A phenomenological approach to the equation of state of a unitary Fermi gas

TL;DR

This paper introduces a phenomenological model for the equation of state of a unitary Fermi gas using Fermi-Dirac integrals, fitting experimental data but not capturing the superfluid phase transition, which can be addressed by complex zeros in the partition function.

Contribution

It presents a new phenomenological parametrization of the equation of state for a unitary Fermi gas that fits experimental data and suggests a method to incorporate phase transition effects.

Findings

Model reproduces experimental data over accessible range

Cannot describe the superfluid phase transition without modification

Introducing complex conjugate zeros improves fit near phase transition

Abstract

We propose a phenomenological approach for the equation of state of a unitary Fermi gas. The universal equation of state is parametrised in terms of Fermi-Dirac integrals. This reproduces the experimental data over the accessible range of fugacity and normalised temperature, but cannot describe the superfluid phase transition found in the MIT experiment \cite{ku}. The most sensitive data for compressibility and specific heat at phase transition can, however, befitted by introducing into the grand partition function a pair of complex conjugate zeros lying in the complex fugacity plane slightly off the real axis.