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.

6 pages, 1 Figure

References in corpus (9)

• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Low velocity quantum reflection of Bose-Einstein condensates
• Casimir-Polder interaction between an atom and a dielectric grating
• Quantum reflection of helium atom beams from a microstructured grating
• Exact Casimir-Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation
• The derivative expansion approach to the interaction between close surfaces
• Scalar Casimir-Polder forces for uniaxial corrugations
• Small distance expansion for radiative heat transfer between curved objects

Cited by in corpus (9)

• Isolelectronic apparatus to probe the thermal Casimir force
• Impact of Casimir-Polder interaction on Poisson-spot diffraction at a dielectric sphere
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Spectroscopic Probe of the van der Waals Interaction between Polar Molecules and a Curved Surface
• Classical Casimir interaction of perfectly conducting sphere and plate
• Derivative expansion for the electromagnetic and Neumann Casimir effects in $2+1$ dimensions with imperfect mirrors
• Exact Casimir interaction of perfectly conducting three-spheres in four euclidean dimensions
• Interplay of curvature and temperature in the Casimir-Polder interaction
• Wave-scattering from a gently curved surface