Invariant imbedding approach to the length-scale dependent conductance of a one-dimensional disordered medium

Abstract

The invariant-imbedding equation for the complex amplitude reflection coefficient ρ(L)=ρ₁ +iρ₂ evolving stochastically in the length L of a disordered one-dimensional conductor is reduced to a linear second order deterministic equation for the probability density P(ρ₁,ρ₂;L). The latter can be used to calculate any averaged quantity of interest, in particular the average conductance using the Landauer formula, and to discuss the fluctuations about the average. The latter has been a subject of much discussion in the recent past.