1.1 ( pwd ) ] |
compressed sensing @xcite has generated enormous interest and research activities in mathematics , statistics , signal processing , imaging and information sciences , among numerous other areas .
one of the basic problems is to reconstruct a sparse signal under a few linear measurements ( linear constraints ) far less than the dimension of the ambient space of the signal . consider a sparse signal @xmath13 , an @xmath14 sensing matrix a and an observation @xmath15 , @xmath16 , such that : @xmath17 where @xmath18 is an @xmath19-dimensional observation error .
if @xmath20 is sparse enough , it can be reconstructed exactly in the noise - free case and in stable manner in the noisy case provided that the sensing matrix @xmath5 satisfies certain incoherence or the restricted isometry property ( @xmath21 ) @xcite .
the direct approach is @xmath1 optimization , including constrained formulation : @xmath22 and the unconstrained @xmath1 regularized optimization : @xmath23 with positive regularization parameter @xmath24 . since minimizing @xmath1 norm
is np - hard @xcite , many viable alternatives are available . greedy methods ( matching pursuit @xcite , othogonal matching pursuits ( omp ) @xcite , and regularized omp ( romp ) @xcite ) work well if the dimension @xmath19 is not too large . for the unconstrained problem ( [ eq : l0 uncons ] ) , the penalty decomposition method @xcite replaces the term @xmath25 by @xmath26 , and minimizes over @xmath27 for a diverging sequence @xmath28 .
the variable @xmath29 allows the iterative hard thresholding procedure .
the relaxation approach is to replace @xmath1 norm @xmath30 by a continuous sparsity promoting penalty functions @xmath31 .
convex relaxation uniquely selects @xmath32 as the @xmath0 norm @xmath33 .
the resulting problems are known as basis pursuit ( lasso in the over - determined regime @xcite ) .
the @xmath0 algorithms include @xmath0-magic @xcite , bregman and split bregman methods @xcite and yall1 @xcite . theoretically , cands and tao introduced rip condition and used it to establish the equivalent and unique global solution to @xmath1 minimization via @xmath0 relaxation among other stable recovery results @xcite .
there are also many choices of @xmath32 for non - convex relaxation .
one is the @xmath3 norm ( @xmath34 ) with @xmath1 equivalence under rip @xcite .
the @xmath35 norm is representative of this class of functions , with the reweighted least squares and half - thresholding algorithms for computation @xcite . near the rip regime
, @xmath35 penalty tends to have higher success rate of sparse reconstruction than @xmath0 .
however , it is not as good as @xmath0 if the sensing matrix is far away from rip @xcite as we shall see later as well . in the highly non - rip ( coherent ) regime
, it is recently found that the difference of @xmath0 and @xmath36 norm minimization gives the best sparse recovery results @xcite .
it is therefore of both theoretical and practical interest to find a non - convex penalty that is consistently better than @xmath0 and always ranks among the top in sparse recovery whether the sensing matrix satisfies rip or not . in the statistics literature of variable selection ,
fan and li @xcite advocated for classes of penalty functions with three desired properties : * unbiasedness , sparsity * and * continuity*. to help identify such a penalty function denoted by @xmath37 , fan and lv @xcite proposed the following condition for characterizing unbiasedness and sparsity promoting properties . the penalty function @xmath38 satisfies : 1 .
@xmath39 is increasing and concave in @xmath40 ; 2 .
@xmath41 is continuous with @xmath42 ; 3 .
if @xmath39 depends on a positive parameter @xmath24 , then @xmath43 is increasing in @xmath44 and @xmath45 is independent of @xmath24 .
it follows that @xmath41 is positive and decreasing , and @xmath45 is the upper bound of @xmath41 .
it is shown in @xcite that penalties satisfying condition 1 and @xmath46 enjoy both unbiasedness and sparsity .
though continuity does not generally hold for this class of penalty functions , a special one parameter family of functions , the so called * transformed @xmath0 functions ( tl1 ) @xmath47 * , where @xmath48 with @xmath49 , satisfies all three desired properties @xcite .
we shall study the minimization of tl1 functions for cs problems , in terms of theory , algorithms and computation .
we proposed the algorithms of tl1 via dc approximation @xcite and implemented numerical tests based on two classes of coherent random sensing matrices .
same as @xmath10 regularization @xcite , there also exists thresholding algorithm for tl1 , which is studied in the companion paper @xcite .
the rest of the paper is organized as follows . in section 2
, we study the properties of tl1 penalty and its regularization models .
one rip condition is given for the consistency of tl1 constrained model with original @xmath1 model .
we also prove that the local minimizers of the tl1 constrained model extract independent columns from the sensing matrix @xmath5 , as well as the local minimizers of the unconstrained model . in section 3 ,
we present two dc algorithms for tl1 optimization ( dcatl1 ) . in section 4 , we compare the performance of dcatl1 with some state - of - the - art methods using two classes of matrices : the gaussian and the oversampled discrete cosine transform ( dct ) .
numerical experiments indicate that dcatl1 is robust and consistently top ranked while maintaining high sparse recovery rates across all sensing matrices .
concluding remarks are in section 5 .
[ cols= " < , > " , ]
we have studied compressed sensing problem with the transformed @xmath0 penalty function for both the unconstrained and constrained models .
we presented a theory on the uniqueness and @xmath1 equivalence of the global minimizer of the unconstrained model under rip and analyzed properties of local minimizers .
we showed two dc algorithms along with a convergence theory . in numerical experiments
, dcatl1 is on par with the best method reweighted @xmath35 ( @xmath50 ) in the unconstrained ( constrained ) model , using incoherent gaussian matrices @xmath5 . for highly coherent over - sampled dct matrices ,
dcatl1 is comparable to the best method dca @xmath51 algorithm . for random matrices of varying degree of coherence
, we tested gaussian and over - sampled dct sensing matrices .
the dcatl1 algorithm is the most robust for constrained and unconstrained models alike . in future work , we plan to develop tl1 algorithms for imaging processing applications such as deconvolution and deblurring .
the authors would like to thank professor wenjiang fu for suggesting reference @xcite and a helpful discussion .
we also wish to thank the reviewers for their constructive comments .
the proof generally follows the lines of arguments in @xcite and @xcite , while using special properties of the penalty function @xmath52 .
+ for simplicity , we denote @xmath53 by @xmath54 and @xmath55 by @xmath56 .
+ define the function : @xmath57 it is continuous and increasing in the parameter @xmath58 . note that at @xmath59 , @xmath60 , and as @xmath61 , @xmath62 by ( [ rip ] ) .
there exists a constant @xmath7 , such that @xmath63 .
the number @xmath7 depends on the rip of matrix @xmath5 only , and so it is independent of the scalar @xmath64 . + for @xmath65 : @xmath66 let @xmath67 , and we want to prove that the vector @xmath68 .
it is clear that , @xmath69 , since @xmath70 is the support set of @xmath56 . by the triangular inequality of @xmath52 , we have : @xmath71 then @xmath72 it follows that : @xmath73 now let us arrange the components at @xmath74 in the order of decreasing magnitude of @xmath75 and partition into @xmath76 parts : @xmath77 , where each @xmath78 has @xmath79 elements ( except possibly @xmath80 with less ) .
also denote @xmath81 and @xmath82 .
since @xmath83 , it follows that @xmath84 now we estimate the @xmath36 norm of @xmath88 from above in terms of @xmath85 .
it follows from @xmath54 being the minimizer of the problem ( [ eq : spar revised ] ) and the definition of @xmath89 ( [ para : scaled pa ] ) that @xmath90 by ( [ rip a ] ) , the factor @xmath100 is strictly positive , hence @xmath101 , and @xmath102 . also by inequality ( [ ineq : ttc ] ) , @xmath103 .
we have proved that @xmath104 .
the equivalence of ( [ eq : spar revised ] ) and ( [ eq : l0 revised ] ) holds .
d. needell and r. vershynin , _ signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit , _ ieee journal of selected topics in signal processing , 4(2):310 - 316 , 2010 .
s. zhang and j. xin , _ minimization of transformed @xmath108 penalty : closed form representation and iterative thresholding algorithms _ , arxiv preprint , arxiv:1412.5240 ( 2014 ) , comm .
math sci , to appear . | we study the minimization problem of a non - convex sparsity promoting penalty function , the transformed @xmath0 ( tl1 ) , and its application in compressed sensing ( cs ) .
the tl1 penalty interpolates @xmath1 and @xmath0 norms through a nonnegative parameter @xmath2 , similar to @xmath3 with @xmath4 $ ] .
tl1 is known in the statistics literature to enjoy three desired properties : unbiasedness , sparsity and lipschitz continuity .
we first consider the constrained minimization problem and prove the uniqueness of global minimizer and its equivalence to @xmath1 norm minimization if the sensing matrix @xmath5 satisfies a restricted isometry property ( rip ) and if @xmath6 , where @xmath7 depends only on @xmath5 . though result contains the well - known equivalence of @xmath0 norm and @xmath1 norm , in the limit @xmath8 , the main difficulty is in treating the lack of scaling property of the tl1 penalty function . for a general sensing matrix @xmath5
, we show that the support set of a local minimizer corresponds to linearly independent columns of @xmath5 , and recall sufficient conditions for a critical point to be a local minimum .
next , we present difference of convex algorithms for tl1 ( dcatl1 ) in computing tl1-regularized constrained and unconstrained problems in cs .
the dcatl1 algorithm involves outer and inner loops of iterations , one time matrix inversion , repeated shrinkage operations and matrix - vector multiplications . for the unconstrained problem , we prove convergence of dcalt1 to a stationary point satisfying the first order optimality condition . finally in numerical experiments ,
we identify the optimal value @xmath9 , and compare dcatl1 with other cs algorithms on two classes of sensing matrices : gaussian random matrices and over - sampled discrete cosine transform matrices ( odct ) . among existing algorithms ,
the iterated reweighted least squares method based on @xmath10 norm is the best in sparse recovery for gaussian matrices , and the dca algorithm based on @xmath11 penalty is the best for odct matrices .
we find that for both classes of sensing matrices , the performance of dcatl1 algorithm ( initiated with @xmath12 minimization ) always ranks near the top ( if not the top ) , and is the _ most robust choice _ insensitive to rip ( incoherence ) of the underlying cs problems .
* keywords : * transformed @xmath0 penalty , sparse signal recovery theory , difference of convex function algorithm , convergence analysis , coherent random matrices , compressed sensing , robust recovery 90c26 , 65k10 , 90c90 |
for the general case of @xmath1 transition into a combination of @xmath27 ( @xmath28 ) and @xmath29 ( @xmath30 ) states one can write the sk , sno cc and sno nc rates as r^el_sk & = & f_b p_ee + f_b r p_ea , [ two ] + r^cc_sno & = & f_b p_ee , [ three ] + r^nc_sno & = & f_b ( p_ee + p_ea ) , [ four ] where @xmath16 and @xmath31 denote the probabilities folded with the detector response function @xcite and averaged over energy . to extract a model independent bound on @xmath16 one has to ensure an equality of the response functions which amounts to slight adjustment of the sk threshold energy and the rate @xcite .
our approach is slightly different .
we treat @xmath16 to be effectively energy independent .
the sk spectrum data indicates a flat probability down to 5 mev @xcite .
this is corroborated by sno @xcite which now has a threshold of 5 mev for kinetic energy of the observed electron .
hence we consider this assumption as justified and expect the results to be insensitive to the differences in the response functions .
it should be noted here that in cotrast to the sno cc events their nc events correspond to a neutrino energy threshold of 2.2 mev .
however it is clear from eq .
( 5 ) that for a @xmath1 to @xmath28 transition there is no reason to expect any energy dependence in @xmath32 .
on the other hand for the general case of @xmath1 transition into a combination of @xmath28 and @xmath30 our approach effectively assumes @xmath33 to be energy independent down to 2.2 mev .
a comparison of the current values @xmath19 with @xmath32 is shown in fig .
1 . it constitutes a 5.3@xmath34 signal for transition to a state containing an active neutrino component or alternatively a 5.3@xmath34 signal against a pure sterile solution .
next we consider the general case where @xmath1 goes to a mixed state = @xmath35
. then one can write @xmath36 ) . substituting this in the equations ( [ two ] ) and ( [ four ] ) and eliminating @xmath16 using equation ( [ three ] )
one gets the following set of equations for @xmath24 and @xmath37 @xcite ^2(f_b - r^cc_sno ) & = & ( r^el_sk - r^cc_snc)/r , [ five ] + ^2(f_b - r^cc_sno ) & = & r^nc_sno - r^cc_sno .
[ six ] we treat @xmath37 as a model parameter . and for different input values of @xmath37 we determine the central value and the @xmath38 and @xmath39 ranges of @xmath24 by taking a weighted average of the equations ( [ five ] ) and ( [ six ] ) .
the corresponding curves are presented in fig .
2 . combining the 2 @xmath34 lower limit of @xmath24 from this fit with the @xmath39 upper limit from the ssm ( vertical lines )
gives a lower limit of @xmath37 @xmath40 0.45 i.e. the probability of the active component is @xmath40 45% .
note that there is no upper limit on this quantity - i.e. the data is perfectly compatible with @xmath1 transition into purely active neutrinos . assuming transition into purely active neutrinos ( @xmath41 ) we show in fig .
3 the @xmath38 and @xmath39 contours in the @xmath42 plane from the combinations sk+snocc and sk+snocc+snonc .
the inclusion of the nc rate narrows down the ranges of @xmath24 and @xmath16 .
the error in @xmath24 after the inclusion of nc data is about half the size of the corresponding error from ssm as is seen from fig .
in this section we present the results of our @xmath43 analysis of solar neutrino rates and sk spectrum data in the framework of two flavour oscillation of @xmath1 to an active flavour .
we use the standard techniques described in our earlier papers @xcite excepting for the fact that instead of the quantities @xmath44 and @xmath19 we now fit the ratios @xmath20 and @xmath21 .
the @xmath0 flux normalisation gets cancelled from these ratios and the analysis becomes independent of the large ( 16 - 20% ) ssm uncertainty associated with this .
we include in our global analyses the 1496 day sk zenith angle spectra @xcite .
since we use both sk rate and sk spectrum data we keep a free normalisation factor for the sk spectrum .
this amounts to taking the information on total rates from the sk rates data and the information of the spectral shape from the sk spectrum data .
the sno cc and nc rates have a large anticorrelation .
we have taken into account this correlation between the measured sno rates in our global analyses .
further details of this fitting method can be found in @xcite . in table 2
we present the best - fit parameters , @xmath45 and goodness of fit ( gof ) .
the best - fit comes in the high(lma ) region as before @xcite .
however as is seen from fig .
4a the incorporation of the nc data narrows down the allowed regions , and in particular the low region becomes much smaller .
we have also performed an alternative @xmath43 fit to the rates of table 1 @xcite along with the 1496 day sk spectra @xcite , keeping @xmath24 as a free parameter . even though we allow @xmath24 to vary freely the nc data serves to control @xmath24 within a range determined by its error . as we see from table 2 and fig . 4b
the results of this fit are very similar to the previous case .
the best fit comes from the high(lma ) region , while no allowed region is obtained for the low solution at the 99% cl level .
maximal mixing is seen to be disallowed at the @xmath3 level . to illustrate the impact of the nc rate on the oscillation solutions we have repeated the free @xmath24 fit without this rate .
the results are shown in fig 4c .
evidently the nc data plays a pivotal role in constraining the oscillation solutions , particularly in the low / qvo region , which is allowed only at the @xmath3 level .
it puts an upper bound on the @xmath46 in the lma region and rules out maximal mixing .
the first sno nc data constitutes a 5.3@xmath34 signal for transition into a state containing an active neutrino component .
the inclusion of this data puts much tighter constraints on @xmath24 and @xmath16 from a model independent analysis involving active neutrinos as compared to the sno cc / sk combination . in this paper
we have discussed two useful strategies , of incorporating the nc data in the global @xmath43 analysis of rates and spectrum data , by which one can avoid the large @xmath0 flux uncertainty from the ssm .
+ @xmath47 we fit the ratios of the sk elastic and sno cc rates w.r.t the nc rate , from which the @xmath24 cancels out .
+ @xmath47 we fit the rates by keeping @xmath24 as a free parameter , where the inclusion of the sno nc rate (= @xmath24 ) serves to control this parameter .
both the analyses give very similar results .
they clearly favour the high(lma ) solution , while a limited region of the low solution is also acceptable at the @xmath3 level .
the maximal mixing solution is disfavoured at the @xmath3 level . as more data
accumulate one expects a substantial reduction in the error bar of the sno nc rate , resulting in further tightening of the allowed regions of neutrino mass and mixing .
+ + _ note added _ : the paper @xcite appeared on the net after completion of our work . in the region of overlap
our results agree with theirs as well as with the updated version of @xcite . it may be added here that the sno cc and nc rates given in table 1 are obtained assuming undistorted energy spectra above 5 mev , which for transitions to active neutrinos has good empirical justification as mentioned above .
we thank prof .
mark chen of sno collaboration for communication on this point .
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the observed solar neutrino rates relative to the @xmath49 predictions ( bp2000 ) are shown along with their compositions for different experiments . for the @xmath50 experiment
the @xmath1 contribution to the rate @xmath51 is shown in parantheses assuming @xmath52 transition . in the combined ga rate we have included the latest data from sage and gno . [ cols="^,^,^ " , ] | we perform model independent and model dependent analyses of solar neutrino data including the neutral current event rate from sno .
the inclusion of the first sno nc data in the model independent analysis determines the allowed ranges of @xmath0 flux normalisation and the @xmath1 survival probability more precisely than what was possible from the sk and sno cc combination .
we perform global @xmath2 oscillation analyses of solar neutrino data using the nc rate instead of the ssm prediction for the @xmath0 flux , in view of the large uncertainty in the latter .
the lma gives the best solution , while the low solution is allowed only at the @xmath3 level .
* implications of the first neutral current data from sno for solar neutrino oscillation * abhijit bandyopadhyay@xmath4 , sandhya choubey@xmath5 , srubabati goswami@xmath6 , d.p .
roy@xmath7 @xmath4saha institute of nuclear physics , bidhannagar , kolkata 700 064 , india + @xmath5 department of physics and astronomy , university of southampton , highfield , southampton s017 1bj , uk + @xmath8 harish - chandra research institute , chhatnag road , jhusi , allahabad - 211 - 019 , india @xmath9tata institute of fundamental research , homi bhabha road , mumbai 400 005 , india + @xmath10physics department , university of california , riverside , ca 92521,usa the neutral current results from the sudbury neutrino observatory measures for the first time the total flux of @xmath0 neutrinos coming from the sun @xcite . in a recent paper @xcite we had examined the role of the anticipated nc data from sno in enhancing our understanding of the solar neutrino problem .
the sno nc rate can be expressed in terms of sno cc and sk elastic scattering rates as @xcite r^nc_sno = r^cc_sno + ( r^el_sk - r^cc_sno)/r , [ one ] where @xmath11 for a threshold energy of 5 mev ( including the detector resolutions and the radiative corrections to @xmath12 scattering cross - sections ) .
all the rates are defined with respect to the bbp2000 standard solar model ( ssm ) @xcite .
we showed in @xcite that because sno has a greater sensitivity to the nc scattering rate as compared to sk , the sno nc measurement will be more precise and hence incorporation of this can be more predictive than the sno cc and sk combination .
we took three representative nc rates @xmath13 = 0.8,1.0 and 1.2 ( @xmath14 ) and showed that 1 . for a general transition of @xmath1 into a mixture of active and sterile neutrinos the size of the sterile component
can be better constrained than before .
2 . for transition to a purely active neutrino the @xmath15 neutrino flux normalisation and the survival probability @xmath16
are determined more precisely .
3 .
we had also performed global two flavour oscillation analysis of the solar neutrino data for the @xmath17 case , where instead of @xmath18 and @xmath19 we used the quantities @xmath20 and @xmath21 .
these ratios are independent of the @xmath22 flux normalisation and hence of the ssm uncertainty .
we showed that use of these ratios can result in drastic reduction of the allowed parameter regions specially in the low - qvo area depending on the value of the nc rate .
we now have the actual experimental result r^nc_sno = 1.01 0.12 while eq .
( [ one ] ) gives @xmath23 .
thus in 306 live days ( 577 days ) the sno nc measurement has achieved a precision , which is already better than that obtained from the sk and sno cc combination .
this paper follows closely the analysis that we have done in @xcite but incorporating the actual data .
in addition we also perform an alternative global analysis for @xmath17 oscillation by letting the @xmath0 normalisation factor @xmath24 vary freely , where the inclusion of @xmath25 in the fit serves to control this parameter .
as we shall see below the two methods of global analysis give very similar results .
in section 1 we discuss the constraints on the electron neutrino survival probability , the @xmath0 normalisation factor @xmath24 and the fraction of sterile component without assuming any particular model for the probabilities . in section 2
we perform the global analyses assuming two flavour @xmath26 oscillation . |
the sunspot number is the solar index most frequently used in the study of long - term solar activity variations and , even more so , in solar - terrestrial relation studies .
the relative sunspot number was defined by rudolf wolf @xcite as @xmath0 where @xmath1 is the number of sunspot groups , @xmath2 is the total number of ` spots ' in all the groups on the visible disk , and @xmath3 is a scale factor to bring the number on to wolf s scale ( thus @xmath4 for wolf himself ) .
it would seem that @xmath1 and @xmath2 should be uniquely determined simply by counting and that a @xmath3-factor would not be necessary .
however , different observers - even using the same instrument - may differ in how they overcome variable seeing and arrive at different numbers of groups .
even more so for the number of spots , where the very definition of what should be counted as a spot may vary from observer to observer .
issues here are the distinction between spots with penumbrae and pores without , the treatment of spots that touch each other , different weighting according to size , whether to count all spots or only the larger ones , observer acuity and snellen ratio , etc .
different observers have different answers to , preferences of , and opinions about these issues . with an appropriate @xmath3-factor
their observed counts are , presumably , reduceable to the wolf - scale .
there is some confusion as to the precise meaning of the reduction factor . strictly speaking
, it should only apply to the standard instrument : 8 cm refractor at magnification 64 . to compensate for a larger or smaller telescope an additional factor should be employed . in practice
this is too cumbersome and the additional factor is folded into the @xmath3-factor . for a detailed discussion of these issues
see @xcite and @xcite .
the f10.7 cm ( 2.8 ghz ) solar index , introduced by covington in 1947 is generally viewed as an excellent index of solar activity @xcite .
the basic minimum level of emission around 67 sfu ( solar flux unit = @xmath5 w m@xmath6 hz@xmath7 ) is presumed to come from the quiet background sun .
an @xmath8-component due to solar activity on time scales longer than those of flares is fashioned into the f10.7 index measured and maintained by the solar radio monitoring programme operated jointly by the national research council and natural resources canada ( http://www.spaceweather.gc.ca/sx-eng.php ) .
routine observations at 1.0 , 2.0 , 3.75 , and 9.4 ghz straddling the 2.8 ghz frequency of the canadian series have been made in japan since the 1950s ( ftp://solar.nro.nao.ac.jp/pub/norp/data ) .
the two microwave datasets [ suitably scaled ] compare favorably with one another and testify to the stability ( to within the accuracy of the measurements ) of the calibration of both @xcite .
in a short 1971 paper , max waldmeier @xcite pointed out that the zrich standard scale [ of the relative sunspot numbers ] has never been calibrated in an objective way " .
he went on to note that the close correlation between monthly , and especially yearly , means of the solar microwave emission at 10.7 cm wavelength and the sunspot numbers yields a possibility of an objective calibration of the scale of the relative sunspot numbers .
figure [ f - relation ] shows the tight relationship [ linear for sunspot number greater than 25 ] deduced by waldmeier for the interval 1947 - 1970 ( black dots ) .
he remarks that as long as this relation holds , the zrich series of sunspot - numbers may be considered to be homogeneous .
if this relation should be subject to changes in the time to come , then the reduction factor used hitherto ought to be changed in such a way that the old r - f relation is reestablished " .
figure [ f - relation ] also shows the relation since 1996 derived from the international sunspot number as determined by sidc ( red dots , http://sidc.oma.be/data/yearssn.dat ) .
the data for the intervening interval 1971 - 1995 are shown as gray dots and open red squares .
it is clear that the recent sunspot numbers no longer follow the relationship found by waldmeier and that therefore , perhaps ,
the reduction factor used hitherto ought to be changed in such a way that the old r - f relation is reestablished " . on the other hand
it is also possible that the sunspot number as currently defined simply is no longer a suitable measure of solar activity , given the progressive discrepancy with the f10.7 flux .
a similar conclusion was reached by @xcite and @xcite based on monthly values .
one can speculate that the reason for this is the recent reduced visibility of sunspots due to diminished contrast to the surrounding photosphere reported by @xcite on account of weaker magnetic field and increased temperature .
recent measurements appear to confirm those trends as seen in figure [ f - umbral ] [ livingston , personal communication ] .
should such deviations from ` normal ' observed sunspot activity be substantiated in the near future , the question naturally arises whether [ and when ] they might have occurred in the past as well , _
e.g. _ during the maunder minimum , 1645 - 1715 .
i thank bill livingston for his measurements of umbral magnetic field and intensities .
i acknowledge the use of sunspot data from sidc , rwc belgium , world data center for the sunspot index , royal observatory of belgium . and of f10.7 cm flux from national research council and natural resources , canada .
penn , m. j. , and w. livingston ( 2006 ) , temporal changes in sunspot umbral magnetic fields and temperatures , _ astrophys .
journal , _ _
649(1 ) _ , l45-l48 , doi : 10.1068/508345 .
hossfield , c. h. ( 2001 ) , a history of the zurich and american relative sunspot number indices , _
star obs . , _
_ 30 _ , 48 - 53 .
schaefer , b. e. ( 1993 ) , visibility of sunspots , _ astrophys .
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svalgaard , l. , and h. s. hudson ( 2010 ) , the solar microwave flux and the sunspot number , _ soho-23 : understanding a peculiar solar minimum , asp conference series _ ,
eds . : s. r. cranmer , j. t. hoeksema , and j. l. kohl , _ 428 _ , 325 - 328 . tapping ,
k. f. , and d. p. charrois ( 1994 ) , limits to the accuracy of the 10.7 cm flux , _ solar phys . , _ _ 150 _ , 305 - 315 . tapping , k. f. , ( 2010 ) , properties of the sunspot number and the 10.7 cm solar flux activity indices , their interrelationship and unusual behaviour since the year 2000 , _ sorce meeting 2010 , keystone , co. _ http://lasp.colorado.edu/sorce/news/2010sciencemeeting/doc/session6/6.03_tapping_f10.7.pdf .
waldmeier , m. ( 1971 ) , an objective calibration of the scale of sunspot - numbers , _ astron . mitt .
sternwarte zrich , _ _ 304 _ , pp10 , [ also available at http://www.leif.org/research/w-ccciv.pdf ] . wolf , j. r. ( 1856 ) , mittheilungen ber der sonnenflecken , _ astron .
sternwarte zrich , _ _ 2 _ , pp13 .
centerline in the darkest part of 1565 sunspot umbrae ( years 1990 - 2010 ) and of the umbral intensity [ small pink dots ] relative to nearby non - spot photosphere ( livingston , 2010 , personal communication ) .
the larger blue and pink circles show yearly mean values .
, title="fig : " ] | @xcite found a very tight relationship between the f10.7 solar radio flux and the sunspot number and suggested using the flux for an objective calibration of the sunspot number .
he suggested that if this relationship changed later on , the sunspot number should be re - calibrated , assuming that the calibration must have drifted with time .
i repeat his analysis using data up to the present and it is , indeed , clear that the relationship has changed significantly
. this could be due to a drift of the calibration or to a secular change in the visibility of sunspots , or both . |