Classical Casimir free energy for two Drude spheres of arbitrary radii: A plane-wave approach

TL;DR

This paper derives an exact analytic expression for the high-temperature Casimir free energy between two Drude spheres of arbitrary radii using a plane-wave scattering approach, including asymptotic expansions for small distances.

Contribution

It introduces a novel analytic method to compute the Casimir free energy for two Drude spheres of arbitrary sizes, extending previous special case results.

Findings

Exact high-temperature Casimir free energy expression derived.

Recovered known results for sphere-plane and equal radii cases.

Provided asymptotic expansion for small sphere separation.

Abstract

We derive an exact analytic expression for the high-temperature limit of the Casimir interaction between two Drude spheres of arbitrary radii. Specifically, we determine the Casimir free energy by using the scattering approach in the plane-wave basis. Within a round-trip expansion, we are led to consider the combinatorics of certain partitions of the round trips. The relation between the Casimir free energy and the capacitance matrix of two spheres is discussed. Previously known results for the special cases of a sphere-plane geometry as well as two spheres of equal radii are recovered. An asymptotic expansion for small distances between the two spheres is determined and analytical expressions for the coefficients are given.