Anomalous transport in low-dimensional systems with correlated disorder

TL;DR

This paper reviews how long-range correlations in disorder can be engineered to achieve selective and controllable anomalous transport properties in low-dimensional systems, including transparency windows for waves and electrons.

Contribution

It introduces the concept that specific correlations in disorder can be designed to produce desired transport behaviors in one-dimensional and quasi-one-dimensional systems.

Findings

Correlated disorder can create transparency windows for waves.

Long-range correlations influence bulk and surface scattering.

Selective transport properties can be engineered through disorder correlations.

Abstract

We review recent results on the anomalous transport in one-dimensional and quasi-one-dimensional systems with bulk and surface disorder. Main attention is paid to the role of long-range correlations in random potentials for the bulk scattering, and in corrugated profiles for the surface scattering. It is shown that with a proper choice of correlations one can construct such a disorder that results in a selective transport with given properties. A particular interest is in the possibility to arrange windows of a complete transparency (or reflection) in the dependence on the wave number of incoming classical waves or electrons.