Generalized DMPK equation for strongly localized regime - numerical solution

TL;DR

This paper develops a numerical algorithm to solve the generalized DMPK equation, confirming its effectiveness in describing electron transport in strongly localized regimes and capturing dimensional differences.

Contribution

It introduces a numerical solution method for the GDMPK equation, extending the original DMPK framework to include system dimensionality effects.

Findings

GDMPK equation accurately describes critical and localized regimes

The algorithm confirms the role of system dimension in electron transport

Distinguishes between 2D and 3D models with same channels

Abstract

Generalized Dorokhov-Mello-Pereyra-Kumar (GDMPK) equation [K. A. Muttalib and J. R. Klauder, Phys. Rev. Lett. {\bf 82}, 4272 (1999)] has been proposed for the description of the electron transport in strongly localized systems. We develop an algorithm for the numerical solution of this equation and confirm that GDMPK equation correctly describes the critical and localized regimes. Contrary to the original DMPK equation, the generalized one contains also an information about the dimension of the system. In particular, it distinguishes between the two and the three dimensional models with the same number of transmission channels.