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AbstractWe 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. © 2008 American Institute of Physics.
CitationAki GL, Markowich PA, Sparber C (2008) Classical limit for semirelativistic Hartree systems. Journal of Mathematical Physics 49: 102110. Available: http://dx.doi.org/10.1063/1.3000059.
SponsorsThis work has been supported by the KAUST Investigator Award and the Wolfson Research Merit Award (Royal Society) of P. Markowich. G. L. Aki acknowledges support by the DEASE project of the EU. C. Sparber has been supported by the APART grant of the Austrian Academy of Sciences (MEST-CT-2005-021122).
JournalJournal of Mathematical Physics