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

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

2002-04-04

arxiv.org/abs/math-ph/0204009v4

Physics

Mathematical Physics

23 pages. This is the final version, to appear in Journal de Mathematiques Pures et Appliquees

Scientific paper

The time-dependent Hartree-Fock equations are derived from the N-particle Schr\"odinger equation with mean-field scaling in the infinite particle limit, for initial data that are like Slater determinants. Only the case of bounded interaction potentials is treated in this work. We prove that, in the infnite particle limit, the first partial trace of the N-particle density operator approaches the solution of the time-dependent Hartree-Fock equations in the trace norm.

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