Year: 2013
Type: preprint
Abstract: Given any compact hyperbolic surface $M$, and a closed geodesic on $M$, we construct of a sequence of quasimodes on $M$ whose microlocal lifts concentrate positive mass on the geodesic. Thus, the Quantum Unique Ergodicity (QUE) property does not hold for these quasimodes. This is analogous to a construction of Faure-Nonnenmacher-De Bièvre in the context of quantized cat maps, and lends credence to the suggestion that large multiplicities play a role in the known failure of QUE for certain "toy models" of quantum chaos. We moreover conjecture a precise threshold for the order of quasimodes needed for QUE to hold--- the result of the present paper shows that this conjecture, if true, is sharp.
Source: arXiv (Cornell University)
Author: Brooks, Shimon
Institution: Bar-Ilan University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2949918321