03724nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001700172072001600189072002300205072001500228100008400243245014100327250001800468264007200486300004200558336002600600337002600626338003600652347002400688490004500712505038600757520152601143650002602669650002502695650002602720650002502746650006402771700008402835710003402919773002602953776003602979776003603015776003603051830005203087856004603139912001403185912001403199999001703213978-981-97-2624-0DE-He21320251030112614.0cr nn 008mamaa240704s2024    si |    s    |||| 0|eng d  a97898197262409978-981-97-2624-07 a10.1007/978-981-97-2624-02doi 4aQC19.2-20.85 7aPHU2bicssc 7aSCI0400002bisacsh 7aPHU2thema1 aSkibsted, Erik.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98004910aSpectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholdsh[electronic resource] /cby Erik Skibsted, Xue Ping Wang.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aIX, 258 p. 1 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aMathematical Physics Studies,x2352-39050 aIntroduction -- 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.  aThis 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. . 0aMathematical physics. 0aFunctional analysis.14aMathematical Physics.24aFunctional Analysis.24aTheoretical, Mathematical and Computational Physics.9655631 aWang, Xue Ping.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9800502 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981972623308iPrinted edition:z978981972625708iPrinted edition:z9789819726264 0aMathematical Physics Studies,x2352-390597277940uhttps://doi.org/10.1007/978-981-97-2624-0  aZDB-2-PHA  aZDB-2-SXP  c61352d61352