### Abstract

We have investigated numerically the quantum evolution of a delta-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 ana in the bandwidth b of the packet width (M) over bar and its fluctuations Delta((M) over bar) with respect to disorder realizations. We confirm that the fluctuations of the packet width in the steady-state show an anomalous scaling Delta((M) over bar)/(M) over bar similar to b(-delta) with delta = 0.75 +/- 0.03. This can be related to the presence of non-Gaussian tails in the distribution of (M) over bar. 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 --> infinity limit, except at the origin, where the corrections are O(1/root b).

Original language | English |
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Pages (from-to) | 673-679 |

Number of pages | 7 |

Journal | The European Physical Journal B - Condensed Matter and Complex Systems |

Volume | 14 |

Issue number | 4 |

Publication status | Published - Apr 2000 |

### Keywords

- BAND RANDOM MATRICES
- SCALING PROPERTIES
- QUANTUM CHAOS
- LOCALIZATION
- DIFFUSION

## Cite this

*The European Physical Journal B - Condensed Matter and Complex Systems*,

*14*(4), 673-679.