Universal Conductance Distributions in the Crossover between Diffusive and Localization Regimes

The full distribution of the conductance $P\left(G\right)$ in quasi-one-dimensional wires with rough surfaces is analyzed from the diffusive to the localization regime. In the crossover region, where the statistics is dominated by only one or two eigenchannels, the numerically obtained $P\left(G\right)$ is found to be independent of the details of the system with the average conductance $〈G〉$ as the only scaling parameter. For $〈G〉<e^2/h$, $P\left(G\right)$ is given by an essentially “one-sided” log-normal distribution. In contrast, for $e^2/h<\mathrm{}〈G〉\le {2e}^2/h$, the shape of $P\left(G\right)$ remarkably agrees with those predicted by random matrix theory for two fluctuating transmission eigenchannels.