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arXiv · 2208.04584

Derivation of the Gross-Pitaevskii Theory for Interacting Fermions in a Trap

Andrea Calignano·Michele Correggi
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Abstract

We study a dilute gas of interacting fermions at temperature $T=0$ and chemical potential $\mu \in \mathbb{R}$. The particles are trapped by an external potential, and they interact via a microscopic attractive two-body potential with a two-body bound state. We prove the emergence of the macroscopic Gross-Pitaevskii theory as first-order contribution to the BCS energy functional in the regime of vanishing micro-to-macro scale parameter.

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Andrea Calignano, Michele Correggi. 2022-08-09. Derivation of the Gross-Pitaevskii Theory for Interacting Fermions in a Trap. https://arxiv.org/abs/2208.04584

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