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