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Lyapunov Exponents for Unitary Anderson Models

Mathematical Physics & Probability

Speaker: Eman Hamza, University of Alabama at Birmingham
Location: 2112 MSB
Start time: Tue, Apr 10 2007, 2:10PM

A unitary version of the one-dimensional Anderson model, is obtained by multiplicatively perturbing a five diagonal deterministic unitary operator 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. We show that, unlike the self adjoint case, for certain distributions a finite number of critical spectral values, with vanishing Lyapunov exponent, exists.