This volume contains the proceedings of the conference on Spectral and Scattering Theory for Quantum Magnetic Systems, which took place at CIRM, Luminy, France, in July 2008. The main purpose of this conference was to bring together a number of specialists in the mathematical modelling of magnetic phenomena in quantum mechanics, to mark the recent progress as well as to outline the future development in this area. This volume contains original results presented by some of the invited speakers and surveys on recent advances in the mathematical theory of quantum magnetic Hamiltonians. Most of the talks at the conference, as well as the articles in this volume, have been dedicated to one of the following topics: Spectral and scattering theory for magnetic Schrodinger operators; Magnetic Pauli and Dirac operators; Magnetic operators on manifolds; Microlocal analysis of magnetic Hamiltonians; Random Schrodinger operators and quantum Hall effect; Ginsburg - Landau equation, supraconductivity, magnetic bottles; Bose - Einstein condensate, Gross - Pitaevski equation; and, Magnetic Lieb - Thirring inequalities, stability of matter.
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