Classical limit for semi-relativistic Hartree systems

Details Classical limit for semi-relativistic Hartree systems Classical limit for semi-relativistic Hartree systems

2008-10-30

arxiv.org/abs/0810.5457v1

J. Math. Phys. 49, 102110 (2008)

Physics

Mathematical Physics

10 pages

Scientific paper

10.1063/1.3000059

We consider the three-dimensional semi-relativistic 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, 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 interaction, with an additional size constraint in the attractive case.

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