Published in

Springer (part of Springer Nature), Annales Henri Poincaré, 6(12), p. 1055-1079

DOI: 10.1007/s00023-011-0096-1



Export citation

Search in Google Scholar

Thermal Effects in Gravitational Hartree Systems

Journal article published in 2011 by Gonca L. Aki, Jean Dolbeault ORCID, Christof Sparber
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Green circle
Postprint: archiving allowed
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO


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.