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Spectral Shift Function for Schr¨odinger Operators in Constant Magnetic Fields

Author
Raikov, Georgi

Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1548
Abstract
We consider the three-dimensional Schr¨odinger operator with constant magnetic field, perturbed by an appropriate short-range electric potential, and investigate various asymptotic properties of the corresponding spectral shift function (SSF). First, we analyse the singularities of the SSF at the Landau levels. Further, we study the strong magnetic field asymptotic behaviour of the SSF; here we distinguish between the asymptotics far from the Landau levels, and near a given Landau level. Finally, we obtain a Weyl-type formula describing the high energy behaviour of the SSF. This is a survey article on recent published results obtained by the author jointly with Vincent Bruneau, Claudio Fern´andez, and Alexander Pushnitski. A shorter version will appear in the Proceedings of the Conference QMath9, Giens, France, September 2004.
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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