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

2009/06/17 by Ammari, Z., Breteaux, S. · 1 citation
#35Q55 #81S05 #81S30 #81T10 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0906.3047

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 (\citeHep, \citeGiVe1,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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