Casimir effect of an ideal Bose gas trapped in a generic power-law potential

TL;DR

This paper systematically investigates the Casimir effect for an ideal Bose gas in a generic power-law potential, analyzing how the Casimir force varies with temperature and boundary conditions, including special cases like free and harmonic traps.

Contribution

It introduces a comprehensive analysis of the Casimir effect in Bose gases under generic power-law potentials, deriving the scaling function and exploring temperature-dependent behaviors.

Findings

Casimir force decays as a power-law below Tc

Casimir force exhibits exponential decay above Tc

Casimir force vanishes when T is much greater than Tc

Abstract

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<Tc (where Tc is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T>Tc, the Casimir force is an exponential decay function; and when T>>Tc, the Casimir force vanishes.