Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential

Zied Ammari (1) , Francis Nier (2, 1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum

We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our previous works with a slightly different strategy.

Mots clés: mean field limit; bosons; semiclassical analysis; Wigner measure; measure transportation

Domaines: Equations aux dérivées partielles [math.AP]

Zied Ammari, Francis Nier. Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential. 2011. ⟨hal-00644656v1⟩