Quantum transport under oscillatory drive with disordered amplitude

TL;DR

This paper studies quantum transport in a disordered one-dimensional chain under oscillatory electric fields, revealing a transition from diffusive to localized behavior as disorder and field strength increase.

Contribution

It derives exact expressions for quantum propagators in disordered fields and extends analysis to time-dependent disorder, highlighting disorder-induced localization effects.

Findings

Disorder causes diffusive transport in static fields.

Increasing field strength suppresses transport, leading to localization.

Time-dependent disorder alters mean-squared displacement dynamics.

Abstract

We investigate the dynamics of non-interacting particles in a one-dimensional tight-binding chain in the presence of an electric field with random amplitude drawn from a Gaussian distribution, and explicitly focus on the nature of quantum transport. We derive an exact expression for the probability propagator and the mean-squared displacement in the clean limit and generalize it for the disordered case using the Liouville operator method. Our analysis reveals that in the presence a random static field, the system follows diffusive transport; however, an increase in the field strength causes a suppression in the transport and thus results in disorder-induced localization. We further extend the analysis for a time-dependent disordered electric field and show that the dynamics of mean-squared-displacement deviates from the parabolic path as the field strength increases, unlike the clean limit where ballistic transport occurs.