Casimir Force Between Dielectric Media with Free Charges

TL;DR

This paper develops a statistical mechanical approach to calculate the Casimir force between dielectric media with free charges, generalizing previous models to include constant permittivity and different geometries, and confirms results with existing theories.

Contribution

It extends earlier Casimir force models by incorporating dielectric permittivity and analyzing various geometries, including parallel plates and spherical dielectrics, at high temperature.

Findings

Generalized Casimir force calculations for dielectric media with free charges.

Confirmed agreement with Pitaevskii's recent results for particle-conductor interactions.

Provided a unified framework for different geometries and dielectric properties.

Abstract

The statistical mechanical approach to Casimir problems for dielectrics separated by a vacuum gap turns out to be compact and effective. A central ingredient of this method is the effect of interacting fluctuating dipole moments of the polarizable particles. At arbitrary temperature the path integral formulation of quantized particles, developed by H{\o}ye-Stell and others, is needed. At high temperature - the limit considered in the present paper - the classical theory is however sufficient. Our present theory is related to an idea put forward earlier by Jancovici and {\v{S}}amaj (2004), namely to evaluate the Casimir force between parallel plates invoking an electronic plasma model and the Debye-H\"uckel theory for electrolytes. Their result was recently recovered by H{\o}ye (2008), using a related statistical mechanical method. In the present paper we generalize this by including a constant permittivity in the description. The present paper generalizes our earlier theory for parallel plates (1998), as well as for spherical dielectrics (2001). We also consider the Casimir force between a polarizable particle and a conductor with a small density of charges, finding agreement with the result recently derived by Pitaevskii (2008).