Casimir interaction between cylinders

TL;DR

This paper calculates the Casimir interaction energy between concentric cylinders using exact and approximate methods, revealing the conditions under which approximations match the exact results and exploring eccentric cylinder configurations.

Contribution

It provides a detailed comparison between exact calculations and approximations for Casimir forces in cylindrical geometries, highlighting the validity of the proximity theorem and semiclassical methods.

Findings

Proximity theorem with a specific effective area matches the semiclassical approximation.

Semiclassical approximation reproduces the exact result beyond its expected validity range.

Analysis of Casimir force measurement advantages in cylindrical geometries.

Abstract

We compute the Casimir interaction energy between two perfectly conducting, concentric cylinders, using the mode-by-mode summation technique. Then we compare it with the approximate results obtained using the proximity theorem and a semiclassical approximation based on classical periodic orbits. We show that the proximity theorem with a particular choice for the effective area coincides with the semiclassical approximation and reproduces the exact result far beyond its expected range of validity. We also compute the force between slightly eccentric cylinders and discuss the advantages of using a cylindrical geometry to measure the Casimir force.