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Generic singular spectrum for ergodic Schrödinger operators

Avila, Artur and Damanik, David (2005) Generic singular spectrum for ergodic Schrödinger operators. Duke Mathematical Journal, 130 (2). pp. 393-400. ISSN 0012-7094. http://resolver.caltech.edu/CaltechAUTHORS:20110513-104707967

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1215/S0012-7094-05-13035-6DOIUNSPECIFIED
http://projecteuclid.org/euclid.dmj/1132064631PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0227289
Classification Code:2000 Mathematics Subject Classification: Primary 82B44; Secondary 47B36
Record Number:CaltechAUTHORS:20110513-104707967
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110513-104707967
Official Citation:Generic Singular Spectrum For Ergodic Schrödinger Operators Artur Avila and David Damanik; 393-400
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23659
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 May 2011 21:45
Last Modified:26 Dec 2012 13:14

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