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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.

##### MSC:
 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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