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| HAL : hal-00512641, version 1 |
| arXiv : 1009.0128 |
| Fiche détaillée |  Récupérer au format |
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| Annales Henri Poincaré 12 (2011) 1055-1079 |
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| Thermal effects in gravitational Hartree systems |
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| Gonca Aki 1Jean Dolbeault 2 |
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| (2011) |
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| 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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| 1 : | Fakultät für Mathematik |
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Universität Wien |
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| 2 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 3 : | Department of Mathematics, Statistics, and Computer Science (UIC) |
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University of Illinois at Chicago |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Physique/Physique mathématique Mathématiques/Physique mathématique |
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| Gravitation – Hartree energy – entropy – ground states – free energy – Casimir functional – pure states – mixed states |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00512641, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00512641 | |
| oai:hal.archives-ouvertes.fr:hal-00512641 | |
| Contributeur : Jean Dolbeault | |
| Soumis le : Mardi 31 Août 2010, 10:53:00 | |
| Dernière modification le : Dimanche 18 Décembre 2011, 18:09:26 | |
