Casimir forces between arbitrary compact objects

TL;DR

This paper introduces an exact method to compute Casimir energies between arbitrary compact objects using scattering matrices, applicable to various shapes and materials, with rapid convergence and low-frequency expansions.

Contribution

The authors develop a comprehensive scattering matrix approach for calculating Casimir forces between arbitrary objects, extending previous methods to more general geometries and materials.

Findings

Exact interaction energy for dielectric and conducting objects.

Rapid convergence of the multipole expansion.

Series expansion for low-frequency regime.

Abstract

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.