The Bogoliubov free energy functional I. Existence of minimizers and phase diagram

Abstract

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 existence of a phase transition in this model and provide its phase diagram.

Published version, 54 pages, 1 figure

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• Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons
• On Ground States of the Bogoliubov Energy Functional: A Direct Proof
• Ground state energy of Bogoliubov energy functional in the high density limit
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
• A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
• Differential Equations of Quantum Mechanics