Statistics of the Lyapunov Exponent in 1D Random Periodic-on-Average Systems

1998/04/30 by Lev Deych, Lev I. Deych, D. Zaslavsky +2 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Gene Regulatory Network Analysis #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.81.5390

published as Phys. Rev. Lett. 1998, V. 81, p. 5390 · 5 pages, 4 PS figures, RevTex

openalex publication_date 1998/12/14 · arxiv created 1999/01/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1D random periodic-on-average systems. States from pass bands and band edges of the underlying band structure demonstrate single parameter scaling with universal behavior. States from the interior of the band gaps do not have universal behavior and require two parameters to describe their scaling properties. The transition between these two types of behavior occurs in an extremely narrow region of frequencies. When the degree of disorder exceeds a certain critical value the single parameter scaling is restored for an entire band gap.

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