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Asymptotic completeness of \(N\)-particle long-range scattering. (English) Zbl 0811.35091
The authors prove asymptotic completeness for \(N\)-particle long-range systems with potential at infinity with a power of \(| x |\) of order greater or equal to \(1 - 2^{-N-2}\). Asymptotic clustering is used to reduce the problem involving an \((N+1)\)-particle Schrödinger operator to that involving a time-dependent operator.
Subspaces of balistic and subbalistic propagation are characterized in terms of singular sets for (or the spectra of) appropriate asymptotic observables.

35P25 Scattering theory for PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
81U10 \(n\)-body potential quantum scattering theory
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