Comptes Rendus
no. 1
Mathematical Physics
Proof of the Kurlberg–Rudnick rate conjecture
[Démonstration de la conjecture du taux de Kurlberg–Rudnick]

Présenté par : Michèle Vergne

Shamgar Gurevich1 ; Ronny Hadani1
1 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 69-72.

Nous proposons une démonstration de la conjecture d'unique ergodicité quantique d'Hecke pour le modèle de Berry–Hannay, un modèle de mécanique quantique sur un tore de dimension deux. Cette conjecture a été proposée par Z. Rudnick à MSRI, Berkeley, 1999 et à l'ECM, Barcelona, 2000.

In this Note we present a proof of the Hecke quantum unique ergodicity conjecture for the Berry–Hannay model, a model of quantum mechanics on a two dimensional torus. This conjecture was stated in Z. Rudnick's lectures at MSRI, Berkeley, 1999 and ECM, Barcelona, 2000.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.033

Shamgar Gurevich 1 ; Ronny Hadani 1

1 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel 
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Shamgar Gurevich; Ronny Hadani. Proof of the Kurlberg–Rudnick rate conjecture. Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 69-72. doi : 10.1016/j.crma.2005.10.033. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.033/

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[7] Z. Rudnick, The quantized cat map and quantum ergodicity, Lecture at the MSRI conference “Random Matrices and their Applications”, Berkeley, June 7–11, 1999

[8] Z. Rudnick On quantum unique ergodicity for linear maps of the torus, European Congress of Mathematics, vol. II, Barcelona, 2000, Progr. Math., vol. 202, Birkhäuser, Basel, 2001, pp. 429-437

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