Mathematical Physics
Proof of the Kurlberg–Rudnick rate conjecture
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 69-72.

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.

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.

Published online:
DOI: 10.1016/j.crma.2005.10.033
Gurevich, Shamgar 1; Hadani, Ronny 1

1 School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
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Gurevich, Shamgar; Hadani, Ronny. 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.

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[4] Hannay, J.H.; Berry, M.V. Quantization of linear maps on the torus – Fresnel diffraction by a periodic grating, Physica D, Volume 1 (1980), pp. 267-291

[5] Kurlberg, P.; Rudnick, Z. Hecke theory and equidistribution for the quantization of linear maps of the torus, Duke Math. J., Volume 103 (2000), pp. 47-78

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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] Rudnick, Z. 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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