Electromagnetic Response of the Electron Gas and the Thermal Casimir Pressure Anomaly

TL;DR

This paper reviews the electromagnetic response of the electron gas and re-analyzes the thermal Casimir pressure anomaly, confirming the conventional Drude model's predictions and discussing the role of Landau diamagnetism.

Contribution

It provides a detailed review of nonlocal response functions for the electron gas and applies them to analyze the Casimir interaction at high temperatures, confirming the Drude model's validity.

Findings

Confirmation of the Drude model's predictions for Casimir pressure

Identification of Landau diamagnetism effects in the electron gas

Analysis of the electromagnetic response functions within perturbation theory

Abstract

A review of the nonlocal electromagnetic response functions for the degenerate electron gas, computed within standard perturbation theory, is given. These expressions due to Lindhard, Klimontovich and Silin are used to re-analyze the Casimir interaction between two thick conducting plates in the leading order at high temperatures (zero'th term of Matsubara series). Up to small corrections that we discuss, the results of the conventional Drude model are confirmed. The difference between longitudinal and transverse permittivities (or polarization tensors) yields the Landau (orbital) diamagnetism of the electron gas.