[Fonctions propres de graphes et l'unique ergodicité quantique]
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.
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.
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@article{CRMATH_2010__348_15-16_829_0,
author = {Brooks, Shimon and Lindenstrauss, Elon},
title = {Graph eigenfunctions and quantum unique ergodicity},
journal = {Comptes Rendus. Math\'ematique},
pages = {829--834},
publisher = {Elsevier},
volume = {348},
number = {15-16},
year = {2010},
doi = {10.1016/j.crma.2010.07.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.07.003/}
}
TY - JOUR AU - Brooks, Shimon AU - Lindenstrauss, Elon TI - Graph eigenfunctions and quantum unique ergodicity JO - Comptes Rendus. Mathématique PY - 2010 SP - 829 EP - 834 VL - 348 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.07.003/ DO - 10.1016/j.crma.2010.07.003 LA - en ID - CRMATH_2010__348_15-16_829_0 ER -
%0 Journal Article %A Brooks, Shimon %A Lindenstrauss, Elon %T Graph eigenfunctions and quantum unique ergodicity %J Comptes Rendus. Mathématique %D 2010 %P 829-834 %V 348 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.07.003/ %R 10.1016/j.crma.2010.07.003 %G en %F CRMATH_2010__348_15-16_829_0
Brooks, Shimon; Lindenstrauss, Elon. Graph eigenfunctions and quantum unique ergodicity. Comptes Rendus. Mathématique, Tome 348 (2010) no. 15-16, pp. 829-834. doi : 10.1016/j.crma.2010.07.003. http://www.numdam.org/articles/10.1016/j.crma.2010.07.003/
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