EVOLUTION OF WAVE-PACKETS IN QUASI-ONE-DIMENSIONAL AND ONE-DIMENSIONAL RANDOM-MEDIA - DIFFUSION VERSUS LOCALIZATION

We study numerically the evolution of wave packets in quasi-one-dimens ional random systems described by a tight-binding Hamiltonian with lon g-range random interactions. Results are presented for the scaling pro perties of the width of packets in three time regimes: ballistic, diff usive, and localized. Particular attention is given to the fluctuation s of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and com pared with a theoretical expression borrowed from the one-dimensional Anderson theory. Analogies and differences with the kicked rotator mod el and the one-dimensional localization are discussed.