Nonlinear Hartree equation as the mean field limit of weakly coupled fermions

Alexander Elgart, László Erdos, Benjamin Schlein, Horng Tzer Yau

Research output: Contribution to journalArticlepeer-review

56 Scopus citations

Abstract

We consider a system of N weakly interacting fermions with a real analytic pair interaction. We prove that for a general class of initial data there exists a fixed time T such that the difference between the one particle density matrix of this system and the solution of the nonlinear Hartree equation is of order N-1 for any time t≤T.

Original languageEnglish
Pages (from-to)1241-1273
Number of pages33
JournalJournal des Mathematiques Pures et Appliquees
Volume83
Issue number10
DOIs
StatePublished - 1 Oct 2004
Externally publishedYes

Keywords

  • BBGKY hierarchy
  • Hartree-Fock theory
  • Mean field system of fermions
  • Nonlinear Vlasov equation

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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