Quantum ergodicity and averaging operators on the sphere

Shimon Brooks; Etienne Le Masson; Elon Lindenstrauss

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 L²(S²), consisting of joint eigenfunctions of the Laplacian on S² 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.

Original language	English
Journal	International Mathematics Research Notices
Publication status	Published - 24 Nov 2015

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title = "Quantum ergodicity and averaging operators on the sphere",

abstract = "We prove quantum ergodicity for certain orthonormal bases of L2(S2), consisting of joint eigenfunctions of the Laplacian on S2 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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language = "English",

journal = "International Mathematics Research Notices",

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T1 - Quantum ergodicity and averaging operators on the sphere

AU - Brooks, Shimon

AU - Le Masson, Etienne

AU - Lindenstrauss, Elon

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N2 - We prove quantum ergodicity for certain orthonormal bases of L2(S2), consisting of joint eigenfunctions of the Laplacian on S2 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.

AB - We prove quantum ergodicity for certain orthonormal bases of L2(S2), consisting of joint eigenfunctions of the Laplacian on S2 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.

M3 - Article (Academic Journal)

SN - 1073-7928

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

ER -

Quantum ergodicity and averaging operators on the sphere

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