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Article Dans Une Revue Asymptotic Analysis Année : 2012

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

Résumé

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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Dates et versions

hal-00396038 , version 1 (16-06-2009)

Identifiants

Citer

Zied Ammari, Sébastien Breteaux. Propagation of chaos for many-boson systems in one dimension with a point pair-interaction. Asymptotic Analysis, 2012, 76 (3-4), pp.123-170. ⟨10.3233/ASY-2011-1064⟩. ⟨hal-00396038⟩
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