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

TL;DR

This paper numerically studies the quantum dynamics of wave-packets in disordered quasi-1D media, revealing anomalous scaling behaviors, non-Gaussian tails, and finite band corrections in the steady state.

Contribution

It provides new numerical data on scaling properties, estimates anomalous scaling exponents, and analyzes finite band corrections in wave-packet evolution in disordered systems.

Findings

Confirmed anomalous scaling of steady-state packet width fluctuations

Identified non-Gaussian tails in the packet width distribution

Found finite band corrections of order 1/b and 1/√b near the origin

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 $O(1/\sqrt{b})$.