Derivation of the effective action of a dilute Fermi gas in the unitary limit of the BCS-BEC crossover

TL;DR

This paper derives the effective action for the gapless mode of a zero-temperature dilute Fermi gas at unitarity, revealing its proportionality to the BCS limit and including next-to-leading order corrections.

Contribution

It provides a derivation of the effective action at unitarity up to next-to-leading order, extending understanding of the BCS-BEC crossover in Fermi gases.

Findings

Effective action proportionality between unitarity and BCS limit.

Next-to-leading order corrections included.

Suppressed terms in the BCS limit.

Abstract

The effective action describing the gapless Nambu-Goldstone, or Anderson-Bogoliubov, mode of a zero-temperature dilute Fermi gas at unitarity is derived up to next-to-leading order in derivatives from the microscopic theory. Apart from a next-to-leading order term that is suppressed in the BCS limit, the effective action obtained in the strong-coupling unitary limit is proportional to that in the weak-coupling BCS limit.