SIMPLE-MODELS OF QUANTUM CHAOS - SPECTRUM AND EIGENFUNCTIONS

The statistical properties of so-called quantum chaos are considered on the basis of the well-known model of a kicked rotator. Attention is paid mainly to the quasienergy spectrum and the structure of the eigenfunctions in the case of strong classical chaos. The influence of quantum localization effects on the statistics of the spectrum is examined for a model with a finite number of states. Both cases of maximal and of intermediate quantum chaos are studied in dependence on the degree of localization. The possible relation to other physical models is also discussed.