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 eigenvaluesof ˜H0 of infinite multiplicity.
@article{1441,
title = {Resonances and SSF Singularities for Magnetic Schr\"odinger Operators},
journal = {CUBO, A Mathematical Journal},
volume = {11},
year = {2009},
language = {en},
url = {http://dml.mathdoc.fr/item/1441}
}
Bony, Jean-François; Bruneau, Vincent; Briet, Philippe; Raikov, Georgi. Resonances and SSF Singularities for Magnetic Schrödinger Operators. CUBO, A Mathematical Journal, Tome 11 (2009) . http://gdmltest.u-ga.fr/item/1441/