Scaling of the conductance distribution near the Anderson transition

TL;DR

This paper demonstrates through numerical analysis that the full conductance distribution in disordered systems near the Anderson transition obeys one-parameter scaling, supporting the foundational hypothesis of the transition.

Contribution

It provides the first clear numerical evidence that the entire conductance distribution, not just average conductance, follows one-parameter scaling near the Anderson transition.

Findings

Conductance distribution obeys one-parameter scaling near the transition

Supports the validity of the single parameter scaling hypothesis

Numerical demonstration clarifies conductance fluctuations behavior

Abstract

The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is essential to investigate the scaling of the full conductance distribution to establish the scaling hypothesis. We present a clear cut numerical demonstration that the conductance distribution indeed obeys one parameter scaling near the Anderson transition.