High Temperature Asymptotics in Terms of Heat Kernel Coefficients: Boundary Conditions with Spherical and Cylindrical Symmetries

TL;DR

This paper develops a universal method using heat kernel coefficients to analyze high temperature asymptotics of electromagnetic fields with spherical and cylindrical boundary conditions, introducing new coefficients and confirming previous results.

Contribution

It introduces a general expansion approach for high temperature asymptotics using heat kernel coefficients, including new calculations for specific boundary conditions.

Findings

Reproduces known asymptotics with a new method

Calculates new heat kernel coefficients and determinants

Identifies additional terms in high temperature expansions

Abstract

The high temperature asymptotics of the Helmholtz free energy of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel coefficients and the related determinant. For this, some new heat kernel coefficients and determinants had to be calculated for the boundary conditions under consideration. The obtained results reproduce all the asymptotics derived by other methods in the problems at hand and involve a few new terms in the high temperature expansions. An obvious merit of this approach is its universality and applicability to any boundary value problem correctly formulated.