Casimir energy of a dilute dielectric ball at zero and finite temperature

TL;DR

This paper calculates the thermodynamic functions of electromagnetic fields around a dilute dielectric ball at various temperatures, using Bessel function summation, and explores their behavior in different temperature regimes.

Contribution

It provides a comprehensive analysis of the thermodynamic properties of a dielectric ball at zero and finite temperatures, including a corrected low-temperature expansion.

Findings

Recovered the $T^3$-term in the low temperature free energy expansion

Derived closed-form expressions for thermodynamic functions

Analyzed high and low temperature behavior of the system

Abstract

The basic results in calculations of the thermodynamic functions of electromagnetic field in the background of a dilute dielectric ball at zero and finite temperature are presented. Summation over the angular momentum values is accomplished in a closed form by making use of the addition theorem for the relevant Bessel functions. The behavior of the thermodynamic characteristics in the low and high temperature limits is investigated. The $T^3$-term in the low temperature expansion of the free energy is recovered (this term has been lost in our previous calculations).