Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Reviews in Mathematical Physics

ALGEBRAIC APPROACH TO THE N-BODY LONG RANGE SCATTERING

Jan Dereziński

Published Mar 1, 1991• 41 citations
Publisher

Abstract

It is proven that if J, h are bounded continuous functions and H is an N-body Schrödinger operator then there exists [Formula: see text]. Limits of this form are used to study the N-body long range scattering.
DOI
10.1142/s0129055x91000023

Related papers

NON-RELATIVISTIC TIME-DEPENDENT SCATTERING THEORY FOR LONG RANGE POTENTIALS

Denis Wren Mark Mulherin

•Jan 1, 1969•0 citations

LARGE ATOMIC AND NUCLEAR THREE-BODY SYSTEMS: SCATTERING AND BINDING

Lauro Tomio, Marcelo Takeshi Yamashita, T. Frederico

The universal character of non-relativistic large three-body bosonic systems is addressed, with focus on highly interesting situations that occur in low-energy nuclear and atomic physics. Investigations on the trajectory of the first excited Efimov state, in a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems, are reported. The approach is applied to n-n-18C, where the n - n virtual energy and the three-body ground state are kept fixed. It is shown that the real part of the elastic s-wave phase-shift ([Formula: see text]) presents a zero, or a pole in [Formula: see text], when the system has an Efimov excited or virtual state. A brief discussion is given on the relevance of the approach for ultracold atom physics with tunable scattering lengths.

Modern Physics Letters A•Apr 30, 2009•0 citations

Asymptotic Observables in the N-Body Quantum Long Range Scattering

Jan Dereziński

Springer eBooks•Jan 1, 1991•2 citations

TIME-DEPENDENT SCATTERING THEORY OF N-BODY QUANTUM SYSTEMS

W. HUNZIKER, Israel Michael Sigal

We give a full and self contained account of the basic results in N-body scattering theory which emerged over the last ten years: The existence and completeness of scattering states for potentials decreasing like r-μ, [Formula: see text]. Our approach is a synthesis of earlier work and of new ideas. Global conditions on the potentials are imposed only to define the dynamics. Asymptotic completeness is derived from the fact that the mean square diameter of the system diverges like t2 as t → ±∞ for any orbit ψt which is separated in energy from thresholds and eigenvalues (a generalized version of Mourre's theorem involving only the tails of the potentials at large distances). We introduce new propagation observables which considerably simplify the phase–space analysis. As a topic of general interest we describe a method of commutator expansions.

Reviews in Mathematical Physics•Aug 1, 2000•55 citations

Two-body scattering for schrödinger operators involving zero-range interactions

Fritz Gesztesy, L. Pittner

Reports on Mathematical Physics•Apr 1, 1984•15 citations

Quantum scattering theory for two- and three-body systems with potentials of short and long range

Volker Enß

Lecture notes in mathematics•Jan 1, 1985•40 citations
The universal character of non-relativistic large three-body bosonic systems is addressed, with focus on highly interesting situations that occur in low-energy nuclear and atomic physics. Investigations on the trajectory of the first excited Efimov state, in a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems, are reported. The approach is applied to n-n-18C, where the n - n virtual energy and the three-body ground state are kept fixed. It is shown that the real part of the elastic s-wave phase-shift ([Formula: see text]) presents a zero, or a pole in [Formula: see text], when the system has an Efimov excited or virtual state. A brief discussion is given on the relevance of the approach for ultracold atom physics with tunable scattering lengths.
We give a full and self contained account of the basic results in N-body scattering theory which emerged over the last ten years: The existence and completeness of scattering states for potentials decreasing like r-μ, [Formula: see text]. Our approach is a synthesis of earlier work and of new ideas. Global conditions on the potentials are imposed only to define the dynamics. Asymptotic completeness is derived from the fact that the mean square diameter of the system diverges like t2 as t → ±∞ for any orbit ψt which is separated in energy from thresholds and eigenvalues (a generalized version of Mourre's theorem involving only the tails of the potentials at large distances). We introduce new propagation observables which considerably simplify the phase–space analysis. As a topic of general interest we describe a method of commutator expansions.