Casimir forces between arbitrary compact objects: Scalar and electromagnetic field

TL;DR

This paper presents an exact, multipole-based method for calculating Casimir energies between arbitrary compact objects, applicable to scalar and electromagnetic fields, with results converging rapidly and including low-frequency expansions.

Contribution

It introduces a comprehensive method that computes Casimir energies for arbitrary shapes and materials using scattering matrices, advancing beyond previous approximate techniques.

Findings

Exact interaction energies for spheres with Robin boundary conditions.

Full interaction calculations for perfectly conducting spheres.

Rapid convergence of the multipole expansion.

Abstract

We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as an interaction between multipoles, generated by quantum source or 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 examples, we obtain this series for two spheres with Robin boundary conditions for a scalar field and dielectric spheres for the electromagnetic field. The full interaction at all separations is obtained for spheres with Robin boundary conditions and for perfectly conducting spheres.