NUMERICAL DEMONSTRATION OF THE BERRY-ROBNIK LEVEL SPACING DISTRIBUTION

We offer a clear numerical demonstration of the Berry-Robnik level spa cing distribution in a dynamical regime in which regular and irregular regions coexist in classical phase space. In order to achieve this we had to go very deeply into the semiclassical limit, which, so far, ha s only been possible for an abstract dynamical system, namely the quan tized standard map on a torus. We have performed an extensive numerica l analysis of the quasi-energy spectra and of the eigenstates in the t wo-dimensional phase-space representation. We have confirmed the valid ity of Percival's conjecture that the eigenstates can be clearly class ified either as regular or irregular where the small set of mixed-type states vanishes extremely slowly as we approach the far semiclassical limit. It has been verified that the assumptions (statistical indepen dence) implicit in the Berry-Robnik theory are indeed satisfied giving rise to the observed excellent agreement between theory and experimen t. The same high quality agreement is also observed in our comparison of the semiclassical theoretical (Seligman and Verbaarschot) and numer ical delta statistics.