Casimir Friction Between Dense Polarizable Media

TL;DR

This paper extends the analysis of Casimir friction to dense media, showing that macroscopic parameters like permittivity can describe the friction, resulting in finite, well-defined expressions at finite temperature, with numerical estimates provided.

Contribution

It introduces a simplified model for dense media using macroscopic parameters, extending previous particle-based analyses of Casimir friction.

Findings

Friction force per unit area is finite and well-defined at finite temperature.

Macroscopic permittivity suffices to describe Casimir friction in dense media.

Numerical estimates align with earlier theoretical results.

Abstract

The present paper - a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity - extends the analysis so as to include dense media. The situation becomes in this case more complex due to induced dipolar correlations, both within planes, and between planes. We show that the structure of the problem can be simplified by regarding the two half-planes as a generalized version of a pair of particles. It turns out that macroscopic parameters such as permittivity suffice to describe the friction also in the finite density case. The expression for the friction force per unit surface area becomes mathematically well-defined and finite at finite temperature. We give numerical estimates, and compare them with those obtained earlier by Pendry (1997) and by Volokitin and Persson (2007). We also show in an appendix how the statistical methods that we are using, correspond to the field theoretical methods more commonly in use.