Interplay of curvature and temperature in the Casimir-Polder interaction

TL;DR

This paper investigates how curvature and temperature jointly influence the Casimir-Polder interaction between a small anisotropic particle and a non-planar surface, providing explicit curvature correction results at different temperature regimes.

Contribution

It introduces a derivative expansion approach to analyze the combined effects of curvature and temperature on the Casimir-Polder interaction, including explicit results in the retarded limit.

Findings

Curvature corrections are derived for low and high temperatures.

Explicit retarded limit results are provided for perfect conductors.

The interplay of curvature and temperature significantly affects the interaction.

Abstract

We study the Casimir-Polder interaction at finite temperatures between a polarizable small, anisotropic particle and a non-planar surface using a derivative expansion. We obtain the leading and the next-to-leading curvature corrections to the interaction for low and high temperatures. Explicit results are provided for the retarded limit in the presence of a perfectly conducting surface.