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From the Hartree dynamics to the Vlasov equation. (English) Zbl 1342.35276

Summary: We consider the evolution of quasi-free states describing \(N\) fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large \(N\), we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise bounds on the rate of convergence.

MSC:

35Q40 PDEs in connection with quantum mechanics
35Q83 Vlasov equations
35B65 Smoothness and regularity of solutions to PDEs
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