Transport in topologically disordered one-particle, tight-binding models

TL;DR

This paper investigates transport properties like conductivity and mean free path in disordered quantum systems, focusing on delocalized states in metallic regimes and comparing different models' behaviors.

Contribution

It provides a quantitative analysis of transport parameters in topologically disordered models, highlighting when Boltzmann-like behavior applies and when it does not.

Findings

Einstein relation holds numerically and analytically.

Transport behavior varies between models, with some fitting Boltzmann equations.

Long mean free paths and exponential decay observed in certain models.

Abstract

We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially completely disordered quantum systems, comparable to the systems which are sometimes referred to as Lifshitz models. While some low-energy eigenstates in such models always show Anderson localization, we focus on models for which most states of the full spectrum are delocalized, i.e., on the metallic regime. For the latter we determine transport parameters in the limit of high temperatures and low fillings using linear response theory. The Einstein relation (proportionality of conductivity and diffusion coefficient) is addressed numerically and analytically and found to hold. Furthermore, we find the transport behavior for some models to be in accord with a Boltzmann equation, i.e., rather long mean free paths, exponentially decaying currents, while this does not apply to other models even though they are also almost completely delocalized.