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dc.contributor.authorAki, Gonca L.
dc.contributor.authorDolbeault, Jean
dc.contributor.authorSparber, Christof
dc.date.accessioned2016-02-28T06:33:56Z
dc.date.available2016-02-28T06:33:56Z
dc.date.issued2011-04-06
dc.identifier.citationAki GL, Dolbeault J, Sparber C (2011) Thermal Effects in Gravitational Hartree Systems. Annales Henri Poincaré 12: 1055–1079. Available: http://dx.doi.org/10.1007/s00023-011-0096-1.
dc.identifier.issn1424-0637
dc.identifier.issn1424-0661
dc.identifier.doi10.1007/s00023-011-0096-1
dc.identifier.urihttp://hdl.handle.net/10754/599991
dc.description.abstractWe consider the non-relativistic Hartree model in the gravitational case, i. e. with attractive Coulomb-Newton interaction. For a given mass M > 0, we construct stationary states with non-zero temperature T 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 T* > 0 (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 critical temperature Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.
dc.description.sponsorshipThis publication has been supported by Award No. KUK-I1-007-43 of the King Abdullah University of Science and Technology (KAUST). J. Dolbeault and C. Sparber have been supported, respectively, by the ANR-08-BLAN-0333-01 project CBDif-Fr and by the University research fellowship of the Royal Society. G. L. Aki acknowledges the support of the FWF, grant no. W 800-N05 and funding by WWTF project (MA45).
dc.publisherSpringer Nature
dc.titleThermal Effects in Gravitational Hartree Systems
dc.typeArticle
dc.identifier.journalAnnales Henri Poincaré
dc.contributor.institutionWeierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
dc.contributor.institutionCentre de Recherche en Mathematiques de la Decision, Paris, France
dc.contributor.institutionUniversity of Illinois at Chicago, Chicago, United States
kaust.grant.numberKUK-I1-007-43
dc.date.published-online2011-04-06
dc.date.published-print2011-09


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