LEVEL STATISTICS AND TIME EVOLUTION AT THE MOBILITY EDGE

We present results for the statistics of the eigenvalues in random mat rix ensembles characterized by an Anderson delocalization-localization transition. The nearest-level-spacing distribution function P(S) and the number variance [(deltaN(E))2] are shown at the mobility edge wher e we obtain universal curves interpolating between Wigner-Dyson and Po isson statistics valid for delocalized and for localized eigenfunction s, respectively. We also discuss the connection of level statistics wi th dynamics by considering the time evolution of a quantum wavepacket in a quasirandom matrix model. The critical quantum dynamics is charac terized by anomalous diffusion, described via continuous sets of multi fractal exponents.