Hartree-Fock dynamics for weakly interacting fermions
Mathematical Physics
2014-05-01 v1 math.MP
Abstract
We review recent results concerning the evolution of fermionic systems. We are interested in the mean field regime, where particles experience many weak collisions. For fermions, the mean field regime is naturally linked with a semiclassical limit. Assuming some regularity of the interaction potential we show that the many body evolution of initial states close to Slater determinants exhibiting the appropriate semiclassical structure can be approximated by the Hartree-Fock equation. Our method provides precise bounds on the rate of the convergence.
Cite
@article{arxiv.1404.7769,
title = {Hartree-Fock dynamics for weakly interacting fermions},
author = {Niels Benedikter and Marcello Porta and Benjamin Schlein},
journal= {arXiv preprint arXiv:1404.7769},
year = {2014}
}
Comments
11 pages. Contribution to the Proceedings of the QMath 12 conference