Resistance fluctuation in a one-dimensional conductor with static disorder

Abstract

The non-self-averaging resistance of a one-dimensional conductor with static disorder is reexamined by the method of invariant imbedding, leading to a Fokker-Planck equation for its probability distribution W_ρ(ρ, l), with varying sample length l. An exact two-point recursion relation for the moments <ρⁿ> is given along with a closed-form solution for W_ρ(ρ, l) for the case of Gaussian white-noise disorder. The latter confirms lnρ as the correct scale variable. The treatment admits generalization to the case of N channels and to general disorder.