Classical limit for semirelativistic Hartree systems

Gonca L. Aki, Peter A. Markowich, Christof Sparber

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case.

Original languageEnglish (US)
Article number102110
JournalJournal of Mathematical Physics
Issue number10
StatePublished - 2008
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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