caa a22 4500 445320249 CHVBK 20180317142701.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00023-011-0096-1 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0096-1 Thermal Effects in Gravitational Hartree Systems [Elektronische Daten] [Gonca Aki, Jean Dolbeault, Christof Sparber] We 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 $${T_c \in (0, T*)}$$ above which mixed states appear. Springer Basel AG, 2011 Aki Gonca Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany aut Dolbeault Jean Ceremade (UMR CNRS no. 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cédex 16, France aut Sparber Christof Department of Mathematics, Statistics, and Computer Science M/C 249, University of Illinois at Chicago, 851 S. Morgan Street, 60607, Chicago, IL, USA aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/6(2011-09-01), 1055-1079 1424-0637 12:6<1055 2011 12 23 https://doi.org/10.1007/s00023-011-0096-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0096-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aki Gonca Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany aut NATIONALLICENCE 700 1- Dolbeault Jean Ceremade (UMR CNRS no. 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cédex 16, France aut NATIONALLICENCE 700 1- Sparber Christof Department of Mathematics, Statistics, and Computer Science M/C 249, University of Illinois at Chicago, 851 S. Morgan Street, 60607, Chicago, IL, USA aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/6(2011-09-01), 1055-1079 1424-0637 12:6<1055 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer