From the Anderson model on a strip to the DMPK equation and random matrix theory

TL;DR

This paper rigorously derives the DMPK equation from the Anderson model on a strip, providing a mathematical foundation for universal metallic behavior in weakly disordered quantum wires of large width.

Contribution

It establishes a twofold scaling limit that connects the Anderson model to the DMPK theory, validating assumptions used in random matrix models for quantum wires.

Findings

Rigorous derivation of DMPK equation from Anderson model

Validation of universal metallic behavior conjectures

Connection between microscopic models and random matrix theory

Abstract

We study weakly disordered quantum wires whose width is large compared to the Fermi wavelength. It is conjectured that such wires diplay universal metallic behaviour as long as their length is shorter than the localization length (which increases with the width). The random matrix theory that accounts for this behaviour - the DMPK theory- rests on assumptions that are in general not satisfied by realistic microscopic models. Starting from the Anderson model on a strip, we show that a twofold scaling limit nevertheless allows to recover rigorously the fundaments of DMPK theory, thus opening a way to settle some conjectures on universal metallic behaviour.