The second order Huang-Yang formula to the 3D Fermi gas: the Gross-Pitaevskii regime

2024/10/22 by Xuwen Chen, Jiahao Wu, Chen, Xuwen +3 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.2410.16620

openalex publication_date 2024/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a system of N Fermions of spin 1/2, with its interaction potential of scattering length a, the classical Huang-Yang formula states that the energy density e(ρ) is of the form e(ρ)=(3)/(5)(3π²)^(2)/(3)ρ^(5)/(3)+2πaρ² +(12)/(35)(11-2ln2)3^(1)/(3)π^(2)/(3)a²ρ^(7)/(3) +o(ρ^(7)/(3)). We consider a general system of N Fermions of spin 1/q with the scattering length of the interaction potential at the scale a∝ N^-1, that is, in the Gross-Pitaevskii regime. We prove the 2nd order ground state energy approximation corresponding to the Huang-Yang formula. The thermodynamic limit case shares a similar logic, and could be dealt with in a separate paper.

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