Casimir interaction between two concentric cylinders: exact versus   semiclassical results
  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. 
Francisco D. Mazzitelli, Mar\'ia J. S\'anchez, Norberto N. Scoccola   and Javier von Stecher