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

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.

arXiv commentContribution to the proceedings of the intensive period "INdAM Quantum Meetings (IQM22)" (https://sites.google.com/view/iqm22), pdfLaTex, 21 pages