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We study numerically the evolution of wavepackets in quasi one-dimensionalrandom systems described by a tight-binding Hamiltonian with long-range randominteractions. Results are presented for the scaling properties of the width ofpackets in three time regimes: ballistic, diffusive and localized. Particularattention is given to the fluctuations of packet widths in both the diffusiveand localized regime. Scaling properties of the steady-state distribution arealso analyzed and compared with theoretical expression borrowed fromone-dimensional Anderson theory. Analogies and differences with the kickedrotator model and the one-dimensional localization are discussed.Comment: 32 pages, LaTex, 11 PostScript figure

Evolution of wave packets in quasi-one-dimensional and one-dimensional random media: Diffusion versus localization