Fonctions propres de graphes et l'unique ergodicité quantique

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

Shimon Brooks*, Elon Lindenstrauss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 contributionGraph eigenfunctions and quantum unique ergodicity
Original languageFrench
Pages (from-to)829-834
Number of pages6
JournalComptes Rendus Mathematique
Volume348
Issue number15-16
DOIs
StatePublished - Aug 2010

Bibliographical 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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