On spectral statistics of classically integrable systems

Abstract

This work is an extensive study of the spectral statistics of three representative classically integrable systems, namely rectangle, torus and circle billiards. We analyse the statistics and focus on the related level spacing distribution P(S) and the delta statistics . The agreement with the Poissonian model is typically found to be perfect up to the outer (unfolded) energy scale , beyond which the saturation is observed, in agreement with Berry's dynamical theory of the spectral rigidity, where as .