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Article Dans Une Revue Annales Henri Poincaré Année : 2011

Thermal effects in gravitational Hartree systems

Résumé

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.
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hal-00512641 , version 1 (31-08-2010)

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Gonca Aki, Jean Dolbeault, Christof Sparber. Thermal effects in gravitational Hartree systems. Annales Henri Poincaré, 2011, 12, pp.1055-1079. ⟨hal-00512641⟩
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