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arXiv · 0906.3047

Propagation of chaos for many-boson systems in one dimension with a point pair-interaction

Z. Ammari·S. Breteaux
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Abstract

We consider the semiclassical limit of nonrelativistic quantum many-boson systems with delta potential in one dimensional space. We prove that time evolved coherent states behave semiclassically as squeezed states by a Bogoliubov time-dependent affine transformation. This allows us to obtain properties analogous to those proved by Hepp and Ginibre-Velo (\cite{Hep}, \cite{GiVe1,GiVe2}) and also to show propagation of chaos for Schrödinger dynamics in the mean field limit. Thus, we provide a derivation of the cubic NLS equation in one dimension.

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Z. Ammari, S. Breteaux. 2009-06-17. Propagation of chaos for many-boson systems in one dimension with a point pair-interaction. https://arxiv.org/abs/0906.3047

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