Résumé en anglais

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⩽n⩽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.