Extensive numerical study of spectral statistics for rational and irrational polygonal billiards

Abstract

An extensive numerical study of level-spacing properties of rational and irrational polygonal billiard systems is carried out. It is found that level statistics of both rational and irrational polygonal billiards deviate from a Gaussian-orthogonal-ensemble-type fluctuation. It is also explored in detail whether the polygonal billiards with the infinite genus number provide different level-spacing characteristics from those with the finite genus number. Some delicate problems in dealing with several types of pseudointegrable systems are also discussed.