We will consider the time evolution of initially confined fermions interacting through a singular potential. In a joint mean-field and semiclassical scaling, we will show that the many-body dynamics can be approximated in Schatten norms by the time-dependent Hartree-Fock equation. Our result holds for mixed states enjoying a semiclassical structure. Moreover, in the semiclassical limit, the dynamics is close to the one described by the Vlasov equation with singular interactions, thus providing a two-step approximation of the many-body evolution. The method used provides explicit bounds on the convergence rate.
Based on joint works with J. Chong and L. Laflèche.
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