2014/11/04 by Benedikter, Niels, Jaksic, Vojkan, Porta, Marcello +2 · 2 citations
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1411.0843
In this paper we study the dynamics of fermionic mixed states in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of such initial data is well approximated by a suitable quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent Hartree-Fock equation. Our result holds for all times, and gives effective estimates on the rate of convergence of the many-body dynamics towards the Hartree-Fock one.