A many-body RAGE theorem

Jonas Lampart (1) , Mathieu Lewin (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Jonas Lampart, Mathieu Lewin. A many-body RAGE theorem. Communications in Mathematical Physics, 2015, 340 (3), pp.1171-1186. ⟨10.1007/s00220-015-2458-x⟩. ⟨hal-01121656v2⟩