Generic singular continuous spectrum for ergodic Schr\"odinger operators
Dynamical Systems
2015-02-24 v1 Mathematical Physics
math.MP
Abstract
We consider Schr\"odinger operators with ergodic potential , , , where is a non-periodic homeomorphism. We show that for generic , the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani Theory.
Keywords
Cite
@article{arxiv.math/0409061,
title = {Generic singular continuous spectrum for ergodic Schr\"odinger operators},
author = {Artur Avila and David Damanik},
journal= {arXiv preprint arXiv:math/0409061},
year = {2015}
}
Comments
6 pages