Conductance distribution in two-dimensional localized systems

TL;DR

This paper derives a universal conductance distribution for two-dimensional localized systems, linking it to the Tracy-Widom distribution, and demonstrates its robustness across models and magnetic field conditions.

Contribution

It establishes a universal conductance distribution related to Tracy-Widom in 2D localized systems, applicable across different models and magnetic field conditions.

Findings

Distribution related to Tracy-Widom distribution

Distribution applies to various models including Anderson model

Distribution remains unchanged under moderate magnetic fields

Abstract

We have obtained the universal conductance distribution of two-dimensional disordered systems in the strongly localized limit. This distribution is directly related to the Tracy-Widom distribution, which has recently appeared in many different problems. We first map a forward scattering paths model into a problem of directed random polymers previously solved. We show numerically that the same distribution also applies to other forward scattering paths models and to the Anderson model. We show that most of the electric current follows a preferential percolation-type path. The particular form of the distribution depends on the type of leads used to measure the conductance. The application of a moderate magnetic field changes the average conductance and the size of uctuations, but not the distribution when properly scaled. Although the presence of magnetic field changes the universality class, we show that the conductance distribution in the strongly localized limit is the same for both classes.