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arXiv · 1302.1319

The DMPK equation for mesoscopic quantum transport revisited

Jean Heinrichs
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Abstract

A recent Drude model description of the metallic regime and of a channel- averaged elastic mean free path (mfp), $\ell_0$, in an $N$-channel tight-binding wire identifies the Thouless localization length, $N\ell_0$, as a proper lower bound of macroscopic length scales ("mean free path") for the DMPK equation describing the localized regime of the wire. The mfp $\ell_0$ leads to a metallic regime which is consistent with Dorokhov's microscopic transmission analysis in terms of a nominal elastic mfp. On the other hand, the validity of Mello's derivation of universal conductance fluctuations in the metallic regime based on the DMPK equation is restored if the mfp $\ell'$, of order $N\ell_0$, in that equation is replaced by the correct mean free path $\ell_0$.

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Jean Heinrichs. 2013-02-06. The DMPK equation for mesoscopic quantum transport revisited. https://doi.org/10.1016/j.ssc.2013.01.023

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