Quantum Ergodicity and Averaging Operators on the Sphere

Shimon Brooks; Etienne Le Masson; Elon Lindenstrauss

doi:10.1093/imrn/rnv337

Quantum Ergodicity and Averaging Operators on the Sphere

Shimon Brooks, Etienne Le Masson, Elon Lindenstrauss^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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	American English
Pages (from-to)	6034-6064
Number of pages	31
Journal	International Mathematics Research Notices
Volume	2016
Issue number	19
DOIs	https://doi.org/10.1093/imrn/rnv337
State	Published - 2016

Bibliographical note

Funding Information:
E.L. and E.L.M. were supported by ERC AdG grant no. 267259. S.B. was supported by NSF grant DMS-1101596, ISF grant 1119/13, and a Marie-Curie Career Integration Grant. This paper was finalized while both E.L. and E.L.M. were in residence at MSRI, supported in part by NSF grant no. 0932078-000.

Publisher Copyright:
© 2015 The Author(s). Published by Oxford University Press. All rights reserved.

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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.

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ER -

Quantum Ergodicity and Averaging Operators on the Sphere

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