Joint quasimodes, positive entropy, and quantum unique ergodicity

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• 作者：Shimon Brooks ; Elon Lindenstrauss
• 刊名：Inventiones Mathematicae
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：198
• 期：1
• 页码：219-259
• 全文大小：358 KB
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• 作者单位：Shimon Brooks (1)
  Elon Lindenstrauss (2)
  
  1. Department of Mathematics, Bar-Ilan University, 5290002?, Ramat-Gan, Israel
  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904?, Jerusalem, Israel
  
• ISSN：1432-1297

文摘

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):165-19, 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 \({\mathbb {H}}\times {\mathbb {H}}\) .