Higher-Harmonic Collective Modes in a Trapped Gas from Second-Order Hydrodynamics

TL;DR

This paper uses second-order hydrodynamics to analyze higher-harmonic collective modes in trapped gases, revealing their frequencies, damping, and sensitivity to shear viscosity, with results matching quantum calculations.

Contribution

It introduces a second-order hydrodynamics approach to calculate higher-order collective modes and non-hydrodynamic modes in trapped gases, extending previous models.

Findings

Higher-order modes are more sensitive to shear viscosity.

Excellent agreement with quantum mechanical calculations.

Higher-harmonic modes up to decapole are characterized.

Abstract

Utilizing a second-order hydrodynamics formalism, the dispersion relations for the frequencies and damping rates of collective oscillations as well as spatial structure of these modes up to the decapole oscillation in both two- and three- dimensional gas geometries are calculated. In addition to higher-order modes, the formalism also gives rise to purely damped "non-hydrodynamic" modes. We calculate the amplitude of the various modes for both symmetric and asymmetric trap quenches, finding excellent agreement with an exact quantum mechanical calculation. We find that higher-order hydrodynamic modes are more sensitive to the value of shear viscosity, which may be of interest for the precision extraction of transport coefficients in Fermi gas systems.