Communications in Mathematical Physics

, Volume 331, Issue 3, pp 1087–1131 | Cite as

Mean–Field Evolution of Fermionic Systems

  • Niels Benedikter
  • Marcello Porta
  • Benjamin SchleinEmail author


The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ω N with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ω N . Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics.


Fermionic System Slater Determinant Hartree Equation Bogoliubov Transformation Canonical Anticommutation Relation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Niels Benedikter
    • 1
  • Marcello Porta
    • 1
  • Benjamin Schlein
    • 1
    Email author
  1. 1.Institute of Applied MathematicsUniversity of BonnBonnGermany

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