Quantum Ergodicity and Averaging Operators on the Sphere

Shimon Brooks; Etienne Le Masson; Elon Lindenstrauss

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arXiv · 1505.03887

Quantum Ergodicity and Averaging Operators on the Sphere

Shimon Brooks·Etienne Le Masson·Elon Lindenstrauss

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Abstract

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.

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BibTeX RIS

Shimon Brooks, Etienne Le Masson, Elon Lindenstrauss. 2015-05-14. Quantum Ergodicity and Averaging Operators on the Sphere. https://arxiv.org/abs/1505.03887

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