Published November 1, 2005
| Published
Journal Article
Open
Generic singular spectrum for ergodic Schrödinger operators
- Creators
- Avila, Artur
-
Damanik, David
Abstract
We consider Schrödinger operators with ergodic potential V_ω(n) = f(T^n(ω)), n Є Z, ω Є Ω, where T : Ω → Ω is a nonperiodic homeomorphism. We show that for generic f Є C(Ω), the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani theory.
Additional Information
© 2005 Duke University Press. Received 3 September 2004. Revision received 24 February 2005. This work was done while Avila was visiting the California Institute of Technology. We thank Svetlana Jitomirskaya and Barry Simon for stimulating discussions.Attached Files
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Additional details
- Eprint ID
- 23659
- Resolver ID
- CaltechAUTHORS:20110513-104707967
- DMS-0227289
- NSF
- Created
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2011-05-13Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field