Derivation of Hartree’s theory for mean-field Bose gases

Mathieu Lewin[1]

  • [1] CNRS & Université de Cergy-Pontoise (UMR 8088) 95000 Cergy-Pontoise, France.

Journées Équations aux dérivées partielles (2013)

  • page 1-21
  • ISSN: 0752-0360

Abstract

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This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of N bosons with an interaction of intensity 1 / N (mean-field regime). In the limit N → ∞ , we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation in these systems.

How to cite

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Lewin, Mathieu. "Derivation of Hartree’s theory for mean-field Bose gases." Journées Équations aux dérivées partielles (2013): 1-21. <http://eudml.org/doc/275585>.

@article{Lewin2013,
abstract = {This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of $N$ bosons with an interaction of intensity $1/N$ (mean-field regime). In the limit $N\rightarrow \infty $, we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation in these systems.},
affiliation = {CNRS & Université de Cergy-Pontoise (UMR 8088) 95000 Cergy-Pontoise, France.},
author = {Lewin, Mathieu},
journal = {Journées Équations aux dérivées partielles},
keywords = {Hartree theory; mean-field limit; Bose-Einstein condensation; quantum de Finetti theorem},
language = {eng},
pages = {1-21},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Derivation of Hartree’s theory for mean-field Bose gases},
url = {http://eudml.org/doc/275585},
year = {2013},
}

TY - JOUR
AU - Lewin, Mathieu
TI - Derivation of Hartree’s theory for mean-field Bose gases
JO - Journées Équations aux dérivées partielles
PY - 2013
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 21
AB - This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of $N$ bosons with an interaction of intensity $1/N$ (mean-field regime). In the limit $N\rightarrow \infty $, we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation in these systems.
LA - eng
KW - Hartree theory; mean-field limit; Bose-Einstein condensation; quantum de Finetti theorem
UR - http://eudml.org/doc/275585
ER -

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