Quantum unique ergodicity
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- by Harold Donnelly
- Proc. Amer. Math. Soc. 131 (2003), 2945-2951
- DOI: https://doi.org/10.1090/S0002-9939-02-06810-7
- Published electronically: December 30, 2002
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Abstract:
Consider a compact Riemannian manifold with ergodic geodesic flow. Quantum ergodicity is generalized from orthonormal bases of eigenfunctions of the Laplacian to packets of eigenfunctions. It is shown that this more general result is sharp. Namely, there may exist exceptional packets of eigenfunctions which concentrate on a submanifold.References
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Bibliographic Information
- Harold Donnelly
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
- Received by editor(s): March 15, 2002
- Received by editor(s) in revised form: April 1, 2002
- Published electronically: December 30, 2002
- Additional Notes: Research supported by the Ellentuck Fund and the National Science Foundation
- Communicated by: Jozef Dodziuk
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2945-2951
- MSC (2000): Primary 58G25
- DOI: https://doi.org/10.1090/S0002-9939-02-06810-7
- MathSciNet review: 1974353