Casimir interaction of two plates inside a cylinder

TL;DR

This paper derives exact formulas for the Casimir force between two plates inside a conducting cylinder at various temperatures, analyzing their energy behavior at different distances.

Contribution

It provides new exact formulas for the Casimir interaction in a cylindrical geometry using zeta function techniques, including temperature effects.

Findings

Exact formulas for Casimir force at zero and finite temperatures

Analysis of free energy behavior at different plate separations

Application of zeta function technique to cylindrical geometry

Abstract

The new exact formulas for the attractive Casimir force acting on each of the two identical perfectly conducting plates moving freely inside an infinite perfectly conducting cylinder with the same cross section are derived at zero and finite temperatures by making use of the zeta function technique. The long and short distance behaviour of the plates' free energy is investigated.