Band-center anomaly of the conductance distribution in one-dimensional Anderson localization

We analyze the conductance distribution function in the one-dimensional Anderson model of localization, for weak disorder but arbitrary energy. For energy at the band center the distribution function deviates from the form that is assumed to be universal in single-parameter scaling theory. A direct link to the breakdown of the random-phase approximation is established. Our findings are confirmed by a parameter-free comparison to the results of numerical simulations.