Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation

2004/09/09 by Juerg Froehlich, Enno Lenzmann · 3 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as Seminaire EDP, Ecole Polytechnique, 2003-2004 · 27 pages, 2 figures

arxiv created 2004/09/09 · arxiv updated 2009/12/01

Abstract

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 Schroedinger 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.

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• Nondegeneracy of bubble solutions to the Choquard equation in two dimension
• Asymptotic behavior of the least energy solutions to the Choquard equation in dimension two
• Global dynamics above the ground state for the energy-critical Hartree equation with radial data

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