|
Quantum unique ergodicity
Author(s):
Harold
Donnelly
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2945-2951.
MSC (2000):
Primary 58G25
Posted:
December 30, 2002
Retrieve article in:
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:
-
- 1.
- Burns, K. and Gerber, M., Real analytic Bernoulli geodesic flows on
 , 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
DOI:
10.1090/S0002-9939-02-06810-7
PII:
S 0002-9939(02)06810-7
Received by editor(s):
March 15, 2002
Received by editor(s) in revised form:
April 1, 2002
Posted:
December 30, 2002
Additional Notes:
Research supported by the Ellentuck Fund and the National Science Foundation
Communicated by:
Jozef Dodziuk
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org