Thermal effects in gravitational Hartree systems
Sparber, Christof; Dolbeault, Jean; Aki, Gonca L. (2011), Thermal effects in gravitational Hartree systems, Annales Henri Poincaré, 12, 6, p. 1055-1079. http://dx.doi.org/10.1007/s00023-011-0096-1
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00512641/fr/
Journal nameAnnales Henri Poincaré
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Abstract (EN)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.
Subjects / Keywordsmixed states; pure states; Casimir functional; free energy; ground states; entropy; Hartree energy; Gravitation
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