Parametric motion of energy levels in quantum chaotic systems. II. Avoided-crossing distributions

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Abstract
Statistical properties of levels of quantum systems chaotic in the classical limit are studied using the distribution of avoided crossings, i.e., of the sizes of local minima of adjacent-level spacings. The results obtained previously for the two-level random-matrix theory are compared with the prediction of the statistical-mechanics description of the equivalent fictitious-particle system. The distributions derived are compared with numerical results obtained for several physical systems. The origin of the discrepancies (in former numerical calculations) of small-avoided-crossing behavior is found. The ratio of the average crossing to the average spacing is shown to have a nonuniversal behavior and seems to provide information on the degree of scarring in the system studied.