Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound

TL;DR

This paper models the low-temperature thermodynamics of the unitary Fermi gas, deriving key properties like superfluid fraction and sound velocities analytically, and compares results with existing theories and experiments.

Contribution

It introduces an analytical model based on zero-temperature spectra to study thermodynamics and superfluid properties of the unitary Fermi gas.

Findings

Analytical expressions for superfluid fraction, critical temperature, and sound velocities.

Good agreement with experimental data and other theoretical predictions.

Insights into the thermodynamic behavior of ultracold atomic and neutron matter.

Abstract

We investigate the low-temperature thermodynamics of the unitary Fermi gas by introducing a model based on the zero-temperature spectra of both bosonic collective modes and fermonic single-particle excitations. We calculate the Helmholtz free energy and from it we obtain the entropy, the internal energy and the chemical potential as a function of the temperature. By using these quantities and the Landau's expression for the superfluid density we determine analytically the superfluid fraction, the critical temperature, the first sound velocity and the second sound velocity. We compare our analytical results with other theoretical predictions and experimental data of ultracold atoms and dilute neutron matter.