Scaling in the one-dimensional anderson localization problem in the region of fluctuation states.

We numerically study the distribution function of the conductivity (transmission) in the one-dimensional tight-binding Anderson model in the region of fluctuation states. We show that while single parameter scaling in this region is not valid, the distribution can still be described within a scaling approach based upon the ratio of two fundamental quantities, the localization length, l(loc), and a new length, l(s), related to the integral density of states. In an intermediate interval of the system's length L, l(loc)<<L<<l(s), the variance of the Lyapunov exponent does not follow the predictions of the central limit theorem, and may even grow with L.