# Spectral and Scattering Theory for Quantum Magnetic Systems

Share this page *Edited by *
*Philippe Briet; François Germinet; Georgi Raikov*

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 Schrödinger operators
- Magnetic Pauli and Dirac operators
- Magnetic operators on manifolds
- Microlocal analysis of magnetic Hamiltonians
- Random Schrödinger operators and quantum Hall effect
- Ginsburg–Landau equation, supraconductivity, magnetic bottles
- Bose–Einstein condensate, Gross–Pitaevski equation
- Magnetic Lieb–Thirring inequalities, stability of matter

#### Readership

Graduate students and research mathematicians interested in mathematics and theoretical physics.

# Table of Contents

## Spectral and Scattering Theory for Quantum Magnetic Systems

- Contents v6 free
- Preface vii8 free
- List of Participants ix10 free
- On the infrared problem for the dressed non-relativistic electron in a magnetic field 114 free
- Absence of singular spectrum for some time-periodic magnetic systems 2538
- Mourre estimates for a 2D magnetic quantum Hamiltonian on strip-like domains 3346
- Perturbation of a magnetic Schrödinger operator near an embedded infinite-multiplicity eigenvalue 4760
- Remarks on eigenvalue estimates and semigroup domination 6376
- Delocalization for random Landau Hamiltonians with unbounded random variables 87100
- A linear criterion for solutions of non-linear equations, with application to the BCS gap equation 101114
- Semiclassical analysis of Schrödinger operators with magnetic wells 105118
- The magnetic formalism; new results 123136
- Norm resolvent convergence to Schrödinger operators with infinitesimally thin toroidal magnetic fields 139152
- Lifshitz tails for alloy type random models in constant magnetic fields: a short review 153166
- New formulae for the Aharonov-Bohm wave operators 159172
- On the spectral properties of the Landau Hamiltonian perturbed by a moderately decaying magnetic field 169182