The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture

TL;DR

This paper develops a mesoscopic conductance theory for disordered rings, using a sparse random matrix model to extend the variable range hopping concept beyond traditional frameworks.

Contribution

It introduces an improved sparse random matrix model that captures the influence of matrix texture and sparsity on conductance, extending the variable range hopping picture.

Findings

Conductance depends on disorder strength, from ballistic to localized regimes.

The model reveals the importance of matrix texture and sparsity in conductance.

A generalized variable range hopping framework is proposed.

Abstract

The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming "mesoscopic" circumstances the analysis of the electro-driven transitions show similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture.