S. Bachmann, W. De Roeck
Published 2009-12-08, updated 2012-01-10Version 3
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.
Comments: 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
Random Matrices and the Anderson Model
Moment matrices and multi-component KP, with applications to random matrix theory
Painleve II in random matrix theory and related fields
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