Orateur
Description
The RAGE theorem is a general statement on the relation of spectrum and dynamics for self-adjoint operators.
It states that the large-time dynamics converge, in a certain weak sense, to the projection of the initial condition onto the bound states of the generator. The contributions of the continuous spectrum disappear in this limit.
The many-body version of the theorem, which is joint work with Mathieu Lewin, refines this statement in the case of N-body systems.
In an appropriate sense, these systems converge for large times to a combination of bound states of systems with n=0,..,N particles.
Including the decomposition into subsystems with strictly fewer particles resolves the contribution of the continuous spectrum on the N body generator, which is due to freely moving clusters of particles.
