Path Integral Treatment of Fluctuations in the BCS-BEC Crossover in Superfluid Fermi Gases

TL;DR

This paper employs a path integral approach to analyze fluctuations in the order parameter of a superfluid Fermi gas across the BCS-BEC crossover, providing explicit temperature-dependent expressions within the s-wave scattering framework.

Contribution

It introduces a path integral formalism to study order parameter fluctuations in a 3D Fermi gas across the BCS-BEC crossover, including explicit temperature dependence.

Findings

Derived general expressions for the partition function and fluctuation averages.

Included the BCS-BEC crossover condition in the analysis.

Provided explicit formulas in terms of BCS-Gor'kov propagators.

Abstract

By using a Path Integral formalism, we study the fluctuating fields in the order parameter for a 3D uniform Fermi gas at T<Tc. The BCS-BEC crossover condition is included into the analysis in the framework of the usual s-wave scattering approximation. The general expressions for the temperature dependence of the partition function and the quadratic average in the fluctuations fields are explicitly established in terms of the BCS-Gor'kov correlation propagators.