Finite Temperature Casimir Effect for a Dilute Ball Satisfying $\epsilon \mu =1$

Abstract

The finite temperature Casimir free energy is calculated for a dielectric ball of radius $a$ embedded in an infinite medium. The condition $\epsilon \mu =1$ 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 $\hat{\omega }={\omega }_0$, the high temperature Casimir free energy to be negative and proportional to $x_0\equiv {\omega }_{0}a$. Also, a physically more realistic dispersion relation involving spatial dispersion is considered, and is shown to lead to comparable results.

18 pages, 5 eps figures; minor extensions of the discussion in sect. 3; 5 new references. To appear in J. Phys. A: Math. Gen

References in corpus (2)

• Casimir's energy of a conducting sphere and of a dilute dielectric ball
• Casimir energy of a compact cylinder under the condition $\epsilon \mu =c^{-2}$

Cited by in corpus (4)

• Nonsmoothness of the boundary and the relevant heat kernel coefficients
• Heat kernel Coefficients and Divergencies of the Casimir Energy for the Dispersive Sphere
• Casimir effect for a dilute dielectric ball at finite temperature
• Divergencies in the Casimir energy for a medium with realistic ultraviolet behavior