Galkowski, J;
(2014)
Quantum ergodicity for a class of mixed systems.
Journal of Spectral Theory
, 4
(1)
pp. 65-85.
10.4171/JST/62.
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Abstract
We examine high energy eigenfunctions for the Dirichlet Laplacian on domains where the billiard flow exhibits mixed dynamical behavior. (More generally, we consider semiclassical Schrödinger operators with mixed assumptions on the Hamiltonian flow.) Specifically, we assume that the billiard flow has an invariant ergodic component, U, and study defect measures, μ, of positive density subsequences of eigenfunctions (and, more generally, of almost orthogonal quasimodes). We show that any defect measure associated to such a subsequence satisfies μ|U=cμL|U, where μL is the Liouville measure. This proves part of a conjecture of Percival [18].
| Type: | Article |
|---|---|
| Title: | Quantum ergodicity for a class of mixed systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/JST/62 |
| Publisher version: | https://doi.org/10.4171/JST/62 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | quantum ergodicity, mixed dynamics, semiclassical |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10083917 |
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