The free energy of dilute Bose gases at low temperatures

TL;DR

This paper rigorously derives a lower bound for the free energy of dilute Bose gases at low temperatures, confirming a Lee--Huang--Yang type correction that accounts for quantum interactions.

Contribution

It provides a rigorous lower bound for the free energy of dilute Bose gases, including a second order correction analogous to the Lee--Huang--Yang correction.

Findings

Confirmed the Lee--Huang--Yang type correction at low temperatures

Established a rigorous lower bound for the free energy

Connected excitation spectrum modifications to free energy corrections

Abstract

We consider a low density Bose gas interacting through a repulsive potential in the thermodynamic limit. We justify, as a rigorous lower bound, a Lee--Huang--Yang type formula for the free energy at suitably low temperatures, where the modified excitation spectrum leads to a second order correction of the same order as the Lee--Huang--Yang correction to the ground state energy.