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Invariant graphs and spectral type of Schrödinger operators

Artur Avila, Konstantin Khanin, Martin Leguil

20/4/20 Published in : arXiv:2004.09137

In this paper we study spectral properties of Schrödinger 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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Phase I & II research project(s)

  • Statistical Mechanics

Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions

Analytic maps of parabolic and elliptic type with trivial centralisers

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The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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