Bose-Einstein Condensation and Casimir Effect of Trapped Ideal Bose Gas in between two Slabs

TL;DR

This paper investigates Bose-Einstein condensation and the Casimir effect in a 3D ideal Bose gas confined between slabs with harmonic trapping, analyzing temperature dependence and boundary conditions.

Contribution

It provides a detailed analysis of the Casimir force in a harmonically trapped Bose gas with slab confinement, highlighting temperature effects and boundary condition impacts.

Findings

Casimir force decreases with temperature below T_c

At T ≳ T_c, Casimir force becomes temperature-independent

The force depends on Planck's constant due to trapping and confinement

Abstract

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of $\hbar$. At finite temperatures the Casimir force for our system depends on $\hbar$. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature($T_c$) the Casimir force for this non-interacting system decreases with temperature($T$) and at $T\gtrsim T_c$, it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.