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

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

2002-07-05

arxiv.org/abs/cond-mat/0207169v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

Phys. Rev. Lett 90, 126601 (2003) 4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.90.126601

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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