Mean field limit for bosons and propagation of Wigner measures

Details Mean field limit for bosons and propagation of Wigner measures Mean field limit for bosons and propagation of Wigner measures

2008-07-19

arxiv.org/abs/0807.3108v1

Physics

Mathematical Physics

10 pages

Scientific paper

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 $\epsilon\to 0$, 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 \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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