How many particles do make a fluid? Qualifying collective behavior in expanding ultracold gases

TL;DR

This paper investigates how many particles are needed in ultracold gases for collective hydrodynamic behavior to emerge, using elliptic flow as an indicator in expanding quantum gases to connect microscopic particle number with macroscopic fluid dynamics.

Contribution

It introduces a method to determine the particle number threshold for hydrodynamic behavior in cold atom gases using elliptic flow measurements.

Findings

Identifies the particle number at which collective behavior emerges.

Shows how elliptic flow varies with particle number.

Connects cold atom experiments to quark-gluon plasma dynamics.

Abstract

Collective phenomena in quantum many-body systems are often described in terms of hydrodynamics, an appropriate framework when the involved particle numbers are effectively macroscopic. We propose to use experiments on expanding clouds of few and many interacting cold atoms to investigate the emergence of hydrodynamics as a function of particle number. We consider gases confined in two-dimensional elliptically-deformed traps, and we employ the manifestation of elliptic flow as an indicator of collective behavior. We quantify the response of the gas to the deformation of the trapping potential, and show how such information can be used to establish how many atoms are needed for the system to develop a degree of collectivity comparable to that expected in the hydrodynamic limit. This method permits one, in particular, to exploit observations made in expanding atomic gases to shed light on the apparent hydrodynamic behaviour of mesoscopic systems of quarks and gluons formed in the scattering of light ions in high-energy collider experiments.