# Three-Body Dispersive Scattering

## TL;DR

This paper analyzes the spectral and scattering properties of a three-body dispersive quantum system, establishing decay and completeness results, and modeling ionization processes with non-conserving interactions.

## Contribution

It introduces a comprehensive framework for three-body dispersive systems, including non-particle-conserving interactions, and proves asymptotic completeness for negative energies.

## Key findings

- Proved local decay and propagation estimates.
- Established asymptotic completeness for non-threshold negative energies.
- Modeled ionization processes with trace class interactions.

## Abstract

We study the spectral and scattering theory of three body dispersive systems, which include a massless particle and a two body non-relativistic pair, along with two body short interactions among the three particles. We prove local decay estimates and propagation estimates, which are then used to prove asymptotic completeness for all non-threshold negative energies of the system. By adding (trace class) non-particle-conserving interactions, this models ionization processes as well. In particular, if the massless particle is interacting only through the non-particle-number conserving interactions, no ionization is possible if the total energy of the system is negative, as predicted by the formal analysis of the photo-electric effect.