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Annalen der Physik

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

Ekrem Aydıner

Published Jul 1, 2020• 7 citations
Publisher

Abstract

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.

DOI
10.1002/andp.202000178

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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.
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.
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.
In this study, we have derived close form of the Casimir force for the non-interacting ideal Bose gas between two slabs in harmonic-optical lattice potential by using Ketterle and van Druten approximation. We find that Bose-Einstein condensation temperature TcT_{c}Tc​ is a critical point for different physical behavior of the Casimir force. We have shown that Casimir force of confined Bose gas in the presence of the harmonic-optical potential decays with inversely proportional to d5d^{5}d5 when T≤TcT\leq T_{c}T≤Tc​. However, in the case of T>TcT>T_{c}T>Tc​, it decays exponentially depends on separation ddd of the slabs. Additionally we have discussed temperature dependence of Casimir force and importance of the harmonic-optical lattice potential on quantum critical systems, quantum phase transition and nano-devices.
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.