Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-05-08
Physics
Condensed Matter
Disordered Systems and Neural Networks
22 pages, 12 eps figures
Scientific paper
10.1103/PhysRevB.68.174203
We numerically study the distribution function of the conductance (transmission) in the one-dimensional tight-binding Anderson and periodic-on-average superlattice models in the region of fluctuation states where single parameter scaling is not valid. We show that the scaling properties of the distribution function depend upon the relation between the system's length $L$ and the length $l_s$ determined by the integral density of states. For long enough systems, $L \gg l_s$, the distribution can still be described within a new scaling approach based upon the ratio of the localization length $l_{loc}$ and $l_s$. 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 this scaling becomes invalid.
Cao Hui
Deych Lev I.
Erementchouk Mikhael V.
Lisyansky Alexander A.
Yamilov Alexey
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