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On non-perturbative Anderson localization for C^αpotentials generated by shifts and skew-shifts

Jackson Chan·Michael Goldstein·Wilhelm Schlag
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Abstract

In this paper we address the question of proving Anderson localization (AL) for the operator [H(x,ω)ψ](n) := - \vp(n+1) - \vp(n-1) + V\bigl(T^n_ωx\bigr)ψ(n), n\in\mathbb Z where T:\tor^2\to\tor^2 is either the shift or the skew-shift and V is only C^α(\tor^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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Jackson Chan, Michael Goldstein, Wilhelm Schlag. 2006-07-28. On non-perturbative Anderson localization for C^αpotentials generated by shifts and skew-shifts. https://arxiv.org/abs/math/0607302

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