The DMPK equation for mesoscopic quantum transport revisited

A recent Drude model description of the metallic regime and of a channel-averaged elastic mean free path (mfp), ℓ 0 , in an N-channel tight-binding wire identifies the Thouless localization length, N ℓ 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 ℓ 0 leads to a metallic regime which is consistent with Dorokhovʹs microscopic transmission analysis in terms of a nominal elastic mfp. On the other hand, the validity of Melloʹs derivation of universal conductance fluctuations in the metallic regime based on the DMPK equation is restored if the mfp ℓ ′ , of order N ℓ 0 , in that equation is replaced by the correct mean free path ℓ 0 .