Casimir force induced by an imperfect Bose gas

Abstract

We present a study of the Casimir effect in an imperfect (mean-field) Bose gas contained between two infinite parallel plane walls. The derivation of the Casimir force follows from the calculation of the excess grand-canonical free energy density under periodic, Dirichlet, and Neumann boundary conditions with the use of the steepest descent method. In the one-phase region, the force decays exponentially fast when distance D between the walls tends to infinity. When the Bose-Einstein condensation point is approached, the decay length in the exponential law diverges with critical exponent ν(IMP) = 1, which differs from the perfect gas case where ν(P) = 1/2. In the two-phase region, the Casimir force is long range and decays following the power law D(-3), with the same amplitude as in the perfect gas.

Thermodynamic equivalence of two-dimensional imperfect attractive Fermi and repulsive Bose gases

“…In the following we give an answer to these questions by considering the model of the so-called imperfect, spinless quantum gases [5][6][7][8][9][10][11][12]. In the occupation number representation the Hamiltonian of the imperfect Fermi gas has the following form…”

“…∞. The model of imperfect quantum gases has been succesfully applied to repulsive bosons [5][6][7][8][9][10][11][12] where, inter alia, the Bose-Einstein condensation and the Casimir forces were discussed. In this paper we discuss both the attractive imperfect Fermi gas and the repulsive imperfect Bose gas and show their thermodynamic equivalence in two dimensions.…”

Fluctuation-induced forces in confined ideal and imperfect Bose gases

“…We will be concerned with three different Bose gas models on a film [0, L] d−1 × [0, D]: the ideal Bose gas, the imperfect Bose gas model investigated in [23], [38], and [39], and the interacting Bose gas with n internal degrees of freedom in the limit n → ∞. In the case of the ideal Bose gas, the interaction u(x) is zero.…”

“…It can be obtained by taking the limit γ → 0 of a repulsive integrable Kac-type pair potential such as u γ (x) = γ d e −γx whose strength and inverse range are both controlled by the same parameter γ > 0 [23,38,39]. This is analogous to the well-known rigorous derivation of the van der Waals theory for a classical gas of particles interacting through an attractive Kac pair potential and a repulsive hard core [40], and hence reveals the mean-field nature of the approximation to which the model corresponds.…”

Oscillating Casimir potential between two impurities in a spin-orbit-coupled Bose-Einstein condensate

“…The interplay between the impurity and the background many-body ground state can lead to many intriguing phenomena [11][12][13][14][15][16][17][18][19][20][21], such as the orthogonality catastrophe of a time-dependent impurity in ultracold fermions [22,23], an electron dressing Bose-Einstein condensate by a Rydberg-type impurity [24], and YuShiba-Rusinov state [25][26][27][28][29], etc. One of the remarkable effect is that an effective interaction may be induced between impurities via exchanging the virtual excitations of the underlying ground state fluctuations, which is also known as the Casimir effect [30][31][32][33][34][35].…”