Conductance fluctuations in the localized regime

TL;DR

This study numerically investigates conductance fluctuations in disordered systems across multiple dimensions, revealing specific variance scaling laws and testing the single-parameter scaling hypothesis in three dimensions.

Contribution

It provides detailed numerical analysis of conductance fluctuations and their size dependence, including higher cumulants, in various dimensional disordered systems.

Findings

Variance of ln g scales as L^{2/5} in 3D

Variance of ln g scales logarithmically in 4D

Third cumulant of ln g diverges with size, indicating non-Gaussian behavior

Abstract

We have studied numerically the fluctuations of the conductance, $g$, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of $\ln g$ varies with the lateral sample size as $L^{2/5}$ in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of $\ln g$ in two- and three-dimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.