Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field

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dc.creatorIvrii, Victor
dc.date2006-05-11
dc.date.accessioned2026-07-07T07:14:07Z
dc.date.available2026-07-07T07:14:07Z
dc.descriptionI continue analysis of the Schrödinger operator with the strong degenerating magnetic field, started in \cite{IRO6}. Now I consider 4-dimensional case, assuming that magnetic field is generic degenerated and under certain conditions I derive spectral asymptotics with the principal part $\asymp h^{-4}$ and the remainder estimate $O(μ^{-1/2}h^{-3})$ where $μ\gg 1$ is the intensity of the field and $h\ll 1$ is the Plank constant; $μh\le 1$. These asymptotics can contain correction terms of magnitude $μ^{5/4}h^{-3/2}$ corresponding to the short periodic trajectories.
dc.description93pp
dc.identifierhttps://arxiv.org/abs/math/0605298
dc.identifierhttp://arxiv.org/abs/math/0605298
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112747
dc.subjectAnalysis of PDEs
dc.subjectSpectral Theory
dc.subject35P20
dc.titleSharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field
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