@article{Aki2011, abstract = {We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct stationary states with non-zero temperature 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(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 positive critical temperature above which mixed states appear.}, author = {Aki, Gonca L. and Dolbeault, Jean and Sparber, Christof}, doi = {10.1007/s00023-011-0096-1}, journal = {Annales Henri Poincaré}, month = {apr}, pages = {1055-1079}, title = {Thermal Effects in Gravitational Hartree Systems}, url = {http://arxiv.org/abs/1009.0128}, volume = {12}, year = {2011} }