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

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arxiv 0810.4282 v2 pith:VOBTAXVF submitted 2008-10-23 math-ph math.MP

Juerg Froehlich , Antti Knowles This is my paper · ORCID
classification math-phmath.MP
keywords dynamicsinteractioncoulombequationhartree-fockmean-fieldbardoscase
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We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field limiting regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. 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 a Heisenberg-picture dynamics of observables. This is a Egorov-type theorem.

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