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Note on converse quantum ergodicity
Author(s):
Boris
Gutkin
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2795-2800.
MSC (2000):
Primary 58J50, 81Q50;
Secondary 37D50
Posted:
March 5, 2009
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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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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