Generalization of the DMPK equation beyond quasi one dimension

TL;DR

This paper extends the DMPK equation to higher-dimensional disordered quantum wires by incorporating eigenvector properties, enabling more accurate modeling beyond quasi-one-dimensional systems.

Contribution

The authors derive a generalized DMPK equation that accounts for higher dimensions through transmission eigenvector properties, surpassing previous phenomenological models.

Findings

Derived a higher-dimensional DMPK equation incorporating eigenvector dependence

Connected the new equation to earlier phenomenological models

Provides a framework for analyzing electronic transport in complex geometries

Abstract

Electronic transport properties in a disordered quantum wire are very well described by the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation, which describes the evolution of the transmission eigenvalues as a function of the length of a multichannel conductor. However, the DMPK equation is restricted to quasi one dimensional systems only. We derive a generalized DMPK equation for higher dimensions, containing dependence on the dimensionality through the properties of the transmission eigenvectors, by making certain statistical assumptions about the transfer matrix. An earlier phenomenological generalization is obtained as a special case.