Mean field dynamics of fermions and the time-dependent Hartree-Fock equation
Mathematical Physics
2015-02-25 v4 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/0204009,
title = {Mean field dynamics of fermions and the time-dependent Hartree-Fock equation},
author = {Claude Bardos and Francois Golse and Alex D. Gottlieb and Norbert J. Mauser},
journal= {arXiv preprint arXiv:math-ph/0204009},
year = {2015}
}
Comments
23 pages. This is the final version, to appear in Journal de Mathematiques Pures et Appliquees