Casimir interaction between two concentric cylinders: exact versus semiclassical results

Abstract

The Casimir interaction between two perfectly conducting, infinite, concentric cylinders is computed using a semiclassical approximation that takes into account families of classical periodic orbits that reflect off both cylinders. It is then compared with the exact result obtained by the mode-by-mode summation technique. We analyze the validity of the semiclassical approximation and show that it improves the results obtained through the proximity theorem.