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Mean field evolution of fermions with Coulomb interaction


Porta, Marcello; Rademacher, Simone; Saffirio, Chiara; Schlein, Benjamin (2017). Mean field evolution of fermions with Coulomb interaction. Journal of Statistical Physics, 166(6):1345-1364.

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.

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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Additional indexing

Item Type:Journal Article, refereed, further contribution
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:January 2017
Deposited On:15 Mar 2017 15:34
Last Modified:23 Apr 2017 05:11
Publisher:Springer
ISSN:0022-4715
Publisher DOI:https://doi.org/10.1007/s10955-017-1725-y
Related URLs:http://arxiv.org/abs/1602.01021

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Embargo till: 2018-01-31