Communications in Mathematical Physics

, Volume 340, Issue 3, pp 1171–1186 | Cite as

A Many-Body RAGE Theorem

  • Jonas Lampart
  • Mathieu Lewin


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.


Compact Operator Lewin Convergent Subsequence Geometric Limit Anderson Localization 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.CNRS and CEREMADE (UMR CNRS 7534)University of Paris-DauphineParis Cedex 16France

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