Casimir effect between spherical objects: proximity-force approximation and beyond using plane waves

TL;DR

This paper reviews and extends the analysis of the Casimir effect between spherical objects using plane-wave basis, including polarization mixing and higher-order corrections beyond the proximity-force approximation.

Contribution

It introduces polarization mixing during reflection and derives higher-order correction terms for perfect electric conductors at zero temperature.

Findings

Explicit results for perfect electromagnetic conductors.

Half-integer order correction terms in the distance.

Extension of previous work to include polarization effects.

Abstract

For the Casimir interaction between two nearby objects, the plane-wave basis proves convenient for numerical calculations as well as for analytical considerations leading to an optical interpretation of the relevant scattering processes of electromagnetic waves. We review work on the proximity-force approximation and corrections to it within the plane-wave basis for systems involving spherical objects. Previous work is extended by allowing for polarization mixing during the reflection at a sphere. In particular, explicit results are presented for perfect electromagnetic conductors. Furthermore, for perfect electric conductors at zero temperature, it is demonstrated that beyond the leading-order correction to the proximity-force approximation, terms of half-integer order in the distance between the sphere surfaces appear.