Derivation of the Ginzburg-Landau Theory for Interacting Fermions in a Trap

Andrea Calignano, Michele Correggi

Published 2022-08-09Version 1

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 Ginzburg-Landau theory as first-order contribution to the BCS energy functional in the regime of vanishing micro-to-macro scale parameter.