KAUST Grant NumberKUK-I1-007-43
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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.
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.
SponsorsThis 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).
JournalAnnales Henri Poincaré