Title: Derivation of Mean-field Dynamics for Fermions
Abstract:
The talk is about the derivation of the time-dependent Hartree(-Fock) equations as
an effective dynamics for fermionic many-particle systems in quantum mechanics. That
is, I start from the microscopic Schr ?odinger dynamics for N particles and show that the
Hartree(-Fock) equations approximate this dynamics well for large N . I concentrate on
the natural scenario where the total kinetic energy is bounded by a constant times N and
the interaction has long range, such that there is interesting quantum mechanical mean-
field behavior. The main results hold for a large class of interactions, including singular
interactions. For Coulomb interaction, the results hold under certain assumptions on the
properties of the solutions. The results are obtained by using a new method to derive
mean-field limits developed by Pickl, which focuses on the correlations that develop due
to the interaction.