Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit

TL;DR

This paper derives an upper bound for the grand canonical free energy of a homogeneous Bose gas in the Gross-Pitaevskii limit, incorporating an effective theory for condensate fluctuations and a temperature-dependent Bogoliubov Hamiltonian for excited particles.

Contribution

It introduces a novel upper bound for the free energy that accounts for particle number fluctuations and thermal excitations in the Bose gas.

Findings

Upper bound expressed via an effective theory for condensate fluctuations.

Free energy of excited particles modeled by a temperature-dependent Bogoliubov Hamiltonian.

Provides insights into the thermodynamics near the critical temperature for Bose-Einstein condensation.

Abstract

We consider a homogeneous Bose gas in the Gross-Pitaevskii limit at temperatures that are comparable to the critical temperature for Bose-Einstein condensation in the ideal gas. Our main result is an upper bound for the grand canonical free energy in terms of two new contributions: (a) the free energy of the interacting condensate is given in terms of an effective theory describing its particle number fluctuations, (b) the free energy of the thermally excited particles equals that of a temperature-dependent Bogoliubov Hamiltonian.