Ground state energy of dense gases of strongly interacting fermions

• URL: http://arxiv.org/abs/2402.08490v1
• Date: Tue, 13 Feb 2024 14:34:58 GMT
• Title: Ground state energy of dense gases of strongly interacting fermions
• Authors: S{\o}ren Fournais, B{\l}a\.zej Ruba, Jan Philip Solovej
• Abstract summary: We study the ground state energy of a gas of $N$ fermions confined to a unit box in $d$ dimensions. Our focus is on the strongly interacting case $alpha1-frac2d$. Our proof is an adaptation of the bosonization technique used to treat the mean-field case.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the ground state energy of a gas of $N$ fermions confined to a unit box in $d$ dimensions. The particles interact through a 2-body potential with strength scaled in an $N$-dependent way as $N^{-\alpha}v$, where $\alpha\in \mathbb R$ and $v$ is a function of positive type satisfying a mild regularity assumption. Our focus is on the strongly interacting case $\alpha<1-\frac2d$. We contrast our result with existing results in the weakly interacting case $\alpha>1-\frac2d$, and the transition happening at the mean-field scaling $\alpha=1-\frac2d$. Our proof is an adaptation of the bosonization technique used to treat the mean-field case.

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