English

Invariant graphs and spectral type of Schr\"odinger operators

Dynamical Systems 2020-04-21 v1 Spectral Theory

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.

Keywords

Cite

@article{arxiv.2004.09137,
  title  = {Invariant graphs and spectral type of Schr\"odinger operators},
  author = {Artur Avila and Konstantin Khanin and Martin Leguil},
  journal= {arXiv preprint arXiv:2004.09137},
  year   = {2020}
}

Comments

20 pages