From bosonic grand-canonical ensembles to nonlinear Gibbs measures

Nicolas Rougerie[1]

  • [1] Université Grenoble 1 & CNRS, LPMMC (UMR 5493), B.P. 166, F-38042 Grenoble, France

Séminaire Laurent Schwartz — EDP et applications (2014-2015)

  • page 1-17
  • ISSN: 2266-0607

Abstract

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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.

How to cite

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Rougerie, Nicolas. "From bosonic grand-canonical ensembles to nonlinear Gibbs measures." Séminaire Laurent Schwartz — EDP et applications (2014-2015): 1-17. <http://eudml.org/doc/275733>.

@article{Rougerie2014-2015,
abstract = {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 $H^\{1/2-\epsilon \}$, has been previously shown to be invariant under the NLS flow by Bourgain.},
affiliation = {Université Grenoble 1 & CNRS, LPMMC (UMR 5493), B.P. 166, F-38042 Grenoble, France},
author = {Rougerie, Nicolas},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {eng},
pages = {1-17},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {From bosonic grand-canonical ensembles to nonlinear Gibbs measures},
url = {http://eudml.org/doc/275733},
year = {2014-2015},
}

TY - JOUR
AU - Rougerie, Nicolas
TI - From bosonic grand-canonical ensembles to nonlinear Gibbs measures
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2014-2015
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 17
AB - 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 $H^{1/2-\epsilon }$, has been previously shown to be invariant under the NLS flow by Bourgain.
LA - eng
UR - http://eudml.org/doc/275733
ER -

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