IMPROVED ENERGY-LEVEL STATISTICS FOR A FAMILY OF BILLIARDS WITH ANALYTIC BOUNDARIES

The energy level statistics of a family of classically chaotic billiards with analytic boundaries is studied numerically with a high chi-2 confidence level for the final results, which go substantially beyond the quality of existing similar results. The hypothesis of Bohigas a al is strongly supported by the present results, showing that the level statistics of classically ergodic systems in the semiclassical limit can indeed be described by the Gaussian orthogonal ensemble of the random matrix theories, contrary to some doubts which have been recently raised e.g. by Wilkinson et al. Nevertheless, some small deviation of the numerical results compared with the Gaussian orthogonal ensemble is observed and shown, but it is believed to be still a deficiency of the statistical significance rather than of the model.