From the Kubo formula to variable range hopping

TL;DR

This paper develops a semi-linear response theory to unify the understanding of conductance in disordered quantum rings, deriving Mott's hopping phenomenology from fundamental principles.

Contribution

It introduces a semi-linear response framework that extends beyond linear response, connecting quantum ergodicity breakdowns to variable range hopping.

Findings

Derivation of Mott's hopping from semi-linear response theory

Unified treatment of strong and weak disorder regimes

Resistor network model for quantum transitions

Abstract

Consider a multichannel closed ring with disorder. In the semiclassical treatment its conductance is given by the Drude formula. Quantum mechanics challenge this result both in the limit of strong disorder (eigenstates are not quantum-ergodic in real space) and in the limit of weak disorder (eigenstates are not quantum-ergodic in momentum space). Consequently the analysis of conductance requires going beyond linear response theory, leading to a resistor network picture of transitions between energy levels. We demonstrate that our semi-linear response theory provides a firm unified framework from which the "hopping" phenomenology of Mott can be derived.