Evolution of wave packets in quasi-1D and 1D random media: diffusion   versus localization
  We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed. 
F.M. Izrailev, T. Kottos, A. Politi and G.P. Tsironis