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

By Juerg Froehlich, E. Lenzmann. 2004

173 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2715c75b408eb098ca41b0a3718545852a060ba6

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In Atomic and Molecular Physics, and Optics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

The Excitation Spectrum for Weakly Interacting Bosons (2010, background): “We refer to [5, 6] for a review and further references.”
Strichartz Estimates in Spherical Coordinates (2012, unknown): “Typical examples of ω are ρ(0 < a 6= 1) , √ 1 + ρ2, ρ √ 1 + ρ2, and ρ √ 1+ρ2 which describe Schrödinger type equation [22], Klein-Gordon or semirelativistic equation[15], iBq, and imBq (see [10] and references therein).”
Positive and sign changing solutions to a nonlinear Choquard equation (2012, background): “This equation arises in many interesting situations related to the quantum theory of large systems of nonrelativistic bosonic atoms and molecules, see for example [10, 15] and the references therein.”
The Excitation Spectrum for Weakly Interacting Bosons in a Trap (2012, methodology): “In this paper, we shall prove the accuracy of the Bogoliubov approximation for the excitation spectrum of a trapped Bose gas, in the mean-field or Hartree limit [21,22], where the interaction is weak and long-range.”
The Schrödinger–Newton equation as a non-relativistic limit of self-gravitating Klein–Gordon and Dirac fields (2012, background): “Compare [2, 3] and references therein for more rigorous statements.”