TY - JOUR
T1 - Graph eigenfunctions and quantum unique ergodicity
AU - Brooks, Shimon
AU - Lindenstrauss, Elon
PY - 2010/8
Y1 - 2010/8
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.
UR - http://www.scopus.com/inward/record.url?scp=77955768642&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2010.07.003
DO - 10.1016/j.crma.2010.07.003
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AN - SCOPUS:77955768642
SN - 1631-073X
VL - 348
SP - 829
EP - 834
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 15-16
ER -