STATISTICS OF AVOIDED CROSSINGS FOR GENERIC QUANTUM-SYSTEMS

The distribution of isolated avoided crossings in quantum systems whose classical counterparts possess a mixed phase space of regular and chaotic dynamics is investigated. The distribution function for the width is shown to consist of two components: a near-Gaussian distribution suggested by random matrix theory for the chaotic component and an approximately delta-shaped component originating from tori in the regular portion of phase space. A statistical measure for overlapping avoided crossing based on parametric correlations of energy levels is introduced and shown to be sensitive to the fraction of classically chaotic phase space.