# Derivation of Vlasov Poisson equation via combined mean-field and semiclassical limits of large fermionic systems

Li Chen (University of Mannheim)
Mathematics Seminar
Monday, 6 December, 2021 | 16:15– | Zoom

We study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $h = N^{-1/3}$ in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation, with regularized Coulomb with a polynomial cutoff depending on $N$, into a Vlasov type equation with semiclassical and mean field remainder terms. In case of repulsive Coulomb interaction, by using the uniform estimates of kinetic energy and the localized number operator, the convergence of both remainder terms has been obtained, and the convergence to Vlasov Poisson equation is proceeded with additional compactness argument. The talk is based on the joint works with M. Liew and J. Lee.