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Propagation and local-decay properties for long-range scattering of quantum three-body systems. (English) Zbl 0568.47007

Quantum three-body scattering is considered for a class of long-range two-body potentials that have arbitrary power like decrease at infinity and a few regularity assumptions. It is shown that, in the continuous spectral subspace of the total hamiltonian, states that are orthogonal to all two-cluster channels represent particles which, asymptotically in time:
- get arbitrarily far separated from each other
- are outgoing or incoming relative to each other, (depending on the sign of the time).
This result is a fundamental step towards a time-dependent proof of three-body asymptotic completeness.

MSC:

47A40 Scattering theory of linear operators
81U10 \(n\)-body potential quantum scattering theory
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References:

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