Finite-size effect on Bose–Einstein condensate mixtures in improved Hartree–Fock approximation

Thụ, Nguyễn Văn; Theu, Luong Thi

doi:10.1142/s0217979219501145

Cited by 10 publications

(5 citation statements)

References 22 publications

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“…In recent years, the subject of the Casimir effect, and the corresponding Casimir force in Bose systems, have begun to gain attention [57][58][59][60][61][62][63][64][65][66][67][68][69]. Casimir force in ideal Bose gas with a film geometry has been studied in [58,59,61].…”

Section: Introductionmentioning

confidence: 99%

“…Prior to this, for the sake of completeness, we note that, in addition to the ideal Bose gas and the imperfect Bose gas, some results are available for the fluctuationinduced interaction between two impurities in a weakly-interacting one-dimensional Bose gas [66,68] and, more generally, in quantum liquids [57,60]. BEC mixtures have been objects of study in [65,67,69]. Furthermore, measurement of the Casimir-Polder force via the center-of-mass oscillations of a BEC has been reported in reference [75].…”

Section: Introductionmentioning

confidence: 99%

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Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry

Dantchev¹

2020

J. Stat. Mech.

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It has recently recently been suggested that a relativistic Bose gas of some type may play a role in issues such as dark matter, dark energy, and in some other cosmological problems. In this article, we investigate one known exactly solvable model of a three-dimensional statistical-mechanical model of relativistic Bose gas which takes into account the existence of both particles and antiparticles. We derive exact expressions for the behavior of the Casimir force for a system subjected to film geometry under periodic boundary conditions. We show that the Casimir force between the plates is attractive, monotonic as a function of the temperature scaling variable, and has a scaling function that, at low temperatures, approaches a universal negative constant equal to the corresponding one for two-component three-dimensional Gaussian system. The force decays with the distance in a power-law near and below the bulk critical temperature Tc of the Bose condensate, and exponentially above Tc. We obtain a closed-form exact expression for the Casimir amplitude . We establish the precise correspondence of the scaling function of the free energy of the model with the scaling functions of two other well-known models of statistical mechanics: the spherical model, and the imperfect Bose gas model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry

Dantchev¹

2020

J. Stat. Mech.

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“…Another method to investigate the Bose gas, including the quantum fluctuations is the Cornwall-Jackiw-Tomboulis (CJT) effective action approach [11]. Recently, this method has been widely employed to study the Casimir effect in Bose gas(es) [12,13] and condensate density [14] in improved Hartree-Fock (IHF) approximation. Furthermore, these works were done in the grand canonical ensemble [15].…”

Section: Introductionmentioning

confidence: 99%

Condensate Density of a Bose Gas Confined between Two Parallel Plates in Canonical Ensemble within Improved Hartree-Fock Approximation

Thụ

2020

MaP

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By means of Cornwall-Jackiw-Tomboulis (CJT) effective action approach, the condensate density of a dilute Bose gas is investigated in the canonical ensemble. Our results show that the condensate density is proportional to a half-integer power law of the s-wave scattering length and distance between two plates. Apart from that, these quantities also depend on the particle number and area of each plate.

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“…In the recent years the topics of the Casimir effect and the corresponding Casimir force in Bose systems that is gaining attention [18][19][20][21][22][23][24][25][26][27][28][29][30]. The Casimir force in ideal Bose gas has been studied in [19,20,22].…”

Section: Introductionmentioning

confidence: 99%

“…The fluctuation-induced interaction between two impurities in a weakly-interacting one-dimensional Bose gas have been studied in [27,29] and, more generally in quantum liquids in [18,21]. BEC mixtures are objects of study in [26,28,30]. Furthermore, measurement of the Casimir-Polder force through center-ofmass oscillations of a BEC has been reported in Ref.…”

Section: Introductionmentioning

confidence: 99%

Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry

Dantchev

2019

Preprint

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Recently it has been suggested that relativistic Bose gas of some type can be playing role in issues like dark matter, dark energy, and in some cosmological problems. In the current article we investigate one known exactly solvable model of three-dimensional statistical-mechanical model of relativistic Bose gas that takes into account the existence of both particles and antiparticles. We derive exact expressions for the behavior of the Casimir force for the system subjected to film geometry under periodic boundary conditions. We show that the Casimir force between the plates is attractive, monotonic as a function of the temperature scaling variable, with a scaling function that approaches at low temperatures a universal negative constant equal to the corresponding one for two-component three dimensional Gaussian system. The force decays with the distance in a power law near and below the bulk critical temperature T c of the Bose condensate and exponentially above T c . We obtain closed form exact expression for the Casimir amplitude ∆ RBG Cas = −4ζ(3)/(5π). We establish the precise correspondence of the scaling function of the free energy of the model with the scaling functions of two other well-known models of statistical mechanics -the spherical model and the imperfect Bose gas model.

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Finite-size effect on Bose–Einstein condensate mixtures in improved Hartree–Fock approximation

Cited by 10 publications

References 22 publications

Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry

Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry

Condensate Density of a Bose Gas Confined between Two Parallel Plates in Canonical Ensemble within Improved Hartree-Fock Approximation

Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry

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