08-139 Z.Ammari, F.Nier

Mean field limit for bosons and propagation of Wigner measures (187K, pdf) Jul 19, 08

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Abstract. We consider the N-body Schr\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \cite{AmNi}, the mean field limit is translated into a semiclassical problem with a small parameter $\varepsilon\to 0$, after introducing an $\varepsilon$-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 \cite{AmNi} 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.

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