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    Classical limit for semirelativistic Hartree systems

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    Type
    Article
    Authors
    Aki, Gonca L.
    Markowich, Peter A. cc
    Sparber, Christof
    Date
    2008-10-21
    Online Publication Date
    2008-10-21
    Print Publication Date
    2008-10
    Permanent link to this record
    http://hdl.handle.net/10754/597779
    
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    Abstract
    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. © 2008 American Institute of Physics.
    Citation
    Aki 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.
    Sponsors
    This 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).
    Publisher
    AIP Publishing
    Journal
    Journal of Mathematical Physics
    DOI
    10.1063/1.3000059
    ae974a485f413a2113503eed53cd6c53
    10.1063/1.3000059
    Scopus Count
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