SPECTRAL STATISTICS FOR QUANTUM CHAOS WITH RAY SPLITTING

We investigate the behavior of ray trajectories and solutions of the w ave equation of two dimensional billiard-like systems with ray splitti ng. By ''ray splitting'' we mean the phenomenon whereby a ray incident on a sharp boundary leads to two or more rays traveling away from the boundary (e.g. a transmitted ray and a reflected ray). Billiard syste ms with the same overall shape, but with and without ray splitting bou ndaries present are examined and compared. It is found that, for the c onfigurations considered, the level spacing distribution and the spect ral rigidity for the case without ray splitting are intermediate betwe en Poisson and Gaussian orthogonal ensemble (GOE) statistics, while th e behavior with ray splitting is very close to GOE.