Dynamical properties of the unitary Fermi gas: collective modes and shock waves

TL;DR

This paper investigates the static and dynamic properties of the unitary Fermi gas, including collective oscillations and shock wave phenomena, using a density functional approach and superfluid hydrodynamics.

Contribution

It introduces an accurate density functional for the unitary Fermi gas and derives collective mode frequencies and shock wave behavior from extended hydrodynamic equations.

Findings

Accurate static properties described by the Thomas-Fermi-von Weizsacker functional.

Derived collective oscillation frequencies in a harmonic trap.

Demonstrated the existence of supersonic and subsonic shock waves.

Abstract

We discuss the unitary Fermi gas made of dilute and ultracold atoms with an infinite s-wave inter-atomic scattering length. First we introduce an efficient Thomas-Fermi-von Weizsacker density functional which describes accurately various static properties of the unitary Fermi gas trapped by an external potential. Then, the sound velocity and the collective frequencies of oscillations in a harmonic trap are derived from extended superfluid hydrodynamic equations which are the Euler-Lagrange equations of a Thomas-Fermi-von Weizsacker action functional. Finally, we show that this amazing Fermi gas supports supersonic and subsonic shock waves.