Casimir-Polder interaction for gently curved surfaces

Abstract

We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a non-planar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, non-retarded and classical high temperature limits.

arXiv comment6 pages, 1 Figure

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• On the Derivative Expansion for the Electromagnetic Casimir Free Energy at High Temperatures
• Spectroscopic Probe of the van der Waals Interaction between Polar Molecules and a Curved Surface
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• Something Can Come of Nothing: Surface Approaches to Quantum Fluctuations and the Casimir Force
• Sign inversion in the lateral van der Waals force
• Exact Casimir interaction of perfectly conducting three-spheres in four euclidean dimensions
• Derivative expansion for the electromagnetic and Neumann Casimir effects in $2+1$ dimensions with imperfect mirrors
• Electromagnetic Casimir-Polder Interaction for a Conducting Cone
• Interplay of curvature and temperature in the Casimir-Polder interaction
• Wave-scattering from a gently curved surface
• Complex orientation dependence of Casimir-Polder interaction induced by curvature and optical properties of the surface and the surrounding medium