Handle URI:
http://hdl.handle.net/10754/599991
Title:
Thermal Effects in Gravitational Hartree Systems
Authors:
Aki, Gonca L.; Dolbeault, Jean; Sparber, Christof
Abstract:
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.
Citation:
Aki 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.
Publisher:
Springer Nature
Journal:
Annales Henri Poincaré
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
6-Apr-2011
DOI:
10.1007/s00023-011-0096-1
Type:
Article
ISSN:
1424-0637; 1424-0661
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAki, Gonca L.en
dc.contributor.authorDolbeault, Jeanen
dc.contributor.authorSparber, Christofen
dc.date.accessioned2016-02-28T06:33:56Zen
dc.date.available2016-02-28T06:33:56Zen
dc.date.issued2011-04-06en
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.en
dc.identifier.issn1424-0637en
dc.identifier.issn1424-0661en
dc.identifier.doi10.1007/s00023-011-0096-1en
dc.identifier.urihttp://hdl.handle.net/10754/599991en
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.en
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).en
dc.publisherSpringer Natureen
dc.titleThermal Effects in Gravitational Hartree Systemsen
dc.typeArticleen
dc.identifier.journalAnnales Henri Poincaréen
dc.contributor.institutionWeierstrass Institute for Applied Analysis and Stochastics, Berlin, Germanyen
dc.contributor.institutionCentre de Recherche en Mathematiques de la Decision, Paris, Franceen
dc.contributor.institutionUniversity of Illinois at Chicago, Chicago, United Statesen
kaust.grant.numberKUK-I1-007-43en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.