Communications in Mathematical Physics

, Volume 233, Issue 1, pp 153–171 | Cite as

Entropy of Quantum Limits

  • Jean Bourgain
  • Elon Lindenstrauss


 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.


Entropy Manifold Quantum Limit Geodesic Flow Positive Entropy 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jean Bourgain
    • 1
  • Elon Lindenstrauss
    • 2
  1. 1.School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA. E-mail: bourgain@ias.eduUS
  2. 2.Department of Mathematics, Stanford University, Stanford, CA 94305, USA. E-mail: elonl@math.stanford.eduUS

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