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Exact expressions for the Casimir interaction between semitransparent spheres and cylinders

Oklahoma Center for High Energy Physics and Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019, USA

^*milton@nhn.ou.edu; http://www.nhn.ou.edu/%7Emilton
^†wagner@nhn.ou.edu

Phys. Rev. D 77, 045005 – Published 4 February, 2008

DOI: https://doi.org/10.1103/PhysRevD.77.045005

Abstract

A multiple scattering formulation is used to calculate the force, arising from fluctuating scalar fields, between distinct bodies described by $δ$ -function potentials, so-called semitransparent bodies. (In the limit of strong coupling, a semitransparent boundary becomes a Dirichlet one.) We obtain expressions for the Casimir energies between disjoint parallel semitransparent cylinders and between disjoint semitransparent spheres. In the limit of weak coupling, we derive power series expansions for the energy, which can be exactly summed, so that explicit, very simple, closed-form expressions are obtained in both cases. The proximity force theorem holds when the objects are almost touching, but is subject to large corrections as the bodies are moved farther apart.

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Exact expressions for the Casimir interaction between semitransparent spheres and cylinders

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