Archive for Rational Mechanics and Analysis

, Volume 229, Issue 3, pp 1037–1090 | Cite as

The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram

  • Marcin Napiórkowski
  • Robin Reuvers
  • Jan Philip Solovej


The Bogoliubov free energy functional is analysed. The functional serves as a model of a translation-invariant Bose gas at positive temperature. We prove the existence of minimizers in the case of repulsive interactions given by a sufficiently regular two-body potential. Furthermore, we prove the existence of a phase transition in this model and provide its phase diagram.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria
  2. 2.Department of Mathematical Methods in Physics, Faculty of PhysicsUniversity of WarsawWarsawPoland
  3. 3.QMATH, Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark
  4. 4.DAMTP, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

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