QUANTUM CHAOS - UNEXPECTED COMPLEXITY

An overview of the most important, in our opinion, recent results (both numerical as well as theoretical) in the studies of a very controversial topic, the so-called quantum chaos, is presented. We focus on the dynamical models and behavior which results, under appropriate conditions, in surprisingly rich statistical properties of the quantum motion, even in case of a discrete energy spectrum of the latter. The results under consideration include the time evolution of an initial narrow wave packet with its diffusion and statistical relaxation to the quantum steady state as well as the statistical properties of the (quasi) energy eigenvalues and eigenfunctions. The guiding line of our discussion is based on the conception of quantum chaos as a new dynamical phenomenon in a domain which has been traditionally considered as that of regular motion. A number of open questions and unsolved problems is also presented.