Statistics of Lyapunov exponent in 1-D random periodic-on-average systems

Details Statistics of Lyapunov exponent in 1-D random periodic-on-average systems Statistics of Lyapunov exponent in 1-D random periodic-on-average systems

1998-04-02

arxiv.org/abs/cond-mat/9804022v2

Phys. Rev. Lett. 1998, V. 81, p. 5390

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 4 PS figures, RevTex

Scientific paper

10.1103/PhysRevLett.81.5390

By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1-{\em D} 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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