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

TL;DR

This paper analyzes the Bogoliubov free energy functional for a translation invariant Bose gas at positive temperature, proving the existence of minimizers for repulsive interactions and establishing the phase transition with its phase diagram.

Contribution

It demonstrates the existence of minimizers and a phase transition in the Bogoliubov free energy model for Bose gases with regular two-body potentials.

Findings

Existence of minimizers for the functional with regular potentials

Proof of a phase transition in the model

Derivation of the 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.