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 \({0 \leqslant n \leqslant N}\) 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.
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Communicated by R. Seiringer
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Lampart, J., Lewin, M. A Many-Body RAGE Theorem. Commun. Math. Phys. 340, 1171–1186 (2015). https://doi.org/10.1007/s00220-015-2458-x
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DOI: https://doi.org/10.1007/s00220-015-2458-x