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arXiv · 2212.11832

An optimal upper bound for the dilute Fermi gas in three dimensions

Emanuela L. Giacomelli
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Abstract

In a system of interacting fermions, the correlation energy is defined as the difference between the energy of the ground state and the one of the free Fermi gas. We consider $N$ interacting spin $1/2$ fermions in the dilute regime, i.e., $\rho\ll 1$ where $\rho$ is the total density of the system. We rigorously derive a first order upper bound for the correlation energy with an optimal error term of the order $\mathcal{O}(\rho^{7/3})$ in the thermodynamic limit. Moreover, we improve the lower bound estimate with respect to previous results getting an error $\mathcal{O}(\rho^{2+1/5})$.

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Emanuela L. Giacomelli. 2022-12-22. An optimal upper bound for the dilute Fermi gas in three dimensions. https://arxiv.org/abs/2212.11832

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