Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 18, 26 p.

We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schrödinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle (Newtonian) limit. Some open problems are described.

@article{SEDP_2003-2004____A18_0,
author = {Fr\"ohlich, J\"urg and Lenzmann, Enno},
title = {Mean-Field {Limit} of {Quantum} {Bose} {Gases} and {Nonlinear} {Hartree} {Equation}},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
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publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2003-2004},
mrnumber = {2117050},
language = {en},
url = {http://www.numdam.org/item/SEDP_2003-2004____A18_0/}
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Fröhlich, Jürg; Lenzmann, Enno. Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 18, 26 p. http://www.numdam.org/item/SEDP_2003-2004____A18_0/

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