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

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.

arXiv comment27 pages, 2 figures

References in corpus (4)

• Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations
• Selection of the ground state for nonlinear Schroedinger equations
• Asymptotic stability of N-soliton states of NLS
• Relaxation of Excited States in Nonlinear Schrödinger Equations

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