TY - JOUR
T1 - Eisenstein Quasimodes and QUE
AU - Brooks, Shimon
N1 - Publisher Copyright:
© 2015, Springer Basel.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - We consider the question of quantum unique ergodicity (QUE) for quasimodes on surfaces of constant negative curvature, and conjecture the order of quasimodes that should satisfy QUE. We then show that this conjecture holds for Eisenstein series on (Formula presented.) , extending results of Luo–Sarnak and Jakobson. Moreover, we observe that the equidistribution results of Luo–Sarnak and Jakobson extend to quasimodes of much weaker order—for which QUE is known to fail on compact surfaces—though in this scenario the total mass of the limit measures will decrease. We interpret this stronger equidistribution property in the context of arithmetic QUE, in light of recent joint work with Lindenstrauss (Invent Math 198(1), 219–259, 2014) on joint quasimodes.
AB - We consider the question of quantum unique ergodicity (QUE) for quasimodes on surfaces of constant negative curvature, and conjecture the order of quasimodes that should satisfy QUE. We then show that this conjecture holds for Eisenstein series on (Formula presented.) , extending results of Luo–Sarnak and Jakobson. Moreover, we observe that the equidistribution results of Luo–Sarnak and Jakobson extend to quasimodes of much weaker order—for which QUE is known to fail on compact surfaces—though in this scenario the total mass of the limit measures will decrease. We interpret this stronger equidistribution property in the context of arithmetic QUE, in light of recent joint work with Lindenstrauss (Invent Math 198(1), 219–259, 2014) on joint quasimodes.
UR - http://www.scopus.com/inward/record.url?scp=84958051951&partnerID=8YFLogxK
U2 - 10.1007/s00023-015-0403-3
DO - 10.1007/s00023-015-0403-3
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AN - SCOPUS:84958051951
SN - 1424-0637
VL - 17
SP - 615
EP - 643
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 3
ER -