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Time evolution of wave-packets in quasi-1D disordered media

A. Politi·S. Ruffo·L. Tessieri
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Abstract

We have investigated numerically the quantum evolution of a 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 and its fluctuations with respect to disorder realizations. We confirm that the fluctuations of the packet width in the steady-state show an anomalous scaling and we give a new estimate of the anomalous scaling exponent. This anomalous behaviour is related to the presence of non-Gaussian tails in the distribution of the packet width. Finally, we have analysed the steady state probability profile and we have found finite band corrections of order 1/b with respect to the theoretical formula derived by Zhirov in the limit of infinite bandwidth. In a neighbourhood of the origin, however, the corrections are $O(1/\sqrt{b})$.

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A. Politi, S. Ruffo, L. Tessieri. 1999-10-27. Time evolution of wave-packets in quasi-1D disordered media. https://doi.org/10.1007/s100510051078

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