The Hartree-von Neumann limit of many body dynamics

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Chadam, J. M. : The time-dependent Hartree-Fock equations with Coulomb two-body interaction . Commun. Math. Phys., 46 (1976), pp. 99–104

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Ginibre J., Velo G.: The classical field limit for nonrelativistic bosons II. Asymptotic expansions for general potentials. Annales de l’institut Henri Poincaré (A) Physique théorique, 33 no. 4 , p. 363-394 (1980)

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Bardos C., Erdös L., Golse F., Mauser N., Yau H-T.: Derivation of the Schrödinger-Poisson equation from the quantum N-body problem . C.R. Acad. Sci. Paris, Ser. I334 (2002) 515-520

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Lieb E. Seiringer R.: Proof of Bose-Einstein condensation for dilute trapped gases . Phys. Rev. Lett. 88, 170409 (2002)

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Bardos C., Golse F., Gittlieb A.D., Mauser N.: Mean field dynamics and the time-dependent Hartree-Fock equation . J. Math. Pures Appl. 82 (2003) 665-683

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Lieb E., Seiringer R., Yngvason J. One-Dimensional bosons in three dimensional traps . Phys. Rev. Lett. 91,150401 (2003)

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Elgart A., Erdös L., Schlein B., Yau H-T.: Nonlinear Hartree equation as the mean field limit of weakly coupled fermions . J. Math. Pure Appl., 83, 1241 (2004)

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Elgart A., Erdös L., Schlein B., Yau H-T.: Gross-Pitaevskii equation as the mean field limit of weakly coupled Bosons . Arch. Rat. Mech. Anal. 179, no. 2, 265-283, (2006)

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Ammari Z., Nier F.: Mean field limit for bosons and infinite dimensional phase space analysis . Annales Henri Poincaré, vol. 9, issue 8, pp. 1503-1574 (2008)

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Erdös L, Schlein B.: Quantum dynamics with mean field interactions: a New Approach . arXiv:0804.3774v1 (2008)

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2008

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Fröhlich J., Knowles A., Schwartz S.: On the mean-field limit of bosons with Coulomb two body interaction . Preprint ArXiv:0805.4299 (2008)

Original

2008

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Grillakis M.G. and Margetis D.: Aprioi estimates for many-body Hamiltonian evolution of interacting boson system . Journal of Hyperbolic Differential Equations Vol.5, No. 4 857-883 (2008)

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Kirkpatrick K., Schlein B., Staffilani G.: Derivation of the two dimensional nonlinear Schödinger equation from many body quantum dynamics . ArXiv:0808.0505 (2008)