Lyapunov Exponents for Unitary Anderson Models

Details Lyapunov Exponents for Unitary Anderson Models Lyapunov Exponents for Unitary Anderson Models

2006-11-28

arxiv.org/abs/math-ph/0611081v1

Physics

Mathematical Physics

18 pages

Scientific paper

10.1063/1.2713996

We study a unitary version of the one-dimensional Anderson model, given by a five diagonal deterministic unitary operator multiplicatively perturbed by a random phase matrix. We fully characterize positivity and vanishing of the Lyapunov exponent for this model throughout the spectrum and for arbitrary distributions of the random phases. This includes Bernoulli distributions, where in certain cases a finite number of critical spectral values, with vanishing Lyapunov exponent, exists. We establish similar results for a unitary version of the random dimer model.

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