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

2008/10/23 by Juerg Froehlich, Antti Knowles, Froehlich, Juerg +1
Mathematics · Physics and Astronomy · #35Q40 (Primary) 37K05 #82C40 (Secondary) #Advanced Mathematical Physics Problems #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum many-body systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0810.4282

openalex publication_date 2008/10/23 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of a Fermi gas with a Coulomb interaction potential,\nand show that, in a mean-field limiting regime, the dynamics is described by\nthe Hartree-Fock equation. This extends previous work of Bardos et al. to the\ncase of unbounded interaction potentials. We also express the mean-field limit\nas a "superhamiltonian" system, and state our main result in terms of a\nHeisenberg-picture dynamics of observables. This is a Egorov-type theorem.\n

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