From the Anderson model on a strip to the DMPK equation 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.

We withdraw the paper because it contains an essential error, as pointed out to us by Max Butz. Whereas the main conclusion ("random matrix predictions can be checked on a microscopic (Hamiltonian) model") is correct, the result, in particular Proposition 3, is not true in the form as stated. A corrected and expanded treatment will appear shortly

References in corpus (3)

• Universality of Random Matrices and Local Relaxation Flow
• Bulk Universality for Wigner Matrices
• Random Schrodinger operators on long boxes, noise explosion and the GOE

Cited by in corpus (8)

• Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
• The scaling limit of the critical one-dimensional random Schrodinger operator
• Multifield Stochastic Particle Production: Beyond a Maximum Entropy Ansatz
• Random Schrodinger operators on long boxes, noise explosion and the GOE
• Relations between Transfer and Scattering Matrices in the presence of Hyperbolic Channels
• A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
• Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law
• Existence of a unique strong solution to the DMPK equation