Random Matrix Theory of Transition Strengths and Universal Magnetoconductance in the Strongly Localized Regime

TL;DR

This paper applies random matrix theory to model transition strengths in strongly localized transport, deriving universal magnetoconductance curves that are confirmed through numerical simulations.

Contribution

It introduces a new application of random matrix theory to predict universal magnetoconductance behavior in the strongly localized regime.

Findings

Derived crossover distribution functions between ensembles.

Predicted universal magnetoconductance curves.

Confirmed predictions with numerical simulations.

Abstract

Random matrix theory of the transition strengths is applied to transport in the strongly localized regime. The crossover distribution function between the different ensembles is derived and used to predict quantitatively the {\sl universal} magnetoconductance curves in the absence and in the presence of spin-orbit scattering. These predictions are confirmed numerically.