TY - JOUR

T1 - Thermal Effects in Gravitational Hartree Systems

AU - Aki, Gonca L.

AU - Dolbeault, Jean

AU - Sparber, Christof

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2011/4/6

Y1 - 2011/4/6

N2 - 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 Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.

AB - 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 Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.

UR - http://hdl.handle.net/10754/599991

UR - http://link.springer.com/10.1007/s00023-011-0096-1

UR - http://www.scopus.com/inward/record.url?scp=79961025490&partnerID=8YFLogxK

U2 - 10.1007/s00023-011-0096-1

DO - 10.1007/s00023-011-0096-1

M3 - Article

SN - 1424-0637

VL - 12

SP - 1055

EP - 1079

JO - Annales Henri Poincaré

JF - Annales Henri Poincaré

IS - 6

ER -