variant Planck's over 2pi expansion for the periodic orbit quantization of chaotic systems.
We report the results of a periodic orbit quantization of classically chaotic billiards beyond Gutzwiller approximation in terms of asymptotic series in powers of the Planck constant (or in powers of the inverse of the wave number kappa in billiards). We derive explicit formulas for the kappa(-1) approximation of our semiclassical expansion. We illustrate our theory with the classically chaotic scattering of a wave on three disks. The accuracy on the real parts of the scattering resonances is improved by one order of magnitude.
Alonso
D.
D
Centre for Nonlinear Phenomena and Complex Systems, Universite Libre de Bruxelles, Campus Plaine, Code Postal 231, Blvd. du Triomphe, B-1050 Brussels, Belgium.
Gaspard
P.
P