The DMPK equation for mesoscopic quantum transport revisited

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 $\ell_0$.