Finite Temperature Casimir Effect for a Dilute Ball Satisfying $εμ=1$

Abstract

The finite temperature Casimir free energy is calculated for a dielectric ball of radius $a$ embedded in an infinite medium. The condition $εμ=1$ is assumed for the inside/outside regions. Both the Green function method and the mode summation method are considered, and found to be equivalent. For a dilute medium we find, assuming a simple "square" dispersion relation with an abrupt cutoff at imaginary frequency $\hat ω= ω_0$, the high temperature Casimir free energy to be negative and proportional to $x_0 \equiv ω_0 a$. Also, a physically more realistic dispersion relation involving spatial dispersion is considered, and is shown to lead to comparable results.