Resonances and SSF Singularities for Magnetic Schrödinger Operators

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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.

Keywords

Magnetic Schrödinger operators , resonances , spectral shift function
  • Jean-François Bony Université Bordeaux I, Institut de Mathématiques de Bordeaux, UMR CNRS 5251, 351, Cours de la Libération, 33405 Talence, France.
  • Vincent Bruneau Université Bordeaux I, Institut de Mathématiques de Bordeaux, UMR CNRS 5251, 351, Cours de la Libération, 33405 Talence, France.
  • Philippe Briet Centre de Physique Théorique, CNRS-Luminy, Case 907, 13288 Marseille, France.
  • Georgi Raikov Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago de Chile.
  • Pages: 23–38
  • Date Published: 2009-12-01
  • Vol. 11 No. 5 (2009): CUBO, A Mathematical Journal

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Published

2009-12-01

How to Cite

[1]
J.-F. Bony, V. Bruneau, P. Briet, and G. Raikov, “Resonances and SSF Singularities for Magnetic Schrödinger Operators”, CUBO, vol. 11, no. 5, pp. 23–38, Dec. 2009.

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