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Long-range many-body scattering. Asymptotic clustering for Coulomb-type potentials. (English) Zbl 0702.35197
The authors study the scattering theory for quantum many-body systems with pair potentials of Coulomb type (i.e. \(O(| x|^{-1})\) at \(\infty)\). The main result of the paper is that the system is asymptotically clustering for any non-threshold energy. Roughly speaking, this means that starting at a state located near a non-threshold energy, as \(t\to \pm \infty\), the system disintegrates into non-interacting, freely moving subsystems. As the authors show, the asymptotic clustering does not imply in general the asymptotic completeness and one can not rule out the possibility that asymptotic completeness breaks down for longe-range systems. However, this can happen only for more than four particles. For three- and four-particle systems the asymptotic completeness has been proved by V. Enss [Lect. Notes Math. 1159, 39-176 (1985; Zbl 0585.35023)] and by the authors in a forthcoming paper, respectively.
Reviewer: P.Stefanov

35P25 Scattering theory for PDEs
81U10 \(n\)-body potential quantum scattering theory
Full Text: DOI EuDML
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