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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on converse quantum ergodicity


Author: Boris Gutkin
Journal: Proc. Amer. Math. Soc. 137 (2009), 2795-2800
MSC (2000): Primary 58J50, 81Q50; Secondary 37D50
Published electronically: March 5, 2009
MathSciNet review: 2497494
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Abstract: Quantum ergodicity asserts that eigenstates of a system with classical ergodic dynamics must be ``equidistributed'' in the phase space. In the present note we show that the converse is not true. We provide an example of billiards which are quantum ergodic but not classically ergodic.


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Additional Information

Boris Gutkin
Affiliation: Fachbereich Physik, Universität Duisburg-Essen, 47048 Duisburg, Germany
Email: boris.gutkin@uni-duisburg-essen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09849-9
PII: S 0002-9939(09)09849-9
Received by editor(s): August 12, 2008
Received by editor(s) in revised form: December 8, 2008
Published electronically: March 5, 2009
Additional Notes: The author would like to thank S. Nonnenmacher for helpful discussions on the converse quantum ergodicity problem and A. Knauf for a careful reading of the manuscript and valuable comments. The financial support of the Minerva Foundation and SFB/TR12 of the Deutsche Forschungsgemainschaft is acknowledged.
Communicated by: Bryna Kra
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.