On the dynamical and statistical properties of complex quantum systems

In this work we have analyzed the following aspects of quantum complex syst ems: I) Quantum-Classical correspondence for eigenfunctions (EFS) and local density of states (LDOS) in dynamical chaotic models; 2) structure of LDOS and EFS in matrix models with random two-body interaction; and 3) quantum localization in ID correlated potentials. In I) we studied various models o f two interacting particles and also a chaotic billiard. In 2), models of r andomly interacting particles were used to analyze the nature of chaotic ei genstates in isolated quantum systems of interacting particles. In 3) analy tical, numerical, and experimental results are presented concerning the phe nomenon of quantum localization in 1D correlated disordered potentials. We discuss briefly the main results with an outline of the analytical and nume rical approaches used to study these three aspects.