Quantum Ergodicity and Averaging Operators on the Sphere

14 May 2015 · Brooks Shimon, Masson Etienne Le, Lindenstrauss Elon ·

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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Quantum Ergodicity and Averaging Operators on the Sphere

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