Casimir Friction Force Between Polarizable Media

TL;DR

This paper extends the analysis of Casimir friction to particles with all-directional polarizability, and explores friction between particles and dielectric media at finite temperature using quantum statistical mechanics.

Contribution

It generalizes previous work by considering full polarizability, and analyzes friction in various configurations including particle-half-space and half-space-half-space interactions.

Findings

Friction occurs at finite temperature when polarizability regions overlap.

Generalized polarizability models show finite-temperature friction effects.

Electrostatic dipole-dipole interaction is used for simplicity.

Abstract

This work is a continuation of our recent series of papers on Casimir friction, for a pair of particles of low relative particle velocity. Each particle is modeled as a simple harmonic oscillator. Our basic method, as before, is the use of quantum mechanical statistical mechanics, involving the Kubo formula, at finite temperature. In this work we begin by analyzing the Casimir friction between two particles polarizable in all spatial directions, this being a generalization of our study in EPL 91, 60003 (2010), which was restricted to a pair of particles with longitudinal polarization only. For simplicity the particles are taken to interact via the electrostatic dipole-dipole interaction. Thereafter, we consider the Casimir friction between one particle and a dielectric half-space, and also the friction between two dielectric half-spaces. Finally, we consider general polarizabilities (beyond the simple one-oscillator form), and show how friction occurs at finite temperature when finite frequency regions of the imaginary parts of polarizabilities overlap.