Year: 2025
Type: article
Abstract: Within the class of Dereziński–Enss pair-potentials which includes Coulomb potentials, a stationary scattering theory for N -body systems was recently developed (Skibsted in Commun Math Phys 401:2193–2267, 2023). 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 Skibsted (Commun Math Phys 401:2193–2267, 2023) in the special case $$N=3$$ 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 the unitary of the scattering matrix 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 (Dereziński in Ann Math 38:427–476, 1993; Enss in Long-range scattering of two- and three-body quantum systems, Publications ecole polytechnique, Palaiseau, 1989).
Source: Annales Henri Poincaré
Author: E. Skibsted
Institution: Aarhus University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4414912866