First and second sound in cylindrically trapped gases

TL;DR

This paper studies how density and temperature waves propagate in a cylindrically trapped gas, revealing the existence of first and second sound modes and discovering new excitations with unique damping properties.

Contribution

It derives effective 1D hydrodynamic equations accounting for viscosity and thermal conductivity in a cylindrically trapped gas, predicting sound velocities and identifying novel excitations.

Findings

Both first and second sound can propagate in the trap.

New excitations spread over a finite frequency interval.

Analytical calculation of non-dissipative damping in classical gases.

Abstract

We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wave length limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wave-lengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a non-dissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.