Non-analyticity in the distribution of conductances in quasi one dimensional wires

TL;DR

This paper demonstrates that the conductance distribution in quasi-one-dimensional wires exhibits non-analytic behavior near g=1, with analytic expressions and scaling laws derived for different disorder strengths.

Contribution

It provides the first analytic characterization of the non-analyticity in conductance distribution near g=1 in disordered wires.

Findings

Distribution P(g) has a discontinuous derivative near g=1

Analytic expressions for P(g) are derived

Scaling behavior near g=1 is characterized

Abstract

We show that the distribution P(g) of conductances g of a quasi one dimensional wire has non-analytic behavior in the insulating region, leading to a discontinuous derivative in the distribution near g=1. We give analytic expressions for the full distribution and extract an approximate scaling behavior valid for different strengths of disorder close to g=1.