SPECTRAL STATISTICS OF THE PI-3 RHOMBUS BILLIARD - A DETAILED INVESTIGATION

We carry out a detailed investigation of the spectral fluctuations for the pi/3 rhombus billiard, a system known to be pseudointegrable with an invariant integral surface of genus g = 2. The equilateral triangle states (which constitute half the total number) show considerable deviations from the Poisson behavior due to degeneracies in the periodic orbit actions. The "pure rhombus states" (the other half), however, have fluctuations closer to that of the Gaussian orthogonal ensemble of matrices (GOE) but are strongly parity dependent. The presence of localized states in the (00) mode affects the nearest-neighbor level statistics significantly. Both the Berry-Robnik and the Brody distributions, however, serve to parametrize the fluctuations of the (10) mode satisfactorily. The spectral rigidity and number variance, however, seem insensitive to the presence of localized states. Deviations from the GOE predictions become very significant for higher-order correlations.