03927nam a22005415i 4500 978-981-97-2624-0 DE-He213 20251030112614.0 cr nn 008mamaa 240704s2024 si | s |||| 0|eng d 9789819726240 978-981-97-2624-0 10.1007/978-981-97-2624-0 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Skibsted, Erik. author. aut http://id.loc.gov/vocabulary/relators/aut 80049 Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds [electronic resource] / by Erik Skibsted, Xue Ping Wang. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. IX, 258 p. 1 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Physics Studies, 2352-3905 Introduction -- Many-Body Schrödinger Operators, Conditions and Notation -- Reduction to a One-Body Problem -- Spectral Analysis of H0 near 0 -- Rellich-Type Theorems -- Resolvent Asymptotics near a Two-Cluster Threshold -- Elastic Scattering at a Threshold -- Non-Transmission at a Threshold for Physical Models -- Threshold Behaviour of Cross-Sections in Atom–Ion Scattering. 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. . Mathematical physics. Functional analysis. Mathematical Physics. Functional Analysis. Theoretical, Mathematical and Computational Physics. 65563 Wang, Xue Ping. author. aut http://id.loc.gov/vocabulary/relators/aut 80050 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819726233 Printed edition: 9789819726257 Printed edition: 9789819726264 Mathematical Physics Studies, 2352-3905 72779 https://doi.org/10.1007/978-981-97-2624-0 ZDB-2-PHA ZDB-2-SXP 61352 61352