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arXiv · 2004.09137

Invariant graphs and spectral type of Schr\"odinger operators

Artur Avila·Konstantin Khanin·Martin Leguil
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Abstract

In this paper we study spectral properties of Schr\"odinger operators with quasi-periodic potentials related to quasi-periodic action minimizing trajectories for analytic twist maps. We prove that the spectrum contains a component of absolutely continuous spectrum provided that the corresponding trajectory of the twist map belongs to an analytic invariant curve.

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Artur Avila, Konstantin Khanin, Martin Leguil. 2020-04-20. Invariant graphs and spectral type of Schr\"odinger operators. https://arxiv.org/abs/2004.09137

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