Quantum Ergodicity and Averaging Operators on the Sphere

Autor:	Brooks, Shimon, Masson, Etienne Le, Lindenstrauss, Elon
Rok vydání:	2015
Předmět:	Mathematics - Spectral Theory Mathematical Physics Mathematics - Dynamical Systems
Zdroj:	Int Math Res Notices (2016) 2016 (19): 6034-6064
Druh dokumentu:	Working Paper
Popis:	We prove quantum ergodicity for certain orthonormal bases of $L^2(\mathbb{S}^2)$, consisting of joint eigenfunctions of the Laplacian on $\mathbb{S}^2$ and the discrete averaging operator over a finite set of rotations, generating a free group. If in addition the rotations are algebraic we give a quantified version of this result. The methods used also give a new, simplified proof of quantum ergodicity for large regular graphs. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1505.03887 Zobrazit plný text záznamu View this record from Arxiv