A mixed-norm estimate of two-particle reduced density matrix of many-body Schrödinger dynamics

We provide a mixed-norm estimate of two-particle reduced density matrix of the solution of N-body Schrödinger equation. Using that we present a new approach to obtain the Vlasov dynamics from the Schrödinger equation through Hartree-Fock dynamics with ℏ = N^−1/3 as the re-scaled Plank constant. Furthermore, we provide that, in the sense of distribution, the mean-field residue term has higher rate than the semi-classical residue term. This is a joint work with Jinyeop Lee, Yue Li, and Matthew Liew.