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Entropy of Quantum Limits

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Abstract:

 In this paper we show that any measure arising as a weak* limit of microlocal lifts of eigenfunctions of the Laplacian on certain arithmetic manifolds have dimension at least 11/9, and in particular all ergodic components of this measure with respect to the geodesic flow have positive entropy.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA. E-mail: bourgain@ias.edu, , , , , , US

    Jean Bourgain

  2. Department of Mathematics, Stanford University, Stanford, CA 94305, USA. E-mail: elonl@math.stanford.edu, , , , , , US

    Elon Lindenstrauss

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  1. Jean Bourgain
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  2. Elon Lindenstrauss
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Received: 14 March 2002 / Accepted: 24 June 2002 Published online: 13 January 2003

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Bourgain, J., Lindenstrauss, E. Entropy of Quantum Limits. Commun. Math. Phys. 233, 153–171 (2003). https://doi.org/10.1007/s00220-002-0770-8

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  • DOI: https://doi.org/10.1007/s00220-002-0770-8

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