Bohr-van Leeuwen theorem and the thermal Casimir effect for conductors

TL;DR

This paper investigates the thermal Casimir effect for conductors, showing that the Bohr-van Leeuwen theorem constrains the low-frequency behavior of the TE reflection coefficient, impacting theoretical models of thermal corrections.

Contribution

It demonstrates that the Bohr-van Leeuwen theorem requires the TE reflection coefficient to vanish at zero frequency, challenging some existing models of thermal Casimir corrections.

Findings

The TE reflection coefficient must vanish at zero frequency for classical consistency.

Some recent models for thermal Casimir effects are incompatible with the Bohr-van Leeuwen theorem.

The theorem constrains the low-frequency extrapolation of reflection coefficients in Casimir physics.

Abstract

The problem of estimating the thermal corrections to Casimir and Casimir-Polder interactions in systems involving conducting plates has attracted considerable attention in the recent literature on dispersion forces. Alternative theoretical models, based on distinct low-frequency extrapolations of the plates reflection coefficient for transverse electric (TE) modes, provide widely different predictions for the magnitude of this correction. In this paper we examine the most widely used prescriptions for this reflection coefficient from the point of view of their consistency with the Bohr-van Leeuwen theorem of classical statistical physics, stating that at thermal equilibrium transverse electromagnetic fields decouple from matter in the classical limit. We find that the theorem is satisfied if and only if the TE reflection coefficient vanishes at zero frequency in the classical limit. This criterion appears to rule out some of the models that have been considered recently for describing the thermal correction to the Casimir pressure with non-magnetic metallic plates.