Thermal Effects in Gravitational Hartree Systems

Gonca L. Aki, Jean Dolbeault, Christof Sparber

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.
Original languageEnglish (US)
Pages (from-to)1055-1079
Number of pages25
JournalAnnales Henri Poincaré
Issue number6
StatePublished - Apr 6 2011
Externally publishedYes


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