Overview
- Contains new results in threshold analysis for many-body Schrödinger operators
- Presents mathematically appealing topics that are important for scattering experiments in physics
- Is a systematic study pinpointing several open problems
Part of the book series: Mathematical Physics Studies (MPST)
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Keywords
- Spectral and Scattering Theory
- Many-Body Schrödinger Operators
- Two-Cluster Thresholds
- Feshbach-Grushin Method
- Mourre Estimate
About this book
This book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the centre of mass motion to a one-body problem at zero energy) is a well-studied subject, the literature on many-body threshold problems is sparse. However, the authors’ analysis covers for example the system of three particles interacting by Coulomb potentials and restricted to a small energy region to the right of a fixed nonzero two-body eigenvalue. In general, the authors address the question: How do scattering quantities for the many-body atomic and molecular models behave within the limit when the total energy approaches a fixed two-cluster threshold? This includes mapping properties and singularities of the limiting scattering matrix, asymptotics of the total scattering cross section, and absence of transmission from one channel to another in the small inter-cluster kinetic energy region. The authors’ principal tools are the Feshbach–Grushin dimension reduction method and spectral analysis based on a certain Mourre estimate. Additional topics of independent interest are the limiting absorption principle, micro-local resolvent estimates, Rellich- and Sommerfeld-type theorems and asymptotics of the limiting resolvents at thresholds. The mathematical physics field under study is very rich, and there are many open problems, several of them stated explicitly in the book for the interested reader.
Authors and Affiliations
About the authors
Erik Skibsted is Associate Professor at Department of Mathematics of Aarhus University.
Xue Ping Wang is Professor at Université de Nantes.
Bibliographic Information
Book Title: Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds
Authors: Erik Skibsted, Xue Ping Wang
Series Title: Mathematical Physics Studies
Publisher: Springer Singapore
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024
Hardcover ISBN: 978-981-97-2623-3Due: 01 July 2024
Softcover ISBN: 978-981-97-2626-4Due: 01 July 2024
eBook ISBN: 978-981-97-2624-0Due: 01 July 2024
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 1
Number of Pages: VIII, 230