On finite temperature Casimir effect for Dirac lattices

TL;DR

This paper investigates the finite temperature Casimir effect between polarizable Dirac lattices, analyzing the heat kernel expansion and high temperature behavior of the free energy for such periodic singular backgrounds.

Contribution

It introduces a model for polarizable sheets as delta function lattices and computes their Casimir interaction at nonzero temperature, linking heat kernel expansion to thermodynamic properties.

Findings

Derived the Casimir interaction for Dirac lattices at finite temperature.

Analyzed the high temperature asymptote of the free energy.

Discussed the heat kernel expansion for periodic singular backgrounds.

Abstract

We consider polarizable sheets modeled by a lattice of delta function potentials. The Casimir interaction of two such lattices is calculated at nonzero temperature. The heat kernel expansion for periodic singular background is discussed in relation with the high temperature asymptote of the free energy.