Spectral Analysis of N-Body Schr dinger Operators at Two-Cluster Thresholds (Mathematical Physics Studies) free ebook download.

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Spectral Analysis of N-Body Schr dinger Operators at Two-Cluster Thresholds (Mathematical Physics Studies) free ebook download

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Author(s):	Erik Skibsted

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	9819726239
Pages:	267	OCR:		Quality:		ISBN13:
Uploader:	alex21s	Upload Date:	7/13/2024 12:57:01 PM

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9819726239 pdf
This book provides a systematic study of spectral and scattering theory for many-body Schrdinger 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 FeshbachGrushin 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.
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Tags: Analysis dinger Mathematical N-Body Operators Physics Schr Spectral Thresholds Two-Cluster

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