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.
Highlights
The Casimir effect is often seen as a quantum effect arising from the vacuum fluctuations of the electromagnetic field between two objects
We have for the first time derived an exact analytical expression for the Casimir free energy of two Drude spheres of arbitrary radii completely within the scattering approach common in Casimir physics
In contrast to previous work on the sphere-plane geometry and two spheres of equal radii, the plane-wave basis was used, which led to a connection with a combinatorial problem
Summary
The Casimir effect is often seen as a quantum effect arising from the vacuum fluctuations of the electromagnetic field between two objects. Even though it was suspected that the extension of the latter to two spheres of different radii might not be possible [6] we will see in the following that an analytical expression for the Casimir free energy in the general setup of two Drude spheres can be obtained within the scattering approach. It is common to treat geometries involving one or more spheres within a spherical or bispherical multipole expansion With such approaches the high-temperature limit of two spheres with different radii has not been explicitly derived so far.
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