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Note on quantum unique ergodicity
Author(s):
Steve
Zelditch
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1869-1872.
MSC (2000):
Primary 58J50, 58J40, 35P99, 81S10
Posted:
November 21, 2003
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Abstract:
We prove that (near) off-diagonal matrix elements  ( ) of pseudodifferential operators relative to eigenfunctions of quantum unique- ly ergodic Laplacians vanish as the eigenvalues tend to infinity. It follows that QUE systems cannot have quasi-modes with singular limits and a bounded number of essential frequencies, as is believed to occur for the stadium and other examples.
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Additional Information:
Steve
Zelditch
Affiliation:
Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email:
zelditch@math.jhu.edu
DOI:
10.1090/S0002-9939-03-07298-8
PII:
S 0002-9939(03)07298-8
Received by editor(s):
January 28, 2003
Received by editor(s) in revised form:
March 10, 2003
Posted:
November 21, 2003
Additional Notes:
This research was partially supported by NSF grant DMS-0071358 and by the Clay Mathematics Institute
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
2003,
American Mathematical Society
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