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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. doi:10.1215/S0012-7094-05-13035-6.

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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.

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Damanik, David0000-0001-5924-3849
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.
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Issue or Number:2
Classification Code:2000 Mathematics Subject Classification: Primary 82B44; Secondary 47B36
Record Number:CaltechAUTHORS:20110513-104707967
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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
Deposited By: Ruth Sustaita
Deposited On:13 May 2011 21:45
Last Modified:09 Nov 2021 16:16

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