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On non-perturbative Anderson localization for Cαpotentials generated by shifts and skew-shifts

Jackson Chan, Michael Goldstein, Wilhelm Schlag

math.DSarXiv:math/0607302

Abstract

In this paper we address the question of proving Anderson localization (AL) for the operator [H(x,ω)ψ](n) := - (n+1) - (n-1) + V(Tnωx)ψ(n), n∈ Z where T:22 is either the shift or the skew-shift and V is only Cα(2) for some α>0. We show that under the assumption of positive Lyapunov exponents, (AL) takes place for a.e. frequency, phase, and energy.

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