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arXiv · 2510.21268

Ground state energy of a dilute inhomogeneous Fermi gas

Thomas Gamet
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Abstract

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.

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Thomas Gamet. 2025-10-24. Ground state energy of a dilute inhomogeneous Fermi gas. https://arxiv.org/abs/2510.21268

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