Evolution of wave packets in quasi-1D and 1D random media: diffusion versus localization

TL;DR

This paper investigates how wave packets evolve in quasi-1D and 1D random media, focusing on diffusion and localization, through numerical simulations of a tight-binding model with long-range interactions.

Contribution

It provides a detailed numerical analysis of wave packet dynamics across different regimes and compares the results with theoretical models from Anderson localization and related systems.

Findings

Wave packet widths exhibit distinct scaling in ballistic, diffusive, and localized regimes.

Fluctuations are significant in diffusive and localized regimes.

Steady-state distributions align with theoretical predictions from Anderson theory.

Abstract

We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed.