Spectral properties of a magnetic quantum Hamiltonian on a strip

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dc.contributor.authorBriet, Philippe
dc.contributor.authorRaikov, Georgi
dc.contributor.authorSoccorsi, Eric
dc.date.accessioned2024-01-10T13:43:38Z
dc.date.available2024-01-10T13:43:38Z
dc.date.issued2008
dc.description.abstractWe consider a 2D Schrodinger operator H(0) with constant magnetic field, on a strip of finite width. The spectrum of H(0) is absolutely continuous, and contains a discrete set of thresholds. We perturb H(0) by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H = H(0) + V. First, we establish a Mourre estimate, and as a corollary prove that the singular continuous spectrum of H is empty, and any compact subset of the complement of the threshold set may contain at most a finite set of eigenvalues of H, each of them having a finite multiplicity. Next, we introduce the Krein spectral shift function (SSF) for the operator pair (H, H(0)). We show that this SSF is bounded on any compact subset of the complement of the threshold set, and is continuous away from the threshold set and the eigenvalues of H. The main results of the article concern the asymptotic behaviour of the SSF at the thresholds, which is described in terms of the SSF for a pair of effective Hamiltonians.
dc.fechaingreso.objetodigital2024-05-23
dc.format.extent29 páginas
dc.fuente.origenWOS
dc.identifier.doi10.3233/ASY-2008-0875
dc.identifier.issn0921-7134
dc.identifier.urihttps://doi.org/10.3233/ASY-2008-0875
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/78704
dc.identifier.wosidWOS:000258079800001
dc.information.autorucMatemática;Raykov G;S/I;1004967
dc.issue.numero3
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final155
dc.pagina.inicio127
dc.publisherIOS PRESS
dc.revistaASYMPTOTIC ANALYSIS
dc.rightsacceso restringido
dc.subjectSchrodinger operators
dc.subjectmagnetic field
dc.subjectMourre estimates
dc.subjectspectral shift function
dc.subjecteffective Hamiltonians
dc.subjectSHIFT FUNCTION
dc.subjectSCHRODINGER-OPERATORS
dc.subjectPOTENTIALS
dc.subjectSCATTERING
dc.subject.ods04 Quality Education
dc.subject.odspa04 Educación y calidad
dc.titleSpectral properties of a magnetic quantum Hamiltonian on a strip
dc.typeartículo
dc.volumen58
sipa.codpersvinculados1004967
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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