Conductance length autocorrelation in quasi one-dimensional disordered wires

Abstract

Employing techniques recently developed in the context of the Fokker--Planck approach to electron transport in disordered systems we calculate the conductance length correlation function $< δg(L) δg(L+ΔL) >$ for quasi 1d wires. Our result is valid for arbitrary lengths L and $ΔL$. In the metallic limit the correlation function is given by a squared Lorentzian. In the localized regime it decays exponentially in both L and $ΔL$. The correlation length is proportional to L in the metallic regime and saturates at a value approximately given by the localization length $ξ$ as $L\ggξ$.