Casimir friction: Relative motion more generally

TL;DR

This paper generalizes the concept of Casimir friction to include non-rectilinear motion, such as rotation, and calculates the resulting Casimir torque on a rotating disc near a plate.

Contribution

It extends previous work on Casimir friction to non-linear motions, deriving a formalism for rotational cases and computing the Casimir torque on a rotating disc.

Findings

Derived a formalism for Casimir friction with non-rectilinear motion.

Calculated the Casimir torque on a rotating disc.

Extended understanding of Casimir forces in complex motions.

Abstract

This paper extends our recent study on Casimir friction forces for dielectric plates moving parallel to each other [J. S. H{\o}ye and I. Brevik, Eur. Phys. J. D {\bf 68}, 61 (2014)], to the case where the plates are no longer restricted to rectilinear motion. Part of the mathematical formalism thereby becomes more cumbersome, but reduces in the end to the form that we could expect to be the natural one in advance. As an example, we calculate the Casimir torque on a planar disc rotating with constant angular velocity around its vertical symmetry axis next to another plate.