Ground state energy of a dilute inhomogeneous Fermi gas
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915573966831616 |
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| author | Gamet, Thomas |
| author_facet | Gamet, Thomas |
| contents | We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the range of the interaction potential is much smaller than the typical inter-particle distance. We show that the energy per particle converges to the Thomas-Fermi energy of the system, with a perturbative term corresponding tot he interaction and exhibiting the scattering length of the potential. The proof is decomposed into two bounds. First, we construct an appropriate test-state to prove the upper bound. Then, we prove the lower bound by the Dyson lemma, which allows us to regularize the interaction potential, and several semi-classical tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ground state energy of a dilute inhomogeneous Fermi gas Gamet, Thomas Mathematical Physics Quantum Gases We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the range of the interaction potential is much smaller than the typical inter-particle distance. We show that the energy per particle converges to the Thomas-Fermi energy of the system, with a perturbative term corresponding tot he interaction and exhibiting the scattering length of the potential. The proof is decomposed into two bounds. First, we construct an appropriate test-state to prove the upper bound. Then, we prove the lower bound by the Dyson lemma, which allows us to regularize the interaction potential, and several semi-classical tools. |
| title | Ground state energy of a dilute inhomogeneous Fermi gas |
| topic | Mathematical Physics Quantum Gases |
| url | https://arxiv.org/abs/2510.21268 |