2023/06/12 by Erik Skibsted, Skibsted, Erik
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability and Risk Models #Spectral Theory (math.SP) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2306.07080
openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 [Sk1]. 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.