The Casimir effect for the Bose-gas in slabs

Martin, Philippe A.; Zagrebnov, Valentin A.

doi:10.1209/epl/i2005-10357-x

Cited by 57 publications

(105 citation statements)

References 14 publications

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“…The cases of periodic, antiperiodic, Dirichlet-Dirichlet, Dirichlet-Neumann, and Neumann-Neumann boundary conditions For the case of the ideal Bose gas (with n = 1 components) the scaling functions Υ P d , Υ DD d , and Υ NN d can be gleaned from [7]. Since their n > 1 analogs follow upon multiplication by n, we set n = 1 unless stated otherwise (see Sec.…”

Section: Scaling Functions Of the Ideal Bose Gasmentioning

confidence: 99%

“…(3.31) These results (3.29) and (3.31) are consistent with the integral expressions given in Eq. (11) of [7] for the total surface contributions of ϕ BC d=3 for DDBCs and NNBCs. They also imply that the surface contribution of ϕ d vanishes for DNBCs.…”

Section: B Case Of Robin Boundary Conditionsmentioning

confidence: 99%

“…(1.9) In [7], the ideal Bose gas functions Υ BC d=3 were computed at d = 3 for the bulk disordered phase µ < 0 in the form of double series. The asymptotic scaling forms of the functions ϕ BC res,d for ξ → ∞ are expected to be independent of quantum effects.…”

Section: Introductionmentioning

confidence: 99%

“…that was used in the calculation of [7] for DDBCs and NNBCs at d Here, we complete our calculations of the scaling func-…”

mentioning

confidence: 99%

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Fluctuation-induced forces in confined ideal and imperfect Bose gases

Diehl

Rutkevich

2017

Phys. Rev. E

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Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d-dimensional films of size ∞ d−1 × D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions, are determined for the ideal gas case with these BCs, where λ th and ξ are the thermal de-Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functionsξ ) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O(2) theory for BC = P, A, DD, DN, NN. For d = 3, they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions Υ BC d (x λ , x ξ , c1D, c2D) and Θ R d (x ξ , c1D, c2D) under the RBCs (∂z − c1)φ|z=0 = (∂z + c2)φ|z=D = 0 with c1 ≥ 0 and c2 ≥ 0 are also determined. The corresponding scaling functions Υ P ∞,d (x λ , x ξ ) and Θ P ∞,d (x ξ ) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n → ∞. Hence, for d = 3, Θ P ∞,d (x ξ ) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n → ∞ of this interacting Bose gas. Numerically and analytically exact results for the scaling function Θ DD ∞,3 (x ξ ) therefore follow from those of the O(2n) φ 4 model for n → ∞.

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Section: Scaling Functions Of the Ideal Bose Gasmentioning

confidence: 99%

Section: B Case Of Robin Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…that was used in the calculation of [7] for DDBCs and NNBCs at d Here, we complete our calculations of the scaling func-…”

mentioning

confidence: 99%

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Fluctuation-induced forces in confined ideal and imperfect Bose gases

Diehl

Rutkevich

2017

Phys. Rev. E

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“…The Casimir effect for massive quantum particles is less explored than its counterpart for the photon gas [2], but the Casimir effect in a confined Bose-Einstein condensate (BEC) system caused by the quantum fluctuations of the ground state at zero temperature or thermal fluctuations at finite temperature has recently attracted considerable interest [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The Casimir effect caused by thermal fluctuations in a Bose gas confined by two slabs was studied under the Dirichlet, Neumann, and periodic boundary conditions by Martin and Zagrebnov [2]. The asymptotic expressions of the grand potential with a universal Casimir term [2], the relationship between the thermodynamic Casimir effect in the Bose gas slabs and the critical Casimir forces [3][4][5], and the scaling function [6] for an ideal Bose gas in the case of the Dirichlet boundary condition were obtained.…”

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confidence: 99%

Casimir effect of an ideal Bose gas trapped in a generic power-law potential

Lin¹,

Su²,

Wang³

et al. 2012

EPL

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-The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T T c (where T c is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T T c  , the Casimir force is an exponential decay function; and when T T c  , the Casimir force vanishes.The original Casimir effect [1] shows that zerotemperature quantum fluctuations in an electromagnetic vacuum give rise to an attractive force between two closely spaced perfectly conducting plates. It is a pure quantum effect because there is no force between the plates in classical electrodynamics. The Casimir effect for massive quantum particles is less explored than its counterpart for the photon gas [2], but the Casimir effect in a confined Bose-Einstein condensate (BEC) system caused by the quantum fluctuations of the ground state at zero temperature or thermal fluctuations at finite temperature has recently attracted considerable interest [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The Casimir effect caused by thermal fluctuations in a Bose gas confined by two slabs was studied under the Dirichlet, Neumann, and periodic boundary conditions by Martin and Zagrebnov [2]. The asymptotic expressions of the grand potential with a universal Casimir term [2], the relationship between the thermodynamic Casimir effect in the Bose gas slabs and the critical Casimir forces [3][4][5], and the scaling function [6] for an ideal Bose gas in the case of the Dirichlet boundary condition were obtained. The Casimir effect of an ideal Bose gas was also considered at finite temperatures with or without traps for the Dirichlet boundary condition [8,9].By using the field-theoretical method [6,7] for the plate geometry instead of the thermodynamic method, it became possible to consider the Casimir effect of a weakly interacting Bose gas. Recently, the Casimir force due to zero-temperature quantum fluctuations and thermal fluctuations at finite temperature of a weakly-interacting dilute BEC confined by a pair of parallel plates with Dirichlet and periodic boundary conditions was also investigated [10][11][12][13]. In addition, it has been noted [10,12] that the quasiparticle vacuum in a zerotemperature dilute weakly-interacting BEC should give rise to a measurable Casimir force.

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Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase

Aydıner

2020

Annalen der Physik

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In this study, ideal free and harmonically trapped Bose gases confined by two plates in the x-y-plane in-between distance d are considered. The Casimir potential is obtained from the grand canonical potential of these quantum Bose gases for the Zaremba and the anti-periodic boundary conditions. The Casimir force is then obtained for the Bose-Einstein condensate phase T ≤ T c and for the non-condensate phase T > T c. It is shown that Casimir forces are repulsive for these boundary conditions. Additionally, it is shown that Casimir forces exponentially decay in the non-condensate phase T > T c with the decay lengths. These decay lengths were discussed and compared for different boundary conditions. As a result, new results are obtained for harmonically trapped Bose gas and the free gas results are compared with previous results.

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The Casimir effect for the Bose-gas in slabs

Cited by 57 publications

References 14 publications

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Casimir effect of an ideal Bose gas trapped in a generic power-law potential

Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase

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