Conductance distribution in a random matrix model

Numerical solutions of the tight-binding Anderson model show that the distribution of conductance P(g) in a disordered conductor near the Anderson metal-insulator transition in three dimensions (3D) is very broad and highly asymmetric. Surprisingly, the distribution is also similarly broad and asymmetric near the smooth metal-insulator crossover in a quasi-one dimensional (Q1D) disordered conductor. There is no analytical framework currently available that can obtain P(g) directly, or study the subtle differences in the distributions between 3D and Q1D. We propose a random matrix model that allows us to study the full distribution in detail in both cases.