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Derivation of the Vlasov equation from many-body quantum dynamics

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FKTW02 - Frontiers in analysis of kinetic equations

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.  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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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