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A Microscopic Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Two-Body Interaction

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Abstract

We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. [J. Math. Pures Appl. 82(6):665–683, 2003] to the case of unbounded interaction potentials. We also express the mean-field limit as a “superhamiltonian” system, and state our main result in terms of the Heisenberg-picture dynamics of observables. This is a Egorov-type theorem.

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Authors and Affiliations

  1. Institute of Theoretical Physics, ETH Hönggerberg, 8093, Zürich, Switzerland

    Jürg Fröhlich

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Antti Knowles

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  1. Jürg Fröhlich
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  2. Antti Knowles
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Correspondence to Antti Knowles.

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Fröhlich, J., Knowles, A. A Microscopic Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Two-Body Interaction. J Stat Phys 145, 23 (2011). https://doi.org/10.1007/s10955-011-0311-y

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  • DOI: https://doi.org/10.1007/s10955-011-0311-y

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