Quantum Monodromy and Non-concentration near a Closed Semi-Hyperbolic Orbit

dc.creatorChristianson, Hans
dc.date2008-03-05
dc.date.accessioned2026-07-07T09:24:56Z
dc.date.available2026-07-07T09:24:56Z
dc.descriptionFor 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.identifierhttps://arxiv.org/abs/0803.0697
dc.identifierhttp://arxiv.org/abs/0803.0697
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156246
dc.subjectAnalysis of PDEs
dc.subject35P20
dc.titleQuantum Monodromy and Non-concentration near a Closed Semi-Hyperbolic Orbit
dc.typetext

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