Z.Ammari, F.Nier
Mean field limit for bosons and propagation of Wigner measures
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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.