An explicit skew-shift Schrödinger operator with positive Lyapunov exponent at small coupling

preprint2012arXivOpen access

Abstract

I give an example of a skew-shift Schrödinger operator with positive Lyapunov exponent in the spectrum for all positive coupling constant with constant frequency. This is the first example of this kind. The proof is based on CMV operators given by the skew-shift. Further results on these are derived.

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