Calculation of nonzero-temperature Casimir forces in the time domain

TL;DR

This paper introduces a method to compute nonzero-temperature Casimir forces using time-domain electromagnetic simulations, with minimal modifications from zero-temperature approaches, validated against analytical and numerical results.

Contribution

The paper presents a novel adaptation of time-domain simulations for nonzero-temperature Casimir force calculations, including handling the zero-frequency contribution.

Findings

Validated the method against analytical and numerical calculations.

Discovered high-temperature disappearance of non-monotonic behavior.

Demonstrated minimal modifications needed from zero-temperature methods.

Abstract

We show how to compute Casimir forces at nonzero temperatures with time-domain electromagnetic simulations, for example using a finite-difference time-domain (FDTD) method. Compared to our previous zero-temperature time-domain method, only a small modification is required, but we explain that some care is required to properly capture the zero-frequency contribution. We validate the method against analytical and numerical frequency-domain calculations, and show a surprising high-temperature disappearance of a non-monotonic behavior previously demonstrated in a piston-like geometry.