PARAMETRIC MOTION OF ENERGY-LEVELS IN QUANTUM CHAOTIC SYSTEMS .1. CURVATURE DISTRIBUTIONS

The motion of energy levels in quantum systems that show a chaotic cla ssical limit is statistically analyzed. A quantitative comparison is m ade between the tails of the curvature distribution and numerical resu lts obtained for various physical models. Approximate analytic express ions for the full curvature distribution are derived from the statisti cal mechanics of a fictitious gas in a refined formulation that recove rs the random-matrix theory for an arbitrary number of levels. They pr ovide a better description of numerical data than just the tail-limiti ng expressions available previously. Good agreement with numerical dat a for various physical systems as well as for a model random dynamics is obtained with the ad hoc introduced very simple analytic expression s containing no free parameter. The nonuniversal behavior of small cur vatures is discussed. The data obtained for the magnetized hydrogen at om support the previous interpretation of this phenomenon as due to th e ''scarred'' wave functions. A large number of analyzed data allows u s to show that the details of the curvature distribution provide a qua litative measure of the degree of scarring in different systems.