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