Scattering Theory Approach to Electrodynamic Casimir Forces

TL;DR

This paper presents a versatile scattering theory method for calculating Casimir forces between objects of arbitrary shapes, materials, and configurations, extending to media other than vacuum and finite temperatures.

Contribution

It introduces a comprehensive scattering approach combining electromagnetic scattering amplitudes with translation matrices, enabling accurate Casimir force calculations in complex scenarios.

Findings

Re-derivation of the Lifshitz formula for half spaces

Demonstration of Casimir-Polder to van der Waals crossover

Calculation of Casimir energies for spheres and cylinders near plates

Abstract

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.