Mathematics Colloquia and Seminars

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The talk is about the derivation of the time-dependent Hartree(-Fock) equations as an eective dynamics for fermionic many-particle systems in quantum mechanics. That is, I start from the microscopic Schrodinger dynamics for N particles and show that the Hartree(-Fock) equations approximate this dynamics well for large N. I concentrate on the natural scenario where the total kinetic energy is bounded by a constant times N and the interaction has long range, such that there is interesting quantum mechanical mean- field behavior. The main results hold for a large class of interactions, including singular interactions. For Coulomb interaction, the results hold under certain assumptions on the properties of the solutions. The results are obtained by using a new method to derive mean-field limits developed by Pickl, which focuses on the correlations that develop due to the interaction.