Casimir interaction between two concentric cylinders at nonzero temperature

TL;DR

This paper analyzes the finite temperature Casimir interaction between two concentric cylinders, deriving asymptotic expansions for small separations and exploring temperature effects, with results aligning with proximity force approximations.

Contribution

It provides new asymptotic formulas for the Casimir interaction at finite temperature between concentric cylinders, including temperature corrections independent of boundary conditions.

Findings

Asymptotic expansions derived for small separations

Leading terms agree with proximity force approximation

Temperature correction at low temperature is boundary-condition independent

Abstract

We study the finite temperature Casimir interaction between two concentric cylinders. When the separation between the cylinders is much smaller than the radii of the cylinders, the asymptotic expansions of the Casimir interaction are derived. Both the low temperature and the high temperature regions are considered. The leading terms are found to agree with the proximity force approximations. The low temperature leading term of the temperature correction is also computed and it is found to be independent of the boundary conditions imposed on the larger cylinder.