Quantum Monodromy and Non-concentration near a Closed Semi-Hyperbolic Orbit
| dc.creator | Christianson, Hans | |
| dc.date | 2008-03-05 | |
| dc.date.accessioned | 2026-07-07T09:24:56Z | |
| dc.date.available | 2026-07-07T09:24:56Z | |
| dc.description | For a large class of semiclassical operators $P(h)-z$ which includes Schrödinger operators on manifolds with boundary, we construct the Quantum Monodromy operator $M(z)$ associated to a periodic orbit $γ$ of the classical flow. Using estimates relating $M(z)$ and $P(h)-z$, we prove semiclassical estimates for small complex perturbations of $P(h) -z$ in the case $γ$ is semi-hyperbolic. As our main application, we give logarithmic lower bounds on the mass of eigenfunctions away from semi-hyperbolic orbits of the associated classical flow. As a second application of the Monodromy Operator construction, we prove if $γ$ is an elliptic orbit, then $P(h)$ admits quasimodes which are well-localized near $γ$. | |
| dc.identifier | https://arxiv.org/abs/0803.0697 | |
| dc.identifier | http://arxiv.org/abs/0803.0697 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156246 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P20 | |
| dc.title | Quantum Monodromy and Non-concentration near a Closed Semi-Hyperbolic Orbit | |
| dc.type | text |