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On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

Fröhlich, Jürg ; Knowles, Antti ; Schwarz, Simon

In: Communications in Mathematical Physics, 2009, vol. 288, no. 3, p. 1023-1059

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    Title
    • On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
    Author
    • Fröhlich, Jürg. Institute of Theoretical Physics, ETH Hönggerberg, CH-8093, Zürich, Switzerland
    • Knowles, Antti. Institute of Theoretical Physics, ETH Hönggerberg, CH-8093, Zürich, Switzerland
    • Schwarz, Simon. Institute of Theoretical Physics, ETH Hönggerberg, CH-8093, Zürich, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Communications in Mathematical Physics, 2009, vol. 288, no. 3, p. 1023-1059. Springer-Verlag
    Other Version
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:316598
    Summary
    In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg- picture dynamics of "observables”, thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical” limit