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

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

2009-06-17

arxiv.org/abs/0906.3047v1

Physics

Mathematical Physics

35 pages

Scientific paper

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 Schr\"odinger dynamics in the mean field limit. Thus, we provide a derivation of the cubic NLS equation in one dimension.

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