Conductance distribution in three dimensions: analytic solution of the Generalized DMPK equation in the strongly disordered regime

TL;DR

This paper derives an analytic solution to the Generalized DMPK equation in three dimensions for strongly disordered systems, providing insights into conductance distribution and Anderson transition behavior.

Contribution

It introduces a systematic perturbative method to solve the Generalized DMPK equation analytically in the strongly disordered regime, advancing understanding of conductance distributions.

Findings

Analytic conductance distribution in the insulating regime

Consistency with numerical simulations of the Anderson model

Insights into the Anderson transition with broad conductance distributions

Abstract

We develop a systematic perturbative method to obtain analytic solution of the Generalized Dorokhov-Mello-Pereyra-Kumar (DMPK) equation in the strongly disordered regime which describes the evolution of the joint probability distribution of the transmission eigenvalues with system size. The solution allows us to obtain the distribution of conductance analytically in the insulating regime. Our results are consistent with existing numerical simulations of the three dimensional tight binding Anderson model, and suggests a possible description of the Anderson transition in the presence of a very broad, highly asymmetric conductance distribution.