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 ls determined by the integral density of states. For long enough systems, L ≫ ls, the distribution can still be described within a new scaling approach based upon the ratio of the localization length lloc and ls. In an intermediate interval of the system's length L, lloc ≫ ls, the variance of the Lyapunov exponent does not follow the predictions of the central limit theorem and this scaling becomes invalid.
L. I. Deych et al., "Statistics of Transmission in One-Dimensional Disordered Systems: Universal Characteristics of States in the Fluctuation Tails," Physical Review B (Condensed Matter), vol. 68, no. 17, pp. 1742031 - 1742039, American Physical Society (APS), Nov 2003.
The definitive version is available at https://doi.org/10.1103/PhysRevB.68.174203
Keywords and Phrases
Conductance; Electric Conductivity; Mathematical Analysis; Prediction; Rating Scale; Reaction Analysis; Statistical Analysis
International Standard Serial Number (ISSN)
Article - Journal
© 2003 American Physical Society (APS), All rights reserved.
01 Nov 2003