Multi-Channel Transport in Disordered Medium under Generic Scattering Conditions

TL;DR

This paper generalizes the DMPK equation to describe universal transport phenomena in disordered media across various dimensions, revealing complex eigenvalue interactions affecting transport statistics.

Contribution

It introduces a generalized evolution equation for transmission eigenvalues governed by a single complexity parameter, highlighting universality and many-body interactions.

Findings

Universal transport behavior across different disordered systems

Eigenvalue interactions resemble many-body systems

Deep connection between complexity parameter and transport statistics

Abstract

Our study of the evolution of transmission eigenvalues, due to changes in various physical parameters in a disordered region of arbitrary dimensions, results in a generalization of the celebrated DMPK equation. The evolution is shown to be governed by a single complexity parameter which implies a deep level of universality of transport phenomena through a wide range of disordered regions. We also find that the interaction among eigenvalues is of many body type that has important consequences for the statistical behavior of transport properties.