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Dynamical resonances and SSF singularities for a magnetic Schroedinger operator

hal.structure.identifierDepartamento de Matemáticas [Santiago de Chile]
dc.contributor.authorASTABURUAGA, Maria Angélica
hal.structure.identifierCentre de Physique Théorique - UMR 6207 [CPT]
hal.structure.identifierCentre de Physique Théorique - UMR 7332 [CPT]
dc.contributor.authorBRIET, Philippe
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBRUNEAU, Vincent
hal.structure.identifierDepartamento de Matemáticas [Santiago de Chile]
dc.contributor.authorFERNANDEZ, Claudio
hal.structure.identifierDepartamento de Matemáticas [Santiago de Chile]
dc.contributor.authorRAIKOV, Georgi
dc.date.accessioned2024-04-04T02:46:37Z
dc.date.available2024-04-04T02:46:37Z
dc.date.issued2008
dc.identifier.issn1310-6600
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191571
dc.description.abstractEnWe consider the Hamiltonian $H$ of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator $H$ has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb $H$ by appropriate scalar potentials $V$ and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic field, and obtain an asymptotic expansion of the resonances as the coupling constant $\varkappa$ of the perturbation tends to zero. Further, under the assumption that the Fermi Golden Rule holds true, we deduce estimates for the time evolution of the resonance states with and without analyticity assumptions; in the second case we obtain these results as a corollary of suitable Mourre estimates and a recent article of Cattaneo, Graf and Hunziker \cite{cgh}. Next, we describe sets of perturbations $V$ for which the Fermi Golden Rule is valid at each embedded eigenvalue of $H$; these sets turn out to be dense in various suitable topologies. Finally, we assume that $V$ decays fast enough at infinity and is of definite sign, introduce the Krein spectral shift function for the operator pair $(H+V, H)$, and study its singularities at the energies which coincide with eigenvalues of infinite multiplicity of the unperturbed operator $H$.
dc.description.sponsorshipEquations hyperboliques dans des espaces-temps de la relativité générale : diffusion et résonances. - ANR-05-JCJC-0087
dc.language.isoen
dc.publisherBulgarian Academy of Sciences, Institute of Mathematics
dc.subject.enmagnetic Schroedinger operators
dc.subject.enresonances
dc.subject.enMourre estimates
dc.subject.enspectral shift function
dc.title.enDynamical resonances and SSF singularities for a magnetic Schroedinger operator
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie spectrale [math.SP]
dc.identifier.arxiv0710.0502
bordeaux.journalSerdica Mathematical Journal
bordeaux.page179-218
bordeaux.volume34
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00176069
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00176069v1
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