ELECTRONIC TRANSPORT THROUGH QUASI-ONE-DIMENSIONAL DISORDERED SYSTEMS

Abstract

This chapter treats the problem of finding the probability distribution of quantities related to quantum transport through a strictly one-dimensional (i.e., 1-channel) and through an N-channel quasi-one-dimensional disordered system. It uses the maximum entropy approach wherein the distribution for the random transfer matrix for an elementary building block is determined by maximizing the associated Shannon entropy, subject to the physically relevant constraints of flux conservation, time-reversal symmetry (when relevant), and the Ohmic small length-scale limit. The contents of this chapter include ensemble of transfer matrices; universality classes — the orthogonal and the unitary classes; invariant measure; the Fokker-Planck equation for a disordered one-dimensional conductor; the maximum-entropy ansatz for the building block; construction of the probability density for a system of finite length; the Fokker-Planck equation for a quasi-one-dimensional multi-channel disordered conductor; the diffusion equation for the orthogonal universality class, β = 1; the diffusion equation for the unitary universality class, β = 2; and universal conductance fluctuations in the good-metallic limit.