Mean Field Evolution of Fermions with Coulomb Interaction |
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Authors: | Marcello Porta Simone Rademacher Chiara Saffirio Benjamin Schlein |
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Institution: | 1.Institute of Mathematics,University of Zurich,Zurich,Switzerland |
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Abstract: | We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree–Fock dynamics. Our result holds under a condition on the solution of the Hartree–Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree–Fock evolution is trivial), but that we expect to hold more generally. |
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