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Multiparticle Quantum Scattering in Constant Magnetic Fields
Christian Gérard, Ecole Polytechnique, Paris, France, and Izabella Łaba, University of British Columbia, Vancouver, BC, Canada
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Mathematical Surveys and Monographs
2002; 242 pp; hardcover
Volume: 90
ISBN-10: 0-8218-2919-X
ISBN-13: 978-0-8218-2919-6
List Price: US$74
Member Price: US$59.20
Order Code: SURV/90
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This monograph offers a rigorous mathematical treatment of the scattering theory of quantum N-particle systems in an external constant magnetic field. In particular, it addresses the question of asymptotic completeness, a classification of all possible trajectories of such systems according to their asymptotic behavior. The book adopts the so-called time-dependent approach to scattering theory, which relies on a direct study of the Schrödinger unitary group for large times. The modern methods of spectral and scattering theory introduced in the 1980s and 1990s, including the Mourre theory of positive commutators, propagation estimates, and geometrical techniques, are presented and heavily used. Additionally, new methods were developed by the authors in order to deal with the (much less understood) phenomena due to the presence of the magnetic field.

The book is a good starting point for graduate students and researchers in mathematical physics who wish to move into this area of research. It includes expository material, research work previously available only in the form of journal articles, as well as some new unpublished results. The treatment of the subject is comprehensive and largely self-contained, and the text is carefully written with attention to detail.

Readership

Graduate students and research mathematicians interested in mathematical physics and differential equations.

Reviews

"The book is well organized and well written ... the authors have successfully achieved their stated aim of writing a book which is of interest both to a wider section of the mathematical physics community ... and to graduate students and researchers in the field of spectral and scattering theory for magnetic Schrödinger operators."

-- Mathematical Reviews

Table of Contents

  • Fundamentals
  • Geometrical methods I
  • The Mourre theory
  • Basic propagation estimates
  • Geometrical methods II
  • Wave operators and scattering theory
  • Open problems
  • Appendix
  • Bibliography
  • Index
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