Bose-Einstein condensation and Casimir effect for ideal Bose Gas confined between two slabs

TL;DR

This paper investigates the temperature-dependent Casimir effect for an ideal Bose gas confined between two slabs, revealing how the force varies across the Bose-Einstein condensation temperature and its quantum or classical nature.

Contribution

It provides a detailed analysis of the Casimir force behavior in a Bose gas system across different temperature regimes, including the effects of Bose-Einstein condensation.

Findings

Casimir force vanishes as (T/Tc)^{3/2} below Tc

Force weakly depends on temperature just above Tc

Force vanishes exponentially at high temperatures

Abstract

We study the Casimir effect for a 3-d system of ideal Bose gas in a slab geometry with Dirichlet boundary condition. We calculate the temperature($T$) dependence of the Casimir force below and above the Bose-Einstein condensation temperature($T_c$). At $T\le T_c$ the Casimir force vanishes as $[\frac{T}{T_c}]^{3/2}$. For $T\gtrsim T_c$ it weakly depends on temperature. For $T\gg T_c$ it vanishes exponentially. 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 $\hbar$.