Electromagnetic Casimir-Polder Interaction for a Conducting Cone

TL;DR

This paper develops a formalism to compute the electromagnetic Casimir-Polder interaction energy between a conducting cone and a polarizable particle, extending previous wedge models and providing numerical evaluation methods.

Contribution

It introduces a new analytical approach using Green's functions for a conducting cone, expanding the understanding of Casimir-Polder interactions in non-trivial geometries.

Findings

Derived the Green's function for a conducting cone

Computed the Casimir-Polder energy numerically

Extended wedge formalism to cone geometry

Abstract

Using the formulation of the electromagnetic Green's function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir-Polder interaction energy of the cone with a polarizable particle. We introduce this formalism by first reviewing the analogous approach for a perfectly conducting wedge, and then demonstrate the calculation through numerical evaluation of the resulting integrals.