The Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors

TL;DR

This paper investigates the validity of the Lifshitz-Matsubara sum formula for Casimir pressure between magnetic metallic mirrors, highlighting the importance of Foucault currents and the impact of material loss models.

Contribution

It clarifies the conditions under which the Lifshitz-Matsubara formula applies to magnetic metals and emphasizes the role of Foucault currents in the lossless limit.

Findings

The formula is valid for lossy models but not for lossless plasma models.

Foucault currents are crucial in the vanishing loss limit.

The role of magnetic properties in Casimir force calculations is elucidated.

Abstract

We examine the conditions of validity for the Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic plane mirrors. As in the previously studied case of non-magnetic materials (Guerout et al, Phys. Rev. E 90 042125), we recover the usual expression for the lossy model of optical response, but not for the lossless plasma model. We also show that the modes associated with the Foucault currents play a crucial role in the limit of vanishing losses, in contrast to expectations.