MCS-MP Seminar: Niels Benedikter

Speaker: Niels Benedikter (Università degli Studi di Milano)

Title: Dynamics of Interacting Fermions in the Mean-Field Scaling Limit

Abstract: Large quantum systems of interacting fermionic particles are ubiquitous in condensed matter theory, ranging from models of metals to models of semiconductors to superconductors. Due to the huge number of particles in condensed matter systems, explicit solutions as well as numerics are generally inaccessible. However, in certain scaling limits, such as the mean field scaling limit where the density is large but the interaction weak, one can derive effective (non-linear) theories that describe some of the behavior of the system corrrectly. The mean-field scaling limit of fermionic systems is naturally coupled to a semiclassical limits, so that second quantization methods have to be combined with semiclassical methods in the rigorous derivation of effective theories. I will discuss recent progress on the derivation of time-dependent Hartree-Fock theory and, time permitting, the random phase approximation.