Lyapunov exponents for unitary Anderson models
نویسندگان
چکیده
منابع مشابه
Lyapunov Exponents for Unitary Anderson Models
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 c...
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We study one-dimensional, continuum Bernoulli-Anderson models with general single-site potentials and prove positivity of the Lyapunov exponent away from a discrete set of critical energies. The proof is based on Fürstenberg’s Theorem. The set of critical energies is described explicitly in terms of the transmission and reflection coefficients for scattering at the single-site potential. In exa...
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The stochastic Anderson model in discrete or continuous space is defined for a class of non-Gaussian space-time potentials W as solutions u to the multiplicative stochastic heat equation u(t, x) = 1 + ∫ t 0 κ∆u(s, x)ds+ ∫ t 0 βW (ds, x)u(s, x) with diffusivity κ and inverse-temperature β. The relation with the corresponding polymer model in a random environment is given. The large time exponent...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2713996