Institut de recherche sur les lois fondamentales de l'Univers

The description of the quantum dynamics of many interacting particles is a great challenge in  many fields of physics. Even simple observables such as the number of particles might be difficult to determine when the system encounters a violent perturbation. This is the case, for instance in collisions of molecules, atomic clusters, or nuclei. Our goal is rather simple: counting the number of transfered particles in such a collision. To keep the amount of work for the physicist and his computer to a reasonable level, mean-field approaches are considered rather than solving the full Schrödinger equation. For the average number of transfered particles, this leads to the time-dependent Hartree-Fock (TDHF) theory. For their fluctuations, however, we need a more elaborated mean-field approach based on the Balian-Veneroni variational principle. These formalisms are applied to heavy-ion collisions.