Wave transport in one-dimensional disordered systems with finite-width potential steps

TL;DR

This paper analyzes wave transport in a one-dimensional disordered system modeled as a chain of potential steps with fixed width and random heights, revealing two distinct regimes of transmission behavior.

Contribution

It introduces a simple correlated disorder model and provides a theoretical analysis predicting two regimes of wave transport, supported by numerical simulations.

Findings

Identification of two regimes: near transparency and exponential resistance growth.

Theoretical predictions match numerical simulations.

Strong motivation for experimental validation.

Abstract

An amazingly simple model of correlated disorder is a one-dimensional chain of n potential steps with a fixed width lc and random heights. A theoretical analysis of the average transmission coefficient and Landauer resistance as functions of n and klc predicts two distinct regimes of behavior, one marked by extreme sensitivity and the other associated with exponential behavior of the resistance. The sensitivity arises in n and klc for klc approximately pi, where the system is nearly transparent. Numerical simulations match the predictions well, and they suggest a strong motivation for experimental study.