Wavepacket Dynamics in One-Dimensional System with Long-Range Correlated Disorder

TL;DR

This study numerically explores wavepacket dynamics in a one-dimensional disordered system with long-range correlations, revealing universal scaling laws and the transition from ballistic to localized behavior depending on disorder strength and spectral exponent.

Contribution

It introduces a detailed numerical analysis of wavepacket spreading in correlated disorder, uncovering universal scaling laws and the behavior of dynamical localization length.

Findings

MSD shows ballistic spread and localization depending on $\alpha$

Dynamical localization length follows a simple scaling law

Universal behavior of scaled MSD across parameters

Abstract

We numerically investigate dynamical property in the one-dimensional tight-binding model with long-range correlated disorder having power spectrum $1/f^\alpha$ ($\alpha:$spectrum exponent) generated by Fourier filtering method. For relatively small $\alpha<\alpha_c(=2)$ time-dependence of mean square displacement (MSD) of the initially localized wavepacket shows ballistic spread and localizes as time elapses. It is shown that $\alpha-$dependence of the dynamical localization length (DLL) determined by the MSD exhibits a simple scaling law in the localization regime for the relatively weak disorder strength $W$. Furthermore, scaled MSD by the DLL almost obeys an universal function from the ballistic to the localization regime in the various combinations of the parameters $\alpha$ and $W$.