Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Quantum unique ergodicity

Author: Harold Donnelly
Journal: Proc. Amer. Math. Soc. 131 (2003), 2945-2951
MSC (2000): Primary 58G25
Published electronically: December 30, 2002
MathSciNet review: 1974353
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Burns, K. and Gerber, M., Real analytic Bernoulli geodesic flows on $S^2$, Ergodic theory and dynamical systems, 9 (1989), pp. 27-45. MR 90e:58126
  • 2. Colin de Verdière, Y., Ergodicité et fonctions propres du laplacian, Communications in Mathematical Physics, 102 (1985), pp. 497-502.
  • 3. Heller, E.J., Wavepacket dynamics and quantum chaology, Chaos and Quantum Physics, Les Houches, 1989, North Holland Publishing Company, Amsterdam, 1991, pp. 547-664. MR 94i:81031
  • 4. Sarnak, P.J., Arithmetic Quantum Chaos, Israel Mathematics Conference Proceedings, 8, Bar-Ilan University, 1995, pp. 183-236. MR 96d:11059
  • 5. Schnirelman, A.I., Ergodic Properties of Eigenfunctions, Uspehi Mat. Nauk, 29 (1974), pp. 181-182.
  • 6. Zelditch, S., Uniform distribution of eigenfunctions on a compact hyperbolic surface, Duke Mathematics Journal, 55 (1987), pp. 919-941. MR 89d:58129

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 58G25

Retrieve articles in all journals with MSC (2000): 58G25

Additional 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
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society