Conference: Special Talk


Mean-field Evolution of Fermionic Systems

{{_Ltalk:R}} Prof. Dr. Marcello Porta
Date: 03.02.14   Time: 16.00 - 18.00   Room: Y27H28

In this seminar I will discuss the dynamics of $N$ interacting fermions in the mean-field regime. Compared to the bosonic case, fermionic mean-field scaling is naturally coupled with a semiclassical scaling, making the analysis more involved. I will consider initial data which are close to a Slater determinant, whose reduced one-particle density matrix $\omega_{N}$ is an orthogonal projection with an appropriate semiclassical structure. Under some regularity assumptions on the interaction potential I will show that the time evolution of such initial data stays close to a Slater determinant, with reduced one-particle density matrix given by the solution of the Hartree-Fock equation with initial data $\omega_{N}$. The result holds for all (semiclassical) times, and gives effective bounds on the rate of convergence towards the Hartree-Fock dynamics as $N$ goes to infinity. This is joint work with Niels Benedikter and Benjamin Schlein.