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    Gonca L. Aki · Jean Dolbeault · Christof Sparber
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    ABSTRACT: We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb–Newton interaction. For a given mass M>0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T*>0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature Tc Î (0, T*){T_c \in (0, T*)} above which mixed states appear.
    Full-text · Article · Sep 2011 · Annales Henri Poincare
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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.
    Full-text · Article · Oct 2008 · Journal of Mathematical Physics

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