New Correlation Length in Bose-Gas Models of Liquid Helium

Goble, D. F.; Trainor, L. E. H.

doi:10.1103/physrev.157.167

Cited by 27 publications

(15 citation statements)

References 8 publications

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“…Although the thermodynamics of finite volume systems has been well studied in classical nonrelativistic statistical mechanics [25][26][27][28][29][30][31][32][33], there appears to be some confusion in the literature in the context of relativistic field theory, particularly in the calculation of critical temperatures. After a brief review of the general theory presented in Refs.…”

Section: Introductionmentioning

confidence: 99%

Bose-Einstein condensation as symmetry breaking in compact curved spacetimes

Smith

Toms

1996

Phys. Rev. D

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We examine Bose-Einstein condensation as a form of symmetry breaking in the specific model of the Einstein static universe. We show that symmetry breaking never occurs in the sense that the chemical potential µ never reaches its critical value. This leads us to some statements about spaces of finite volume in general. In an appendix we clarify the relationship between the standard statistical mechanical approaches and the field theory method using zeta functions. 03.70.+k, 04.62.+v, 11.15.Ex, 11.30.Qc Typeset using REVT E X Bose-Einstein condensation (BEC) for non-relativistic spin-0 particles is standard textbook material [1-3]. In the infinite volume limit, there is a critical temperature at which a phase transition occurs. For a real system, such as liquid helium, the effects of interactions may be important. (See [4] for a recent review.) The study of Bose-Einstein condensation for relativistic bosons is more recent. In particular, Refs. [5][6][7] applied the methods of relativistic quantum field theory at finite temperature and density to study BEC. The phase transition, which occurs at high temperatures, can be interpreted as spontaneous symmetry breaking. Subsequent work [8,9] extended the analysis to self-interactions in scalar field theory.The generalization from flat Minkowski spacetime to curved spacetime has also been considered. The non-relativistic Bose gas in the Einstein static universe was given by Al'taie [10]. The extension to relativistic scalar fields was given for conformal coupling in Ref. [11] and for minimal coupling in Ref. [12]. The higher dimensional version of the Einstein static universe was studied by Shiraishi [13]. More recently, the case of hyperbolic universes [14] and the Taub universe [15] have received attention. Anti-de Sitter space was studied in Ref.[16] where some of the issues of our paper where considered from a different viewpoint.One advantage of dealing with specific spacetimes of the type mentioned above is that the eigenvalues of the Laplacian are known, and as a consequence the partition function and the thermodynamic potential can be obtained in closed form. Another approach to studying BEC is to try to keep the spacetime fairly general, and to calculate the thermodynamic potential only in the high temperature limit. This has been done by a variety of people [17][18][19][20][21][22][23]. In particular the symmetry breaking interpretation of BEC was given in Refs. [22,23]. The effects of interactions have been given recently [24].The purpose of the present paper is to re-examine BEC in the case where the spatial manifold is compact. We will be particularly concerned with the Einstein static universe for which the spatial manifold is S 3 . Because the volume is finite the general theory presented

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Section: Introductionmentioning

confidence: 99%

Bose-Einstein condensation as symmetry breaking in compact curved spacetimes

Smith

Toms

1996

Phys. Rev. D

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“…[29]) reignited a huge interest in the topic [30][31][32][33]. Relevant to our research, let us mention a theoretical analysis of the influence of the different forms of the confining potential [30,[34][35][36][37][38][39] and/or BC [6][7][8][9][10][11][12][13][14][15][16][17][18] on the properties of the ideal Bose gas. A quantitative measure of the BE condensation is provided by the ground state occupation n 0 (E ; β), i.e., a ratio of the number of bosons N 0 in the ground state Table 1: Peak values of the specific heat per particle c N max and temperatures β −1 max at which they are achieved for the canonical and several numbers of particles N of the two grand canonical ensembles at some weak electric fields to the total number of corpuscles in the system:…”

Section: Bosonsmentioning

confidence: 99%

“…(10) - (12) have to be multiplied by N . Before discussing the electric field influence on the thermodynamics of the system, it does make sense to analyze first a zero-voltage case.…”

Section: /3mentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Olendski

2016

Annalen der Physik

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A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length Λ in the electric field E that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage-free configuration support negative-energy bound state. For the canonical ensemble, the heat capacity at Λ < 0 exhibits a nonmonotonic behavior as a function of the temperature T with its pronounced maximum unrestrictedly increasing for the decreasing fields as ln 2 E and its location being proportional to (− ln E ) −1 . For the Fermi-Dirac distribution, the specific heat per particle cN is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the T axis by the plateau whose magnitude at the vanishing E is defined as 3(N − 1)/(2N )kB, with N being a number of the particles. The maximum of cN is the largest for N = 1 and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose-Einstein ensemble, a formation of the sharp asymmetric feature on the cN -T dependence with the increase of N is shown to be more prominent at the lower voltages. This cusp-like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of cN (T ), is an indication of the phase transition to the condensate state. Some other physical characteristics such as the critical temperature Tcr and ground-level population of the Bose-Einstein condensate are calculated and analyzed as a function of the field and extrapolation length. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.

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“…Equation (80) shows that the resonance rapidly sharpens on the T axis for the decreasing | | with its simultaneous shift to colder temperatures, as it follows from Equation (77). Both these features are vividly seen in Figure 7.…”

Section: Canonical Ensemblementioning

confidence: 64%

“…The latter rekindled the huge interest in the study of BE systems. [64][65][66][67] As a prerequisite to the analysis below, we would like to point out on the theoretical discussion of the influence of the miscellaneous forms of the confining potential [4,64,[68][69][70][71][72][73] and/or BCs [2,4,[74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90] (including Robin ones [86,88,89] ) on the properties of the noninteracting bosons. In the physics of the boson thermodynamics, in addition to heat capacity, two other important physical quantities are used: ground-state population n 0 and critical temperature β −1 cr .…”

Section: Bosonsmentioning

confidence: 99%

Thermodynamic Properties of the 1D Robin Quantum Well

Olendski

2018

Annalen der Physik

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The thermodynamic properties of the Robin quantum well with extrapolation length are analyzed theoretically both for the canonical and two grand canonical ensembles, with special attention being paid to the situation when the energies of one or two lowest-lying states are split off from the rest of the spectrum by the large gap that is controlled by the varying . For the single split-off level, which exists for the geometry with the equal magnitudes but opposite signs of the Robin distances on the confining interfaces, the heat capacity c V of the canonical averaging is a nonmonotonic function of the temperature T with its salient maximum growing to infinity as ln 2 for the decreasing to zero extrapolation length and its position being proportional to 1/( 2 ln ). The specific heat per particle c N of the Fermi-Dirac ensemble depends nonmonotonically on the temperature too, with its pronounced extremum being foregone on the T axis by the plateau, whose value at the dying is (N − 1)/(2N)k B , with N being the number of fermions. The maximum of c N , similar to the canonical averaging, unrestrictedly increases as goes to zero and is largest for one particle. The most essential property of the Bose-Einstein ensemble is the formation, for a growing number of bosons, of the sharp asymmetric shape on the c N −T characteristics, which is more protrusive at the smaller Robin distances. This cusp-like structure is a manifestation of the phase transition to the condensate state. For two split-off orbitals, one additional maximum emerges whose position is shifted to colder temperatures with the increase of the energy gap between these two states and their higher-lying counterparts and whose magnitude approaches a -independent value. All these physical phenomena are qualitatively and quantitatively explained by the variation of the energy spectrum by the Robin distance. Parallels with other structures are drawn and similarities and differences between them are highlighted. Generalization to higher dimensions is also provided.

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New Correlation Length in Bose-Gas Models of Liquid Helium

Abstract: 157 4.08 s O> 4.o4 4.oo -/ 1 ' P = 2.oo x 10 22 /cm 3 ooxosxD J 1 1 J ! J Thickness D in A

Cited by 27 publications

References 8 publications

Bose-Einstein condensation as symmetry breaking in compact curved spacetimes

Bose-Einstein condensation as symmetry breaking in compact curved spacetimes

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Thermodynamic Properties of the 1D Robin Quantum Well

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