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- W2086873563 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." @default.
- W2086873563 created "2016-06-24" @default.
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- W2086873563 date "2015-02-25" @default.
- W2086873563 modified "2023-10-18" @default.
- W2086873563 title "Logarithmic-Scale Quasimodes that do not Equidistribute" @default.
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- W2086873563 doi "https://doi.org/10.1093/imrn/rnv050" @default.
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