Casimir-Foucault interaction: Free energy and entropy at low temperature

TL;DR

This paper demonstrates that eddy current modes are responsible for the large low-temperature correction to the Casimir effect in Drude metals, explaining the discrepancy between theory and experiments.

Contribution

It explicitly shows that low-temperature corrections to the Casimir free energy are dominated by eddy current interactions, clarifying their role in thermodynamic anomalies.

Findings

Eddy current contributions match the leading low-temperature correction terms.

Casimir free energy separates into eddy current and propagating mode contributions.

Eddy currents explain the large temperature correction predicted but not observed experimentally.

Abstract

It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [Phys. Rev. Lett. 103, 130405 (2009)]. We show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates, are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that the Casimir free energy, as given by the Lifshitz theory, separates in a natural manner in contributions from eddy currents and propagating cavity modes, respectively. The latter have long been known to be of little importance to the low-temperature Casimir anomalies. This convincingly demonstrates that eddy current modes are responsible for the large temperature correction to the Casimir effect between Drude metals, predicted by the Lifshitz theory, but not observed in experiments.