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

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.

25 pages, 3 figures; includes changes after first review round

References in corpus (4)

• The Casimir effect within scattering theory
• Casimir energy between a plane and a sphere in electromagnetic vacuum
• Fluctuation induced quantum interactions between compact objects and a plane mirror
• Plane-wave approach to the exact van der Waals interaction between colloid particles

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• Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures
• Casimir effect between spherical objects: proximity-force approximation and beyond using plane waves