Work

Stationary completeness: The N-body short-range case

Year: 2025

Type: article

Abstract: For a general class of N -body Schrödinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. This holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Dereziński-Enss type. In this paper we improve for short-range models on the known weak continuity properties in that we show that all non-threshold energies are stationary complete , resolving in this case a conjecture from [21] . A consequence is that the above scattering quantities depend strongly continuously on the energy parameter at all non-threshold energies (improving on previously almost everywhere proven properties). Another consequence is that the scattering matrix is unitary at any such energy. As a side result we obtain a new and purely stationary proof of asymptotic completeness for N -body short-range systems.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110544

Author: E. Skibsted

Institution: Aarhus University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funder: Natur og Univers, Det Frie Forskningsråd