Sharp Spectral Asymptotics for two-dimensional Schrödinger operator with a strong degenerating magnetic field

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dc.creatorIvrii, Victor
dc.date2006-03-04
dc.date.accessioned2026-07-07T07:06:32Z
dc.date.available2026-07-07T07:06:32Z
dc.descriptionI consider two-dimensional Schrödinger operator with degenerating magnetic field and in the generic situation I derive spectral asymptotics as $h\to +0$ and $μ\to +\infty$ where $h$ and $μ$ are Planck and coupling parameters respectively. The remainder estimate is $O(μ^{-{\frac 1 2}}h^{-1})$ which is between $O(μ^{-1}h^{-1})$ valid as magnetic field non-degenerates and $O(h^{-1})$ valid as magnetic field is identically 0. As $μ$ is close to its maximal reasonable value $O(h^{-2})$ the principal part contains correction terms associated with short periodic trajectories of the corresponding classical dynamics.
dc.description79 pages
dc.identifierhttps://arxiv.org/abs/math/0603114
dc.identifierhttp://arxiv.org/abs/math/0603114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110064
dc.subjectAnalysis of PDEs
dc.subjectSpectral Theory
dc.subject35P20
dc.titleSharp Spectral Asymptotics for two-dimensional Schrödinger operator with a strong degenerating magnetic field
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