Mean field dynamics of fermions and the time-dependent Hartree-Fock equation
arXiv:math-ph/0204009
Abstract
The time-dependent Hartree-Fock equations are derived from the N-particle Schrödinger 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.
23 pages. This is the final version, to appear in Journal de Mathematiques Pures et Appliquees