Casimir-Polder interaction for gently curved surfaces

TL;DR

This paper develops a derivative expansion method to calculate curvature corrections to the Casimir-Polder interaction between a small polarizable particle and gently curved surfaces, providing explicit results for perfect conductors across various physical regimes.

Contribution

It introduces a derivative expansion approach that resums perturbative series to compute curvature effects on Casimir-Polder forces for non-planar surfaces.

Findings

Derived leading and next-to-leading curvature corrections.

Explicit results for perfect conductors in different regimes.

Showed the derivative expansion stems from perturbative series resummation.

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.