Invariant graphs and spectral type of Schrödinger operators

Abstract

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.

20 pages

References in corpus (2)

• The absolutely continuous spectrum of the almost Mathieu operator
• Almost reducibility and absolute continuity I