Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    6 0 0 0


Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 829-834 (août 2010)
Doi : 10.1016/j.crma.2010.07.003
Received : 23 June 2010 ;  accepted : 2 July 2010
Graph eigenfunctions and quantum unique ergodicity
Fonctions propres de graphes et l'unique ergodicité quantique
 

Shimon Brooks a, Elon Lindenstrauss b, 1
a Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY 11794, USA 
b Einstein Institute of Mathematics, Givaat Ram, 91904 Jerusalem, Israel 

Abstract

We apply the techniques of Brooks and Lindenstrauss (2010) [[5]] to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of  . In both cases, we show that quantum limit measures of such sequences of eigenfunctions carry positive entropy on almost every ergodic component. Together with the work of Lindenstrauss (2006) [[9]], this implies Quantum Unique Ergodicity for such functions.

The full text of this article is available in PDF format.
Résumé

On applique les techniques de Brooks et Lindenstrauss (2010) [[5]] pour étudier fonctions propres jointes du laplacien et d'un opérateur Hecke sur des surfaces compactes de congruence, et les fonctions propres jointes de deux laplaciens partiels sur les quotients compacts de  . Dans les deux cas, on montre entropie strictement positive sur presque toutes les composantes ergodiques des limites quantiques. De plus, les travaux de Lindenstrauss (2006) [[9]] ce implique Unique Ergodicité Quantique pour ces fonctions.

The full text of this article is available in PDF format.
1  The author was supported in part by NSF grants DMS-0554345 and DMS-0800345 and the Israel Science Foundation.


© 2010  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline
@@#110903@@