A many-body RAGE theorem
arXiv:1503.00496 · doi:10.1007/s00220-015-2458-x
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 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.
Final version to appear in Comm. Math. Phys.; specifically: Communications in Mathematical Physics, Springer Verlag (Germany), 2015, in press