Scattering and transport properties of tight-binding random networks.

We study numerically scattering and transport statistical properties of tight-binding random networks characterized by the number of nodes N and the average connectivity α. We use a scattering approach to electronic transport and concentrate on the case of a small number of single-channel attached leads. We observe a smooth crossover from insulating to metallic behavior in the average scattering matrix elements <|S(mn)|(2)>, the conductance probability distribution w(T), the average conductance <T>, the shot noise power P, and the elastic enhancement factor F by varying α from small (α→0) to large (α→1) values. We also show that all these quantities are invariant for fixed ξ=αN. Moreover, we proposes a heuristic and universal relation between <|S(mn)|(2)>, <T>, and P and the disorder parameter ξ.