MAXIMUM ENTROPY MODELS OF TRANSPORT IN MESOSCOPIC WIRES

We review the maximum entropy models for the probability distribution of the transfer matrix of a disordered mesoscopic wire. We relate this distribution to the zero temperature conductance of the wire using the Landauer formula and discuss the extent to which the maximum entropy models describe accurately the weak localisation effect and universal conductance fluctuations which occur in the diffusive regime. A detailed comparison between numerical simulations and the maximum entropy models is also presented. For “long” wires there is a crossover from diffusive to localised behaviour and we review the predictions of the maximum entropy models in this regime, chiefly the symmetry dependence of the localisation length and the log-normal distribution of the conductance. In conclusion we discuss the limitations of the maximum entropy models and in particular the property of isotropy.