# Casimir Friction Between a Magnetic and a Dielectric Material, in the Nonretarded Limit

## TL;DR

This paper investigates the quantum mechanical friction force between magnetic and dielectric materials in the nonretarded limit, extending previous static Casimir force studies to dynamic, sliding scenarios with explicit finite and zero temperature results.

## Contribution

It introduces a harmonic oscillator model to analyze Casimir friction between magnetodielectric objects, providing explicit calculations for various configurations at finite and zero temperatures.

## Key findings

- Friction force depends on material properties and relative motion.
- Explicit formulas derived for particle, half-plane, and half-space interactions.
- Results applicable to nonretarded regime at different temperatures.

## Abstract

The repulsive nature of the static Casimir force between two half-spaces, one perfectly dielectric and the other purely magnetic, has been known since Boyer's work [T. H. Boyer, Phys. Rev. A {\bf 9}, 2078 (1974)]. We here analyze the corresponding friction force in the magnetodielectric case. Our main method is that of quantum mechanical statistical mechanics. The basic model we introduce is a harmonic oscillator model: an electric dipole oscillating in the $x$ direction and a magnetic one oscillating in the $y$ direction, while their separation is in the $z$ direction. This is then extended to particles with isotropic polarizabilities. We evaluate the friction force in a variety of cases: force between moving particles, between a moving particle and a half-plane, and between half-spaces sliding against each other. At the end explicit results are obtained both for finite and zero temperatures. We restrict ourselves to the nonretarded limit.