Graph eigenfunctions and quantum unique ergodicity

Shimon Brooks; Elon Lindenstrauss

doi:10.1016/j.crma.2010.07.003

Graph eigenfunctions and quantum unique ergodicity

Translated title of the contribution: Graph eigenfunctions and quantum unique ergodicity

Shimon Brooks
, Elon Lindenstrauss

Stony Brook University
Hebrew University of Jerusalem

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

4 Scopus citations

Abstract

We apply the techniques of Brooks and Lindenstrauss (2010) [5] to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of H×H. In both cases, we show that quantum limit measures of such sequences of eigenfunctions carry positive entropy on almost every ergodic component. Together with the work of Lindenstrauss (2006) [9], this implies Quantum Unique Ergodicity for such functions.

Translated title of the contribution	Graph eigenfunctions and quantum unique ergodicity
Original language	English
Pages (from-to)	829-834
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	15-16
DOIs	https://doi.org/10.1016/j.crma.2010.07.003
State	Published - Aug 2010
Externally published	Yes

Bibliographical note

Funding Information:
The author was supported in part by NSF grants DMS-0554345 and DMS-0800345 and the Israel Science Foundation.

Funding

The author was supported in part by NSF grants DMS-0554345 and DMS-0800345 and the Israel Science Foundation.

Funders	Funder number
National Science Foundation	DMS-0554345, DMS-0800345
Israel Science Foundation

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10.1016/j.crma.2010.07.003

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abstract = "We apply the techniques of Brooks and Lindenstrauss (2010) [5] to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of H{\texttimes}H. In both cases, we show that quantum limit measures of such sequences of eigenfunctions carry positive entropy on almost every ergodic component. Together with the work of Lindenstrauss (2006) [9], this implies Quantum Unique Ergodicity for such functions.",

author = "Shimon Brooks and Elon Lindenstrauss",

note = "Funding Information: The author was supported in part by NSF grants DMS-0554345 and DMS-0800345 and the Israel Science Foundation.",

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doi = "10.1016/j.crma.2010.07.003",

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AU - Lindenstrauss, Elon

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N2 - We apply the techniques of Brooks and Lindenstrauss (2010) [5] to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of H×H. In both cases, we show that quantum limit measures of such sequences of eigenfunctions carry positive entropy on almost every ergodic component. Together with the work of Lindenstrauss (2006) [9], this implies Quantum Unique Ergodicity for such functions.

AB - We apply the techniques of Brooks and Lindenstrauss (2010) [5] to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of H×H. In both cases, we show that quantum limit measures of such sequences of eigenfunctions carry positive entropy on almost every ergodic component. Together with the work of Lindenstrauss (2006) [9], this implies Quantum Unique Ergodicity for such functions.

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Graph eigenfunctions and quantum unique ergodicity

Abstract

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