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Journal of Statistical Physics

, Volume 166, Issue 6, pp 1345–1364 | Cite as

Mean Field Evolution of Fermions with Coulomb Interaction

  • Marcello PortaEmail author
  • Simone Rademacher
  • Chiara Saffirio
  • Benjamin Schlein
Article

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.

Keywords

Many-body quantum dynamics Mean field scaling Semiclassical scaling Hartree–Fock dynamics Coulomb interaction 

Notes

Acknowledgements

We acknowledge the support of the NCCR SwissMAP. Furthermore, M.P. has been supported by the Swiss National Science Foundation through the grant “Mathematical aspects of many-body quantum systems”. C.S. was supported by the Forschungskredit UZHFK-15-108. B.S. is happy to acknowledge support from the Swiss National Science Foundation through the grant “Effective equations from quantum dynamics”.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Marcello Porta
    • 1
    Email author
  • Simone Rademacher
    • 1
  • Chiara Saffirio
    • 1
  • Benjamin Schlein
    • 1
  1. 1.Institute of MathematicsUniversity of ZurichZurichSwitzerland

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