Mean field limit for bosons and propagation of Wigner measures

Zied Ammari (1) , Francis Nier (2)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 IRMAR - Institut de Recherche Mathématique de Rennes

We consider the N-body Schr¨odinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [AmNi], the mean field limit is translated into a semiclassical problem with a small parameter epsilon→0, after introducing an epsilon- dependent bosonic quantization. The limit is expressed as a push-forward by a nonlinear flow (e.g. Hartree) of the associated Wigner measures. These object and their basic properties were introduced in a previous article in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for rather general class of quantum states in their mean field limit.

Mots clés: Champ moyen; limite semiclassique; dimension infinie

Domaines: Equations aux dérivées partielles [math.AP]

Zied Ammari, Francis Nier. Mean field limit for bosons and propagation of Wigner measures. 2008. ⟨hal-00295082⟩