Joint quasimodes, positive entropy, and quantum unique ergodicity

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We study joint quasimodes of the Laplacian and one Hecke operator on compact congruence surfaces, and give conditions on the orders of the quasimodes that guarantee positive entropy on almost every ergodic component of the corresponding semiclassical measures. Together with the measure classification result of (Lindenstrauss, Ann Math (2) 163(1):165–219, 2006), this implies Quantum Unique Ergodicity for such functions. Our result is optimal with respect to the dimension of the space from which the quasi-mode is constructed. We also study equidistribution for sequences of joint quasimodes of the two partial Laplacians on compact irreducible quotients of (formula presented).

Original languageEnglish
Pages (from-to)219-259
Number of pages41
JournalInventiones Mathematicae
Issue number1
StatePublished - 1 Oct 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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