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COUNTING FUNCTION OF MAGNETIC RESONANCES FOR EXTERIOR PROBLEMS

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBRUNEAU, Vincent
hal.structure.identifierFacultad de Matemáticas [Santiago de Chile]
dc.contributor.authorSAMBOU, Diomba
dc.date.accessioned2024-04-04T03:18:21Z
dc.date.available2024-04-04T03:18:21Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194398
dc.description.abstractEnWe study the asymptotic distribution of the resonances near the Landau levels $\Lambda_q =(2q+1)b$, $q \in \mathbb{N}$, of the Dirichlet (resp. Neumann, resp. Robin) realization in the exterior of a compact domain of $\mathbb{R}^3$ of the 3D Schr\"odinger operator with constant magnetic field of scalar intensity $b>0$. We investigate the corresponding resonance counting function and obtain the main asymptotic term. %giving a precise asymptotic formula of the rate accumulation of the resonances near a given Landau level $\Lambda_q$.In particular, we prove the accumulation of resonances at the Landau levels and the existence of resonance free sectors. In some cases, it provides the discreteness of the set of embedded eigenvalues near the Landau levels.
dc.language.isoen
dc.title.enCOUNTING FUNCTION OF MAGNETIC RESONANCES FOR EXTERIOR PROBLEMS
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halPhysique [physics]/Physique mathématique [math-ph]
dc.identifier.arxiv1505.06026
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01154417
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01154417v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BRUNEAU,%20Vincent&SAMBOU,%20Diomba&rft.genre=preprint


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