Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917716818919424 |
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| author | Lauritsen, Asbjørn Bækgaard |
| author_facet | Lauritsen, Asbjørn Bækgaard |
| contents | We prove an upper bound on the energy density of the dilute spin-$\frac{1}{2}$ Fermi gas capturing the leading correction to the kinetic energy $8πa ρ_\uparrowρ_\downarrow$ with an error of size smaller than $aρ^{2}(a^3ρ)^{1/3-\varepsilon}$ for any $\varepsilon > 0$, where $a$ denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237--260). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_08005 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion Lauritsen, Asbjørn Bækgaard Mathematical Physics We prove an upper bound on the energy density of the dilute spin-$\frac{1}{2}$ Fermi gas capturing the leading correction to the kinetic energy $8πa ρ_\uparrowρ_\downarrow$ with an error of size smaller than $aρ^{2}(a^3ρ)^{1/3-\varepsilon}$ for any $\varepsilon > 0$, where $a$ denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237--260). |
| title | Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2301.08005 |