The second order Huang-Yang approximation to the Fermi thermodynamic pressure
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| Format: | Preprint |
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2025
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| _version_ | 1866912426605150208 |
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| author | Chen, Xuwen Wu, Jiahao Zhang, Zhifei |
| author_facet | Chen, Xuwen Wu, Jiahao Zhang, Zhifei |
| contents | We consider a dilute Fermi gas in the thermodynamic limit with interaction potential scattering length $\mathfrak{a}_0$ at temperature $T>0$. We prove the 2nd order Huang-Yang approximation for the Fermi pressure of the system, in which there is a 2nd order term carrying the positive temperature efffect.Our formula is valid up to the temperature $T<ρ^{\frac{2}{3}+\frac{1}{6}}$, which is, by scaling, also necessary for the Huang-Yang formula to hold. Here, $T_F\simρ^{\frac{2}{3}}$ is the Fermi temperature. We also establish during the course of the proof, a conjecture regarding the second order approximation of density $ρ$ by R. Seiringer \cite{FermithermoTpositive}. Our proof uses frequency localization techniques from the analysis of nonlinear PDEs and does not involve spatial localization or Bosonization. In particular, our method covers the classical Huang-Yang formula at zero temperature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_23136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The second order Huang-Yang approximation to the Fermi thermodynamic pressure Chen, Xuwen Wu, Jiahao Zhang, Zhifei Mathematical Physics Analysis of PDEs We consider a dilute Fermi gas in the thermodynamic limit with interaction potential scattering length $\mathfrak{a}_0$ at temperature $T>0$. We prove the 2nd order Huang-Yang approximation for the Fermi pressure of the system, in which there is a 2nd order term carrying the positive temperature efffect.Our formula is valid up to the temperature $T<ρ^{\frac{2}{3}+\frac{1}{6}}$, which is, by scaling, also necessary for the Huang-Yang formula to hold. Here, $T_F\simρ^{\frac{2}{3}}$ is the Fermi temperature. We also establish during the course of the proof, a conjecture regarding the second order approximation of density $ρ$ by R. Seiringer \cite{FermithermoTpositive}. Our proof uses frequency localization techniques from the analysis of nonlinear PDEs and does not involve spatial localization or Bosonization. In particular, our method covers the classical Huang-Yang formula at zero temperature. |
| title | The second order Huang-Yang approximation to the Fermi thermodynamic pressure |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2505.23136 |