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We study the electronic transport properties of the Anderson model on astrip, modeling a quasi one-dimensional disordered quantum wire. In theliterature, the standard description of such wires is via random matrix theory(RMT). Our objective is to firmly relate this theory to a microscopic model. Wecorrect and extend previous work (arXiv:0912.1574) on the same topic. Inparticular, we obtain through a physically motivated scaling limit an ensembleof random matrices that is close to, but not identical to the standard transfermatrix ensembles (sometimes called TOE, TUE), corresponding to the Dysonsymmetry classes \beta=1,2. In the \beta=2 class, the resulting conductance isthe same as the one from the ideal ensemble, i.e.\ from TUE. In the \beta=1class, we find a deviation from TOE. It remains to be seen whether or not thisdeviation vanishes in a thick-wire limit, which is the experimentally relevantregime. For the ideal ensembles, we also prove Ohm's law for all symmetryclasses, making mathematically precise a moment expansion by Mello and Stone.This proof bypasses the explicit but intricate solution methods that underliemost previous results.

Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law