Localization by bichromatic potentials versus Anderson localization

TL;DR

This paper compares the Aubry-André model's localization transition in bichromatic potentials to Anderson localization, revealing that the former's transition has a classical origin unlike the quantum nature of Anderson localization.

Contribution

It demonstrates that the Aubry-André transition is classically driven, contrasting with the quantum suppression mechanism in Anderson localization, supported by comparisons with experiments and models.

Findings

Aubry-André transition has a classical origin.

Contrasts between Aubry-André and Anderson localization.

Experimental and theoretical comparisons support the classical mechanism.

Abstract

The one-dimensional propagation of waves in a bichromatic potential may be modeled by the Aubry-Andr\'e Hamiltonian. The latter presents a delocalization-localization transition, which has been observed in recent experiments using ultracold atoms or light. It is shown here that, in contrast to Anderson localization, this transition has a classical origin, namely the localization mechanism is not due to a quantum suppression of a classically allowed transport process. Explicit comparisons with the Anderson model, as well as with experiments, are done.