Localization and delocalization properties in quasi-periodically driven one-dimensional disordered system

TL;DR

This paper systematically studies how quasi-periodic driving influences localization and delocalization in a one-dimensional disordered quantum system, revealing a transition dependent on parameters like disorder, perturbation strength, and number of frequencies.

Contribution

It provides a detailed analysis of localization-delocalization transitions in a quasi-periodically driven Anderson model, highlighting the role of the number of frequencies and perturbation strength.

Findings

Localization-delocalization transition exists for M≥3.

Normal diffusion occurs above a critical perturbation strength.

Diffusion characteristics resemble those of stochastically perturbed models.

Abstract

Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson model perturbed by the quasi-periodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by the preliminary letter [PRE {\bf 103}, L040202(2021)]. We investigate in detail the localization-delocalization characteristics of the model with respect to three parameters: the disorder strength $W$, the perturbation strength $\epsilon$ and the number of the colors $M$ which plays the similar role of spatial dimension. In particular, attentions are focused on the presence of localization-delocalization transition (LDT) and its critical properties. For $M\geq 3$ the LDT exists and a normal diffusion is recovered above a critical strength $\epsilon$, and the characteristics of diffusion dynamics mimic the diffusion process predicted for the stochastically perturbed Anderson model even though $M$ is not large. These results are compared with the results of time-discrete quantum maps, i.e., Anderson map and the standard map. Further, the features of delocalized dynamics is discussed in comparison with a limit model which has no static disordered part.