Landauer and Thouless Conductance: a Band Random Matrix Approach

TL;DR

This paper investigates the relationship between Landauer and Thouless conductances in disordered wires using banded random matrices, revealing proportionality in the diffusive regime and quadratic relation in the localized regime, with numerical fluctuations aligning with theory.

Contribution

It introduces a band random matrix approach to compare Landauer and Thouless conductances, highlighting their proportionality and quadratic relations across regimes.

Findings

Proportionality between conductances in the diffusive regime

Landauer conductance ~ square of Thouless conductance in localized regime

Numerical fluctuations approach theoretical predictions

Abstract

We numerically analyze the transmission through a thin disordered wire of finite length attached to perfect leads, by making use of banded random Hamiltonian matrices. We compare the Landauer and the Thouless conductances, and find that they are proportional to each other in the diffusive regime, while in the localized regime the Landauer conductance is approximately proportional to the square of the Thouless one. Fluctuations of the Landauer conductance were also numerically computed; they are shown to slowly approach the theoretically predicted value.