FM 07-2016 (arXiv:1608.05268)

Authors: Marcello Porta, Simone Rademacher, Chiara Saffirio, Benjamin Schlein 

Title: Mean field evolution of fermions with Coulomb interaction
Abstract: We study the many body Schroedinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree-Fock dynamics. Our result holds under a condition on the solution of the Hartree-Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree-Fock evolution is trivial), but that we expect to hold more generally.