Maximum-entropy model for quantum-mechanical interference effects in metallic conductors

Abstract

We show that all the known quantum-mechanical interference effects characteristic of disordered conductors in the metallic limit can be obtained from a ‘‘maximum-entropy model,’’ based on a transfer-matrix formulation, which is independent of any particular form of the disordered microscopic Hamiltonian. In particular, we have derived the weak-localization effect and the associated backscattering peak, as well as the universal conductance fluctuations and the associated long-range correlations in transmission probabilities. We find precise quantitative agreement with microscopic Green-function calculations evaluated in the quasi-one-dimensional limit. We define two random-matrix ensembles characterizing systems with and without time-reversal symmetry (the analogs of the well-known orthogonal and unitary ensembles), and show that, within the model, breaking of time-reversal symmetry has the expected effect on these phenomena. The model has not been shown to yield behavior characteristic of the two- or three-dimensional limits, which appear to be outside its current range of validity.