Z. Ammari; S. Breteaux
Propagation of chaos for many-boson systems in one dimension 
with a point pair-interaction
(360K, pdf)

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