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Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds

By Erik Skibsted

Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds Mathematics

Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds

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Description
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.
Product details
Binding:
Paperback
Number of Pages:
268
Release Date:
2025-07-05
Publication Date:
2025-07-05
Publisher:
Springer
Languages:
Original: English
ISBN10:
9819726263
ISBN13:
9789819726264
GPSR Manufacturer Reference:
[email protected]
Weight:
411 g
Height:
155 cm
Width:
235 cm
Thickness:
15 cm
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