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 ${\ell }^{\prime }$, of order $N{\ell }_0$, in that equation is replaced by the correct mean free path ${\ell }_0$.

To be published in Solid State Communications

References in corpus (4)

• Localization fom conductance in few-channel disordered wires
• Conductance and localization in disordered wires: role of evanescent states
• Localization length in Dorokhov's microscopic model of multichannel wires
• Mean Free Path in Disordered Multichannel Tight-Binding Wires