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

DOI: 10.1007/s00023-011-0096-1

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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.

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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, 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.