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arXiv:1712.08200 · Journal of Statistical Mechanics Theory and Experiment

Repulsive Casimir force in Bose–Einstein Condensate

Mir Mehedi Faruk, Shovon Biswas

Published Apr 1, 2018• 17 citations
arXivHTMLPDF

Abstract

Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.

DOI
10.1088/1742-5468/aab01b

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Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.
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.
Abstract 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 and for the non‐condensate phase . 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 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.
The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T c , where T c is the critical temperature of the Bose—Einstein condensation.
The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.
Abstract We study the thermal Casimir effect in ideal Bose gases with spin–orbit (S–O) coupling of Rashba type below the critical temperature for Bose–Einstein condensation. In contrast to the standard situation involving no S–O coupling, the system exhibits long-ranged Casimir forces in both two and three dimensions ( d = 2 and d = 3). We identify the relevant scaling variable involving the ratio D / ν of the separation between the confining walls D and the S–O coupling magnitude ν . We derive and discuss the corresponding scaling functions for the Casimir energy. In all the considered cases, the resulting Casimir force is attractive and the S–O coupling ν has impact on its magnitude. In d = 3 the exponent governing the decay of the Casimir force becomes modified by the presence of the S–O coupling, and its value depends on the orientation of the confining walls relative to the plane defined by the Rashba coupling. In d = 2 the obtained Casimir force displays a singular behavior in the limit of vanishing ν .