(Seminar) Mean-field evolution of fermionic mixed states with singular interaction potentials

Abstract: We will consider the many-body evolution of initially confined fermions interacting through a singular potential. In a joint mean-field and semiclassical scaling and using second quantization techniques, we will show that, for mixed states enjoying a semiclassical structure, the many-body dynamics can be approximated in Schatten norms by the time-dependent Hartree-Fock equation. In particular, we will highlight the advantages and drawbacks of considering such strong topology instead of the quantum Wasserstein distance introduced in [F. Golse, C. Mouhot and T. Paul, Commun. Math. Phys. 343, 165-205 (2016]).

analysis of PDEs

Audience: researchers in the topic

Open PDE and analysis seminar and lectures