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

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

2009-12-08

arxiv.org/abs/0912.1574v3

Physics

Mathematical Physics

We withdraw the paper because it contains an essential error, as pointed out to us by Max Butz. Whereas the main conclusion ("

Scientific paper

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.

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