Localization properties of driven disordered one-dimensional systems

TL;DR

This paper extends the concept of localization length to driven disordered one-dimensional systems using Floquet theory, analyzing how periodic driving influences localization properties depending on frequency and amplitude.

Contribution

It introduces a generalized localization length for driven systems and explores its dependence on driving parameters, revealing new behaviors not present in autonomous systems.

Findings

Localization length varies with driving frequency and amplitude.

Maximum localization length is not at the band center in driven systems.

Low-frequency driving effects are limited by inelastic scattering.

Abstract

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.