This volume contains the Proceedings of the Conference “Spectral and Scatter-
ing 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.
Quantum magnetic systems are studied by various mathematical “schools” or
“communities”, which investigate different mathematical aspects of related prob-
lems, developing their specific appropriate techniques. The meeting was meant to
give the researchers from these communities the opportunity to discuss and ex-
change ideas, as well as to attract young scientists to this area of research.
There were two mini-courses given by Bernard Helffer and Hajo Leschke, twenty
six invited talks given by Rafael Benguria, Vincent Bruneau, Horia Cornean, Mouez
Dimassi, Daniel Elton, Maria Esteban, Claudio Fern´ andez, Soeren Fournais, Ru-
pert Frank, Gian Michele Graf, Benoˆ ıt Gr´ ebert, Ira Herbst, Peter Hislop, Victor
Ivrii, Abel Klein, Fr´ ed´ eric Klopp, Yuri Kordyukov, Marius antoiu, Takuya Mine,
Vesselin Petkov, Alexander Pushnitski, Serge Richard, Grigori Rozenblum, Robert
Seiringer, Eric Soccorsi, Rafael Tiedra de Aldecoa, and five students’ mini-talks
given by Mathieu Beau, Nicolas Dombrowski, Abdallah Khochman, Max Lein, and
Nicolas Raymond.
This volume contains a number of original results presented by some of the
invited speakers, and also 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 Schr¨ odinger operators;
Magnetic Pauli and Dirac operators;
Magnetic operators on manifolds;
Microlocal analysis of magnetic Hamiltonians;
Random Schr¨ odinger operators and quantum Hall effect;
Ginsburg-Landau equation, supraconductivity, magnetic bottles;
Bose-Einstein condensate, Gross-Pitaevski equation;
Magnetic Lieb-Thirring inequalities, stability of matter.
We are grateful to the International Center for Mathematical Meetings (CIRM)
for the hospitality, for the financial and logistic support which made this meeting
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