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Ground state energy of the dilute spin-polarized Fermi gas: Lower bound

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arxiv 2402.17558 v1 pith:QQO6SIZE submitted 2024-02-27 math-ph math.MP

Asbj{o}rn B{ae}kgaard Lauritsen , Robert Seiringer This is my paper · ORCID
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keywords boundenergycorrectiondilutefermigroundlowerspin-polarized
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abstract

We prove a lower bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. This correction depends on the $p$-wave scattering length of the interaction and matches the corresponding upper bound in [J. Funct. Anal. 286.7 (2024), p. 110320].

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Huang-Yang conjecture for the low-density Fermi gas

    math-ph 2025-05 conditional novelty 7.0 of 10

    For dilute spin-1/2 Fermi gases with repulsive short-range interactions, the ground state energy density equals the free Fermi term plus 8πa ρ↑ρ↓ plus the Huang-Yang a²ρ^{7/3} correction, with error o(ρ^{7/3}).

  2. A Lee-Huang-Yang type expansion for the thermodynamic energy density of a dilute mixture of Bose gases

    math-ph 2025-05 accept novelty 7.0 of 10

    For dilute 3D two-species Bose gases with soft repulsive interactions, the energy density equals the mean-field term plus the Lee-Huang-Yang correction, with error smaller than the correction.

  3. Semi-classical limit of an attractive Fermi gas in one or two dimensions

    math-ph 2026-02 conditional novelty 6.0 of 10

    For trapped attractive Fermi gases in 1D and 2D, as N grows the ground-state energy approaches the Thomas-Fermi energy, and ground states converge via Husimi functions.

  4. Mesoscopic Observables of the Dilute Fermi Gas at Low Energy

    math-ph 2026-02 conditional novelty 6.0 of 10

    For a trial state with Huang–Yang-precision energy, the averaged momentum distribution of the dilute Fermi gas is rigorously shown to match Belyakov's 1961 formula, with subleading error.

  5. Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation

    math-ph 2025-11 accept novelty 6.0 of 10

    A rigorous proof shows the momentum distribution of a Fermi-gas trial state is the Fermi step plus the RPA correction, with k_F^{-2+ε} errors for summable interactions.

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