Geodesic
Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation
Fröhlich, Jürg1 ; Lenzmann, Enno2 
1 Institute for Theoretical Physics, ETH Zürich-Hönggerberg, CH-8093 Zürich, Switzerland
2 Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 18, 26 p.

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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.

Fröhlich, Jürg 1 ; Lenzmann, Enno 2

1 Institute for Theoretical Physics, ETH Zürich-Hönggerberg, CH-8093 Zürich, Switzerland
2 Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland 
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     title = {Mean-Field {Limit} of {Quantum} {Bose} {Gases} and {Nonlinear} {Hartree} {Equation}},
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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://geodesic.mathdoc.fr/item/SEDP_2003-2004____A18_0/