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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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.|
|Classification Code:||2000 Mathematics Subject Classification: Primary 82B44; Secondary 47B36|
|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.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||13 May 2011 21:45|
|Last Modified:||26 Dec 2012 13:14|
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