Conductance distribution across the Anderson transition in a random matrix model

Abstract

A model based on random matrix theory (RMT) is used to obtain the full conductance distribution $P(g)$ in three dimensions (3D) across the Anderson metal-insulator transition, and compared with the corresponding quasi-one-dimensional (Q1D) case where there is only a smooth crossover. We show that while the differences between the two are subtle, the details of the results from the RMT model agree very well with the existing numerical studies of the tight-binding Anderson model in 3D vs Q1D, including the critical region in 3D.