From bosonic grand-canonical ensembles to nonlinear Gibbs measures
Séminaire Laurent Schwartz — EDP et applications (2014-2015), Exposé no. 5, 17 p.

In a recent paper, in collaboration with Mathieu Lewin and Phan Thành 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 lives over H 1/2-ϵ , has been previously shown to be invariant under the NLS flow by Bourgain.

DOI : 10.5802/slsedp.71
Rougerie, Nicolas 1

1 Université Grenoble 1 & CNRS, LPMMC (UMR 5493), B.P. 166, F-38042 Grenoble, France
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Rougerie, Nicolas. From bosonic grand-canonical ensembles to nonlinear Gibbs measures. Séminaire Laurent Schwartz — EDP et applications (2014-2015), Exposé no. 5, 17 p. doi : 10.5802/slsedp.71. http://www.numdam.org/articles/10.5802/slsedp.71/

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