The unitary Anderson model: Lyapunov exponent and localization

We review some results for the Unitary Anderson Model. We start by characterizing positivity and vanishing of the Lyapunov exponent for this model throughout the spectrum and for arbitrary distributions of the random phases. We prove that, unlike the self adjoint Anderson Model, for certain distributions a nite number of critical spectral values, with vanishing Lyapunov exponent, exists. We then show how positivity of the Lyapunov exponent, in the case of absolutely continuous distributions with bounded density, leads the model to be dynamically localized.
This talk is based on joint work with : A. Joye and G. Stolz.