UBC DG MP PDE Seminar: Chiara Saffirio

The derivation of effective macroscopic theories approximating microscopic systems of interacting particles is a major question in non-equilibrium statistical mechanics. For non-interacting particles this is a relatively easy task. However when particles interact among them, the many-body theory becomes very complicated and non-approachable from a computational viewpoint. In this lecture we will be concerned with the dynamics of systems made of many interacting fermions. We will focus on the mean-field regime, i.e. weakly interacting particles whose collective effect can be approximated by an averaged potential in convolution form, and review recent mean-field techniques based on second quantization approaches. More precisely we will study the time evolution of many fermions interacting via a Coulomb potential and show that, for quasi-free states exhibiting a semiclassical structure, the dynamics is well approximated by the time-dependent Hartree-Fock equation.