O ct 1 99 9 Time evolution of wave - packets in quasi - 1 D disordered media

We have investigated numerically the quantum evolution of a δ-like wave-packet in a quenched disordered medium described by a tight-binding Hamiltonian with long-range hopping (band random matrix approach). We have obtained clean data for the scaling properties in time and in the bandwidth b of the packet width˜M and its fluctuations ∆ ˜ M with respect to disorder realizations. We confirm that the fluctuations of the packet width in the steady-state show an anomalous scaling ∆ ˜ M / ˜ M ∼ b −δ with δ = 0.75 ± 0.03. This can be related to the presence of non-Gaussian tails in the distribution of˜M. Finally , we have analysed the steady state probability profile and we have found 1/b corrections with respect to the theoretical formula derived by Zhirov in the b → ∞ limit, except at the origin, where the corrections are O(1/ √ b).