Behavior of heat capacity of an attractive Bose-Einstein condensate approaching collapse

Goswami, Sanchari; Das, Tapan Kumar; Biswas, Anindya

doi:10.1103/physreva.84.053617

Cited by 10 publications

(6 citation statements)

References 23 publications

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“…(69). There has been a lively discussion of the influence of the shape and dimensionality of the confining potential on the existence, form and evolution of this feature [6,31,33,35,36,[40][41][42][43]. As our results show, the sharpness of the resonance can be effectively controlled by the voltage applied to the attractive Robin surface.…”

Section: Bosonsmentioning

confidence: 63%

“…10(a) demonstrate. The cusp-like structure of the heat capacity that was predicted theoretically for a number of the confining potentials [35,36,[40][41][42][43] and observed experimentally for, e.g., the dilute Bose gas of 87 Rb atoms [44], for the infinite number of particles, N = ∞, turns at T = T cr into the discontinuity that is a manifestation of the phase transition; in our case, it is a transition from the BE condensate to the normal phase of the noninteracting particles in the linear potential. This justifies the definition of the critical temperature from Eq.…”

Section: Bosonsmentioning

confidence: 99%

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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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Section: Bosonsmentioning

confidence: 63%

Section: Bosonsmentioning

confidence: 99%

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

Olendski

2016

Annalen der Physik

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“…Another method to arrive at it is to zero the denominator in Equation (56) what results in infinite specific heat at the transition point. This highly asymmetric cusp-like shape of the specific heat was intensively analyzed theoretically [4,5,65,67,69,70,[91][92][93][94] and demonstrated experimentally. At the infinite number of bosons, N = ∞, the cusp-like shape at T = T cr becomes a discontinuity disclosing in this way a phase transition; namely, in this particular situation, it is a transition from the BE condensate to the normal phase of the noninteracting corpuscles in the asymmetric Robin QW.…”

Section: Bosonsmentioning

confidence: 94%

“…At the infinite number of bosons, N = ∞, the cusp-like shape at T = T cr becomes a discontinuity disclosing in this way a phase transition; namely, in this particular situation, it is a transition from the BE condensate to the normal phase of the noninteracting corpuscles in the asymmetric Robin QW. This highly asymmetric cusp-like shape of the specific heat was intensively analyzed theoretically [4,5,64,66,68,69,[90][91][92][93] and demonstrated experimentally [94]. For the single Robin wall with the negative extrapolation length, it was shown that the sharpness of this feature can be effectively controlled by the applied voltage [4].…”

Section: Bosonsmentioning

confidence: 94%

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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“…Note that throughout this study the density n is kept fixed, thus T 0 serves below as a scaling unit in all temperature and energy-related dependencies. In contrast, the effect of finite number of particles and the trap curvature in the weakly-intaracting Bose gas above the transition temperature can be found, e.g., in [16,17].…”

Section: Formalismmentioning

confidence: 95%

Thermodynamics of a weakly interacting Bose gas above the transition temperature

et al. 2021

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We study thermodynamic properties of weakly interacting Bose gases above the transition temperature of Bose–Einstein condensation in the framework of a thermodynamic perturbation theory. Cases of local and non-local interactions between particles are analyzed both analytically and numerically. We obtain and compare the temperature dependencies for the chemical potential, entropy, pressure, and specific heat to those of noninteracting gases. The results set reliable benchmarks for thermodynamic characteristics and their asymptotic behavior in dilute atomic and molecular Bose gases above the transition temperature.

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Behavior of heat capacity of an attractive Bose-Einstein condensate approaching collapse

Cited by 10 publications

References 23 publications

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

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

Thermodynamic Properties of the 1D Robin Quantum Well

Thermodynamics of a weakly interacting Bose gas above the transition temperature

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