Critical temperature and Ginzburg-Landau equation for a trapped Fermi gas

TL;DR

This paper derives a Ginzburg-Landau equation for a trapped Fermi gas to analyze its superfluid phase transition, providing insights into the critical temperature and order parameter behavior near the transition.

Contribution

It introduces a Ginzburg-Landau framework for trapped Fermi gases, analogous to Bose gases, to study superfluid phase transitions.

Findings

Derived the Ginzburg-Landau equation for the system

Estimated the critical temperature $T_c$ for superfluid transition

Analyzed the spatial and temperature dependence of the order parameter

Abstract

We discuss a superfluid phase transition in a trapped neutral-atom Fermi gas. We consider the case where the critical temperature greatly exceeds the spacing between the trap levels and derive the corresponding Ginzburg-Landau equation. The latter turns out to be analogous to the equation for the condensate wave function in a trapped Bose gas. The analysis of its solution provides us with the value of the critical temperature $T_{c}$ and with the spatial and temperature dependence of the order parameter in the vicinity of the phase transition point.