Resonances and SSF Singularities for Magnetic Schrödinger Operators
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Jean-François Bony
bony@math.u-bordeaux1.fr
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Vincent Bruneau
vbruneau@math.u-bordeaux1.fr
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Philippe Briet
briet@cpt.univ-mrs.fr
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Georgi Raikov
graikov@mat.puc.cl
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Abstract
The aim of this note is to review recent articles on the spectral properties of magnetic Schrödinger operators. We consider H0, a 3D Schrödinger operator with constant magnetic field, and ˜H0, a perturbation of H0 by an electric potential which depends only on the variable along the magnetic field. Let H (resp. ˜H ) be a short range perturbation of H0 (resp. of ˜H0). In the case of (H,H0), we study the local singularities of the Krein spectral shift function (SSF) and the distribution of the resonances of H near the Landau levels which play the role of spectral thresholds. In the case of ( ˜H, ˜H0), we study similar problems near the eigenvalues
of ˜H0 of infinite multiplicity.
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