Statistical properties of localisation--delocalisation transition in one dimension

TL;DR

This paper analyzes a one-dimensional disordered electron model, calculating exact probability distributions for key transport properties, and distinguishes features caused by rare configurations from those due to the transition.

Contribution

It provides exact probability distribution functions for the Wigner time and transmission coefficient in a disordered 1D model, clarifying the effects of rare configurations and the transition.

Findings

Exact distributions for Wigner time and transmission coefficient

Identification of features due to rare trapping configurations

Distinction between effects of rare configurations and the transition

Abstract

We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission coefficient are calculated. We identify and distinguish those features of probability densities that are due to rare, trapping configurations of the random potential from those which are due to the proximity to the delocalisation transition.