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

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arxiv math-ph/0409019 v1 pith:MFPOZY72 submitted 2004-09-09 math-ph math.MP

Juerg Froehlich , Enno Lenzmann This is my paper · ORCID
classification math-phmath.MP
keywords hartreeequationlimitbosonslargemean-fieldnonlinearquantum
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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 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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  1. The fractional in time Schr\"{o}dinger equation with a Hartree perturbation

    math-ph 2019-07 unverdicted novelty 4.0 of 10

    Proves existence, uniqueness and regularity for the time-fractional nonlinear Schrödinger equation with Hartree perturbation.

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