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Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane
Giuseppe Bimonte1, Thorsten Emig
1Dipartimento di Scienze Fisiche, Università di Napoli Federico II, Complesso Universitario MSA, Via Cintia, I-80126 Napoli, Italy and INFN Sezione di Napoli, I-80126 Napoli, Italy.
Abstract:
Analytic expressions that describe Casimir interactions over the entire range of separations have been limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit of Casimir interactions between two spheres (interior and exterior configurations), including the sphere-plane geometry as a special case, using bispherical coordinates. We consider both Dirichlet boundary conditions and metallic boundary conditions described by the Drude model. At short distances, closed-form expansions are derived from the exact result, displaying an intricate structure of deviations from the commonly employed proximity force approximation.
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