Comment on “The Casimir effect for the Bose-gas in slabs” by P. A. Martin and V. A. Zagrebnov. Relation between the thermodynamic Casimir effect in Bose-gas slabs and critical Casimir forces

Gambassi, Andrea; Dietrich, S.

doi:10.1209/epl/i2006-10021-1

Cited by 31 publications

(40 citation statements)

References 4 publications

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“…The authors of [18] furthermore showed that these functions agree with those previously determined for a free Gaussian theory with an n-component real-valued order parameter φ [19] for the choice n = 2.…”

Section: Introductionsupporting

confidence: 77%

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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: Introductionsupporting

confidence: 77%

“…This was pointed out and verified in [18]. We have explicitly shown that the same holds true for ABCs, DNBCs, and RBCs.…”

supporting

confidence: 73%

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Diehl

Rutkevich

2017

Phys. Rev. E

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“…We now compare the above result with the analogous properties of the decay length κ imp of the thermodynamic Casimir force derived by us in [32]. The thermodynamic Casimir force can be presented with the help of the scaling function Υ(z) [10,32]…”

Section: Imperfect Bose Gasmentioning

confidence: 60%

The Bulk Correlation Length and the Range of Thermodynamic Casimir Forces at Bose-Einstein Condensation

Napiórkowski

Piasecki

2012

J Stat Phys

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The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length and the correlation length are the same, equal to 1/2 for the perfect gas, and 1 for the imperfect gas.

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“…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].…”

mentioning

confidence: 99%

“…between the two slabs are no longer long-ranged; therefore, the confining boundaries are subject to a vanishing Casimir force [3].…”

mentioning

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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Comment on “The Casimir effect for the Bose-gas in slabs” by P. A. Martin and V. A. Zagrebnov. Relation between the thermodynamic Casimir effect in Bose-gas slabs and critical Casimir forces

Cited by 31 publications

References 4 publications

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Fluctuation-induced forces in confined ideal and imperfect Bose gases

The Bulk Correlation Length and the Range of Thermodynamic Casimir Forces at Bose-Einstein Condensation

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

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