From bosonic grand-canonical ensembles to nonlinear Gibbs measures | Zendy

Nicolas Rougerie | Zendy

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From bosonic grand-canonical ensembles to nonlinear Gibbs measures

Author(s) -

Nicolas Rougerie

Publication year - 2015

Publication title -

séminaire laurent schwartz — edp et applications

Language(s) - English

Resource type - Journals

ISSN - 2266-0607

DOI - 10.5802/slsedp.71

Subject(s) - limit (mathematics) , nonlinear system , grand canonical ensemble , measure (data warehouse) , invariant (physics) , statistical physics , canonical ensemble , statistical mechanics , physics , mathematical physics , quantum , statistical ensemble , mathematics , quantum mechanics , mathematical analysis , computer science , statistics , monte carlo method , database

In a recent paper, in collaboration with Mathieu Lewin and Phan Th{\`a}nh Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This text summarizes these findings. It focuses on the simplest, but most physically relevant, case we could treat so far, namely that of the defocusing cubic NLS functional on a 1D interval. The measure obtained in the limit, which (almost) lives over H^{1/2} , has been previously shown to be invariant under the NLS flow by Bourgain.

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