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March 12, 2026Open Access

The Free Energy of Dilute Bose Gases at Low Temperatures Interacting Via Strong Potentials

Key Points

This research aims to establish a lower bound on the free energy of dilute Bose gases at low temperatures, specifically under strong interaction conditions.
Applied techniques from previous works by Fournais and Solovej, as well as Haberberger et al.
Focused on the thermodynamic limit of dilute Bose gases.
Addressed the case of hard-core potentials for strong interactions.
Successfully proved a lower bound on the free energy for low temperatures.
Findings align with the Lee–Huang–Yang conjecture regarding the excitation spectrum.
Provided a simpler and more concise proof for strong interaction scenarios.

Abstract

Abstract We consider a dilute Bose gas in the thermodynamic limit and prove a lower bound on the free energy for low temperatures which is in agreement with the conjecture of Lee–Huang–Yang on the excitation spectrum of the system. Combining techniques of Fournais and Solovej (Invent Math 232(2):863–994, 2023) and Haberberger et al. (The free energy of dilute Bose gases at low temperatures, 2023), we give a simpler and shorter proof resolving the case of strong interactions, including the hard-core potential.

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