An optimal lower bound for the low density Fermi gas in three dimensions

We consider the dilute Fermi gas in three dimensions interacting through a positive, radially symmetric, compactly supported and integrable potential in the thermodynamic limit. We establish a second order lower bound for the ground state energy density with an error term which is optimal in the sense that it matches the order of the next correction term conjectured by Huang-Yang in 1957.

💡 Research Summary

The paper establishes a rigorous second‑order lower bound for the ground‑state energy density of a three‑dimensional dilute Fermi gas with two spin components, interacting via a positive, radially symmetric, compactly supported and integrable potential. Working in the thermodynamic limit (volume → ∞, particle numbers N↑, N↓ such that densities ρ↑ = N↑/L³, ρ↓ = N↓/L³ remain fixed and tend to zero), the authors prove that the energy per unit volume satisfies

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