Ergodic billiards that are not quantum unique ergodic
| dc.creator | Hassell, Andrew | |
| dc.creator | Hillairet, Luc | |
| dc.date | 2008-07-04 | |
| dc.date | 2008-12-04 | |
| dc.date.accessioned | 2026-07-07T12:08:59Z | |
| dc.date.available | 2026-07-07T12:08:59Z | |
| dc.description | Partially rectangular domains are compact two-dimensional Riemannian manifolds $X$, either closed or with boundary, that contain a flat rectangle or cylinder. In this paper we are interested in partially rectangular domains with ergodic billiard flow; examples are the Bunimovich stadium, the Sinai billiard or Donnelly surfaces. We consider a one-parameter family $X_t$ of such domains parametrized by the aspect ratio $t$ of their rectangular part. There is convincing theoretical and numerical evidence that the Laplacian on $X_t$ with Dirichlet or Neumann boundary conditions is not quantum unique ergodic (QUE). We prove that this is true for all $t \in [1,2]$ excluding, possibly, a set of Lebesgue measure zero. This yields the first examples of ergodic billiard systems proven to be non-QUE. | |
| dc.description | 11 pages, 1 figure. The paper, authored by Andrew Hassell, now includes an appendix by Andrew Hassell and Luc Hillairet, extending the result to all partially rectangular billiards | |
| dc.identifier | https://arxiv.org/abs/0807.0666 | |
| dc.identifier | http://arxiv.org/abs/0807.0666 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209480 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35P20, 58J50 | |
| dc.title | Ergodic billiards that are not quantum unique ergodic | |
| dc.type | text |