Localization length versus level repulsion in 1-D driven disordered quantum wires

TL;DR

This paper investigates how level repulsion relates to localization length in a driven disordered 1D quantum wire, revealing frequency-dependent behaviors and the influence of external field parameters.

Contribution

It demonstrates that the relationship between localization length and level repulsion in a driven 1D disordered system varies with frequency, extending understanding from static to driven models.

Findings

High frequency regime shows linear scaling similar to static Anderson model.

Low frequency regime's level repulsion depends mainly on field amplitude.

Proportionality between level repulsion and localization length breaks down at low frequencies.

Abstract

We study the level repulsion and its relationship with the localization length in a disordered one-dimensional quantum wire excited with monochromatic linearly polarized light and described by the Anderson-Floquet model. In the high frequency regime, the linear scaling between the localization length divided by the length of the system and the spectral repulsion is the same as in the one-dimensional Anderson model without driving, although both quantities depend on the parameters of the external field. In the low frequency regime the level repulsion depends mainly on the value of the amplitude of the field and the proportionality between level repulsion and localization length is lost.