Resonant enhancement of Anderson localization: Analytical approach

TL;DR

This paper develops an analytical approach to understand how resonances enhance Anderson localization in a one-dimensional system with random potential barriers, providing new insights into wave transport and localization length.

Contribution

It introduces a theoretical method to derive localization length near resonances in a discrete model, extending conventional continuous potential theories.

Findings

Analytical expressions match numerical data accurately.

Resonances significantly increase localization length.

Single parameter scaling may not hold near resonances.

Abstract

We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced Anderson localization, is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between wells/barriers. Our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them. We examine how the transport properties of finite samples can be described in terms of this length. It is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model, in spite of the presence of resonances that cannot be described by conventional theories. We also discuss whether the single parameter scaling is valid in view of the suggested modification of the theory. All our results are illustrated with numerical data manifesting an excellent agreement with the theory.