Possible resolution of the Casimir force finite temperature correction "controversies"

TL;DR

This paper revises the finite temperature correction to the Casimir force by including diffusion effects, resolving previous controversies and thermodynamic inconsistencies, and analyzing Debye screening in germanium.

Contribution

It introduces a modified approach to the Casimir force correction at finite temperature, accounting for diffusion effects, and clarifies thermodynamic and experimental issues.

Findings

No large correction for good conductors as previously suggested

Thermodynamic violations are resolved with the new model

Debye screening effects are quantified for germanium surfaces

Abstract

By considering the effect of diffusion on the external electric field response of charge carriers in metals and semiconductors, it is shown that the finite temperature correction proposed Bostrom and Sernelius requires substantial modification, and there is no large correction as suggested for good conductors. The apparent violation of the Third Law of Thermodynamics of the various proposed temperature corrections to the Casimir force is also resolved. Finally, the effect of Debye screening on electrostatic calibrations between pure germanium surfaces is calculated