A RAGE theorem for many-body systems

The famous RAGE theorem relates the spectral properties of a self-adjoint operator $H$ to the long-time behaviour of the unitary group it generates. In particular, the ergodic mean of a time-evolved state converges (weakly-*) to a state on the space spanned by the eigenvectors of $H$.

I will present a joint work with Mathieu Lewin, showing that for $N$-body Hamiltonians a similar statement holds also for subsystems with $n< N$ particles.