2022/05/30 by Erik Skibsted, Skibsted, Erik
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2205.15028
openalex publication_date 2022/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Within the class of Dereziński-Enss pair-potentials which includes Coulomb potentials a stationary scattering theory for N-body systems was recently developed \cite Sk1. In particular the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy, and this holds without imposing any a priori decay condition on channel eigenstates. In this paper we improve for the case of 3-body systems on the known weak continuity properties in that we show that all non-threshold energies are stationary complete in this case, resolving a conjecture from \cite Sk1 in the special case N=3. A consequence is that the above scattering quantities depend strongly continuously on the energy parameter at all non-threshold energies, hence not only almost everywhere as previously demonstrated (for an arbitrary N). Another consequence is that the scattering matrix is unitary at any such energy. As a side result we give an independent stationary proof of asymptotic completeness for 3-body systems with long-range pair-potentials. This is an alternative to the known time-dependent proofs \citeDe, En.