QUANTUM CHAOS - UNEXPECTED COMPLEXITY

An overview of the most important, in our opinion, recent results (bot h numerical as well as theoretical) in the studies of a very controver sial topic, the so-called quantum chaos, is presented. We focus on the dynamical models and behavior which results, under appropriate condit ions, in surprisingly rich statistical properties of the quantum motio n, even in case of a discrete energy spectrum of the latter. The resul ts under consideration include the time evolution of an initial narrow wave packet with its diffusion and statistical relaxation to the quan tum steady state as well as the statistical properties of the (quasi) energy eigenvalues and eigenfunctions. The guiding line of our discuss ion is based on the conception of quantum chaos as a new dynamical phe nomenon in a domain which has been traditionally considered as that of regular motion. A number of open questions and unsolved problems is a lso presented.