Mean field dynamics of fermions and the time-dependent Hartree-Fock equation

By Claude Bardos, François Golse, A. Gottlieb, Norbert J. Mauser. 2002

134 citations recorded by the source corpus.

The time-dependent Hartree–Fock equations are derived from the N-body linear Schrodinger equation with the mean-field scaling in the limit N →+ ∞and for initial data that are close to Slater determinants. Only the case of bounded, symmetric binary interaction potentials is treated in this work. We prove that, as N →+ ∞, the first partial trace of the N-body density operator approaches the solution of the time-dependent Hartree–Fock equations (in operator form) in the sense of the trace norm.  2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved. Resume

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0e841e2c0e7b4bb57df4a5c7f175d9b1282c7a82

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Mean–Field Evolution of Fermionic Systems (2013, background): “1) for bosonic systems) has been considered in [4] (for regular interactions) and in [16] (for potentials with Coulomb singularity).”
From atoms to crystals: a mathematical journey (2005, background): “Golse and collaborators (see [9] and other references by the same authors) have recently shown that the TDHF equation approaches the Schrödinger equation in the limit of an infinite number of electrons.”
The mean-field limit for the dynamics of large particle systems (2003, methodology): “In fact, the result in [3] shows that the same result holds verbatim if DN(t) is the solution of the N -body von Neumann equation (II.”
Effective Evolution Equations from Quantum Dynamics (2015, methodology): “Concerning other scaling limits, the Hartree-Fock equation has been derived in [10] and (for a Coulomb potential) [31] starting from a many-body Hamilton operator of the form (6.”
A review of the mean field limits for Vlasov equations (2014, background): “• Quantum mechanics and the derivation of non linear Schrödinger equations (in particular Schrödinger-Poisson and Gross-Pitaevskii) from linear, N -particles Schrödinger; see for example [9], [8], [61], [62] and the references therein.”