Exact Casimir-Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation

TL;DR

This paper derives the exact Casimir-Polder potential for a particle near an ideal metal cylindrical shell, confirming previous results and comparing with the proximity force approximation, with implications for topological defect theory.

Contribution

It provides the first exact Green function-based derivation of the Casimir-Polder potential inside and outside a cylindrical shell, validating the proximity force approximation at short distances.

Findings

Exact potential derived for inside and outside the shell.

Good agreement between exact and approximate methods below 0.1R.

Method applicable to topological defect studies.

Abstract

We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1$R$, where $R$ is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.