# From the Anderson Model on a Strip to the DMPK Equation and Random Matrix Theory

@article{Bachmann2009FromTA, title={From the Anderson Model on a Strip to the DMPK Equation and Random Matrix Theory}, author={Sven Bachmann and Wojciech de Roeck}, journal={Journal of Statistical Physics}, year={2009}, volume={139}, pages={541-564} }

We study weakly disordered quantum wires whose width is large compared to the Fermi wavelength. It is conjectured that such wires display universal metallic behavior as long as their length is shorter than the localization length (which increases with the width). The random matrix theory that accounts for this behavior—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…

## 14 Citations

### Disordered Quantum Wires: Microscopic Origins of the DMPK Theory and Ohm’s Law

- Physics
- 2012

We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is…

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- 2012

For the transmission of electrons in a weakly disordered strip of material Dorokhov, Mello, Pereyra and Kumar (DMPK) proposed a diffusion process for the transfer matrices. The correspoding…

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- 2011

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements Hxy, indexed by $${x,y \in \Lambda \subset \mathbb{Z}^d}$$, are independent, uniformly distributed…

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- Mathematics, PhysicsElectronic Journal of Probability
- 2019

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- 2011

AbstractWe consider two models of one-dimensional discrete random Schrödinger operators
$$(H_n\psi)_\ell =\psi_{\ell -1}+\psi_{\ell +1}+v_\ell \psi_\ell$$, $${\psi_0=\psi_{n+1}=0}$$ in the cases $${…

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### The Scaling Limit of the Critical One-Dimensional Random Schrödinger Operator

- Materials ScienceCommunications in Mathematical Physics
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We consider two models of one-dimensional discrete random Schrödinger operators \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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