A many-body RAGE theorem

TL;DR

This paper extends the RAGE theorem to N-body quantum systems, showing that only bound states persist over time, using a specialized weak topology based on reduced density matrices.

Contribution

It introduces a generalized RAGE theorem for many-body quantum systems, utilizing a novel weak topology framework related to algebraic state topologies.

Findings

Bound states are the only persistent states in long-term evolution.

The weak topology based on reduced density matrices effectively captures the asymptotic behavior.

The results unify algebraic and analytical perspectives in many-body quantum dynamics.

Abstract

We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with $0\leq n\leq N$ particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.