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 | References | Similar Articles | Additional Information

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

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.