Delocalization for Strong Uncorrelated Disorder

TL;DR

This paper demonstrates that in continuous random potentials, delocalization occurs regardless of disorder strength as the roughness length approaches zero, contrasting with discrete models where all states are localized.

Contribution

It provides a new analytical expression for localization length applicable to all disorder strengths in continuous potentials, revealing delocalization in the zero roughness limit.

Findings

Delocalization occurs in continuous potentials as roughness length approaches zero.

Maximum localization occurs when roughness length is comparable to wavelength.

Results explain difficulties in observing localization in certain physical systems.

Abstract

Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for strong disorder and low dimensions. In one dimension and for discrete uncorrelated random potentials, such as tight binding models, all states are localized for any disorder strength. This is in contrast to continuous random potentials, where we show here that regardless of the strength of the random potential, we have delocalization in the limit where the roughness length goes to zero. This result was obtained by deriving an expression for the localization length valid for all disorder strengths. We solved a non-linear wave equation, whose average over disorder yields the localization properties of the desired linear wave equation. Our results, not only explain the origin of the difficulty to observe localization in certain physical systems, but also show that maximum localization occurs when the roughness length is comparable to the wavelength, which is relevant to many experiments in a random medium.