Resonances and spectral shift function near the Landau levels

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dc.contributor.authorBony, Jean Francois
dc.contributor.authorBruneau, Vincent
dc.contributor.authorRaikov, Georgi
dc.date.accessioned2024-01-10T12:42:09Z
dc.date.available2024-01-10T12:42:09Z
dc.date.issued2007
dc.description.abstractWe consider the 3D Schrodinger operator H = H-0 + V where H-0 = (-i del - A)(2) - b, A is a magnetic potential generating a constant magneticfield of strength b > 0, and V is a short-range electric potential which decays superexponentially with respect to the variable along the magnetic field. We show that the resolvent of H admits a meromorphic extension from the upper half plane to an appropriate Riemann surface M, and define the resonances of H as the poles of this meromorphic extension. We study their distribution near any fixed Landau level 2bq, q is an element of N. First, we obtain a sharp upper bound of the number of resonances in a vicinity of 2bq. Moreover, under appropriate hypotheses, we establish corresponding lower bounds which imply the existence of an infinite number of resonances, or the absence of resonances in certain sectors adjoining 2bq. Finally, we deduce a representation of the derivative of the spectral shift function (SSF) for the operator pair (H, H-0) as a sum of a harmonic measure related to the resonances, and the imaginary part of a holomorphic function. This representation justifies the Breit-Wigner approximation, implies a trace formula, and provides information on the singularities of the SSF at the Landau levels.
dc.format.extent43 páginas
dc.fuente.origenWOS
dc.identifier.doi10.5802/aif.2270
dc.identifier.issn0373-0956
dc.identifier.urihttps://doi.org/10.5802/aif.2270
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/77485
dc.identifier.wosidWOS:000247024900010
dc.information.autorucMatemática;Raikov G;S/I;1004967
dc.issue.numero2
dc.language.isoen
dc.nota.accesoSin adjunto
dc.pagina.final671
dc.pagina.inicio629
dc.publisherANNALES DE L INSTITUT FOURIER
dc.revistaANNALES DE L INSTITUT FOURIER
dc.rightsregistro bibliográfico
dc.subjectmagnetic Schrodinger operators
dc.subjectresonances
dc.subjectspectral shift function
dc.subjectBreit-Wigner approximation
dc.subjectMAGNETIC SCHRODINGER-OPERATORS
dc.subjectTRACE FORMULA
dc.subjectHYDROGEN-ATOM
dc.subjectPERTURBATIONS
dc.subjectASYMPTOTICS
dc.subjectFIELDS
dc.subject.ods04 Quality Education
dc.subject.odspa04 Educación y calidad
dc.titleResonances and spectral shift function near the Landau levels
dc.typeartículo
dc.volumen57
sipa.codpersvinculados1004967
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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