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arXiv · 2409.17914

The Huang-Yang formula for the low-density Fermi gas: upper bound

Emanuela L. Giacomelli·Christian Hainzl·Phan Thành Nam·Robert Seiringer
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Abstract

We study the ground state energy of a gas of spin $1/2$ fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density $\rho$, with the Huang-Yang conjecture. The latter captures the first three terms in an asymptotic low-density expansion, and in particular the Huang-Yang correction term of order $\rho^{7/3}$. Our trial state is constructed using an adaptation of the bosonic Bogoliubov theory to the Fermi system, where the correlation structure of fermionic particles is incorporated by quasi-bosonic Bogoliubov transformations. In the latter, it is important to consider a modified zero-energy scattering equation that takes into account the presence of the Fermi sea, in the spirit of the Bethe-Goldstone equation.

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Emanuela L. Giacomelli, Christian Hainzl, Phan Thành Nam, Robert Seiringer. 2024-09-26. The Huang-Yang formula for the low-density Fermi gas: upper bound. https://doi.org/10.1002/cpa.70040

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