Universal Thermodynamics of Degenerate Quantum Gases in the Unitarity Limit

TL;DR

This paper investigates the thermodynamics of degenerate quantum gases at unitarity, proposing a universal framework supported by experiments and theory, which simplifies understanding of properties like density profiles and sound velocities.

Contribution

It introduces a universal thermodynamic description for quantum gases at unitarity based on a new hypothesis, supported by experiments and theoretical analysis.

Findings

Universal form of grand potential characterized by universal numbers

Simplified determination of density profiles in trapped fermion superfluids

Prediction of second sound velocity in homogeneous superfluids at unitarity

Abstract

We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported by recent experiments and can be proven in Boltzmann regime. It implies a universal form for the grand potential which is characterized by only a few universal numbers in degenerate limit. This universal form provides a simple way to determine the density profile of a trapped fermion superfluid as well as the second sound velocity of a homogeneous superfluid at unitarity.