 0417 Silvius Klein
 Anderson localization for the discrete onedimensional quasiperiodic Schroedinger operator with potential defined by a Gevreyclass function
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Jan 22, 04

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Abstract. In this paper we consider the discrete onedimensional Schroedinger operator with quasiperiodic potential v_n = \lambda v (x + n \omega). We assume that the frequency \omega satisfies a strong Diophantine condition and that the function v belongs to a Gevrey class, and it satisfies a transversality condition. Under these assumptions we prove  in the perturbative regime  that for large disorder \lambda and for most frequencies \omega the operator satisfies Anderson localization. Moreover, we show that the associated Lyapunov exponent is positive for all energies, and that the Lyapunov exponent and the integrated density of states are continuous functions with a certain modulus of continuity. We also prove a partial nonperturbative result assuming that the function v belongs to some particular Gevrey classes.
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