Presence and Absence of Delocalization-localization Transition in Coherently Perturbed Disordered Lattices

TL;DR

This paper investigates how coherent harmonic perturbations affect localization in disordered lattices, revealing a transition similar to Anderson transition that depends on the number of perturbation frequencies and exhibits a critical dimension of 3.

Contribution

It introduces a new delocalization mechanism in disordered systems under coherent perturbations and clarifies the nature of the transition and its critical dimension.

Findings

Normal diffusion occurs with few frequencies.

Transition to localization happens below a critical perturbation strength.

Critical dimension for the transition is identified as 3.

Abstract

A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to localized state always occurs as the perturbation strength is weakened below a critical value. The nature of the transition qualitatively follows the Anderson transition (AT) if the number of degrees of freedom $M+1$ is regarded as the spatial dimension $d$, but the critical dimension is not $d=M+1-2$ of the ordinary AT but $d=3$.