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

L. I. Deych·M. V. Erementchouk·A. A. Lisyansky
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Abstract

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 $L$, $l_{loc}\ll L\ll l_s$, the variance of the Lyapunov exponent does not follow the predictions of the central limit theorem, and may even grow with $L$.

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L. I. Deych, M. V. Erementchouk, A. A. Lisyansky. 2003-03-29. Scaling in the one-dimensional Anderson localization problem in the region of fluctuation states. https://doi.org/10.1103/physrevlett.90.126601

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