Conductance for the two dimensional discrete random Schroedinger operator with small disorder

TL;DR

This paper discusses conductance in 2D discrete random Schrödinger operators with small disorder, connecting numerical results to the Thouless criterion to understand Anderson localization.

Contribution

It introduces a new numerical approach to analyze Anderson localization and links conductance behavior with the Thouless criterion in two-dimensional systems.

Findings

Numerical results support the relationship between conductance and the Thouless parameter.

The study clarifies the role of small disorder in 2D Anderson localization.

Connections between conductance measurements and localization criteria are established.

Abstract

As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson (de)localization" from a physics perspective. Further, we discover a relationship with the so-called Thouless criterion - a dimensionless scaling parameter often used as the sole indicator whether or not the system exhibits Anderson localization.