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Journal of Experimental and Theoretical Physics

Casimir and Surface Tension Forces on a Single Interacting Bose–Einstein Condensate in Canonical Ensemble

Nguyễn Văn Thụ, Luong Thi Theu, Dang Thanh Hai

Published Mar 1, 2020• 8 citations
Publisher

Abstract

Abstract The forces on a single Bose–Einstein condensate confined between two parallel plates consist of two components, namely, surface tension force and Casimir force. In canonical ensemble, these forces are quite different from the one in grand canonical ensemble. In small region with distance $$\ell $$ between two parallel plates, using double parabola approximation, we find that surface tension force decreases as $${{\ell }^{{ - 3}}}$$, whereas the Casimir force, in one-loop approximation of the quantum field, is proportional to $${{\ell }^{{ - 13/2}}}$$. The total force is also considered and its veer is found.

DOI
10.1134/s1063776120020168

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Abstract The forces on a single Bose–Einstein condensate confined between two parallel plates consist of two components, namely, surface tension force and Casimir force. In canonical ensemble, these forces are quite different from the one in grand canonical ensemble. In small region with distance ℓ\ell ℓ between two parallel plates, using double parabola approximation, we find that surface tension force decreases as ℓ−3{{\ell }^{{ - 3}}}ℓ−3, whereas the Casimir force, in one-loop approximation of the quantum field, is proportional to ℓ−13/2{{\ell }^{{ - 13/2}}}ℓ−13/2. The total force is also considered and its veer is found.
In this study, we consider motion of the massive and charged Bose gas trapped in electric and magnetic fields between two parallel plates in the x−yx-yx−y plane that are separated by a distance ddd in the zzz direction. We derive analytical expression of the grand canonical potential of the quantum particles by using of Ketterle and van Druten approximation. By evaluating canonical potential, we obtain Casimir potential and force at the Bose-Einstein condensation temperature TcT_{c}Tc​. We also show that Casimir force oscillates depends on distance ddd for fixed parameters.
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 By means of the Cornwall–Jackiw–Tomboulis effective potential formalism, the Casimir effect in binary Bose–Einstein condensate mixtures is investigated. The study conditions are that the mixtures are confined between two parallel plates at zero temperature and within the improved Hartree–Fock approximation featuring higher-order terms in the momentum integrals. Our results show that both effective masses and order parameters strongly depend on the distance between the two plates. The Casimir energy and resulting Casimir force are scrutinized, confirming that the contribution of the higher-order terms of the momentum integrals is significant. Importantly, the Casimir force is proved to be non-zero in limit of the full strong segregation, which is an acceptable answer for the controversial problem.
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.