Coherent resistance of a disordered 1D wire: Expressions for all moments and evidence for non-Gaussian distribution

TL;DR

This paper derives analytical expressions for all moments of resistance in a disordered 1D wire and demonstrates that the distribution of resistance-related variables is non-Gaussian, even under weak disorder conditions.

Contribution

It provides the first complete analytical characterization of all moments of resistance and proves the non-Gaussian nature of the resistance distribution in 1D disordered wires.

Findings

Distribution of resistance variable is non-Gaussian.

Analytical expressions for all moments of resistance are derived.

Non-Gaussian behavior persists even in weak disorder limit.

Abstract

We study coherent electron transport in a one-dimensional wire with disorder modeled as a chain of randomly positioned scatterers. We derive analytical expressions for all statistical moments of the wire resistance $\rho$. By means of these expressions we show analytically that the distribution $P(f)$ of the variable $f=\ln(1+\rho)$ is not exactly Gaussian even in the limit of weak disorder. In a strict mathematical sense, this conclusion is found to hold not only for the distribution tails but also for the bulk of the distribution $P(f)$.