Note on quantum unique ergodicity
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- by Steve Zelditch PDF
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Abstract:
We prove that (near) off-diagonal matrix elements $\langle A \varphi _i, \varphi _j \rangle$ ($i \not = j$) 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.References
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Additional Information
- Steve Zelditch
- Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
- MR Author ID: 186875
- Email: zelditch@math.jhu.edu
- Received by editor(s): January 28, 2003
- Received by editor(s) in revised form: March 10, 2003
- Published electronically: 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 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1869-1872
- MSC (2000): Primary 58J50, 58J40, 35P99, 81S10
- DOI: https://doi.org/10.1090/S0002-9939-03-07298-8
- MathSciNet review: 2051153