TY - JOUR
T1 - Joint quasimodes, positive entropy, and quantum unique ergodicity
AU - Brooks, Shimon
AU - Lindenstrauss, Elon
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84908211439&partnerID=8YFLogxK
U2 - 10.1007/s00222-014-0502-7
DO - 10.1007/s00222-014-0502-7
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AN - SCOPUS:84908211439
SN - 0020-9910
VL - 198
SP - 219
EP - 259
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -