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- ItemThermal effects in gravitational Hartree systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Aki, Gonca L.; Dolbeault, Jean; Sparber, ChristofWe 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 T_c in (0, T^*) above which mixed states appear.