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arXiv:2306.00250

Viscous damping in weltering motion of trapped hydrodynamic dipolar Fermi gases

Reuben R. W. Wang, John L. Bohn

Published May 31, 2023• 0 citations
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Abstract

We consider collective motion and damping of dipolar Fermi gases in the hydrodynamic regime. We investigate the trajectories of collective oscillations -- here dubbed ``weltering'' motions -- in cross-dimensional rethermalization experiments via Monte Carlo simulations, where we find stark differences from the dilute regime. These observations are interpreted within a semi-empirical theory of viscous hydrodynamics for gases confined to anisotropic harmonic potentials. The derived equations of motion provide a simple effective theory that show favorable agreement with full numerical solutions. To do so, the theory must carefully account for the size and shape of the effective volume within which the gas' behavior is hydrodynamic. Although formulated for dipolar molecules, our theoretical framework retains a flexibility to accommodate arbitrary elastic cross sections.

DOI
10.48550/arxiv.2306.00250

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We consider collective motion and damping of dipolar Fermi gases in the hydrodynamic regime. We investigate the trajectories of collective oscillations -- here dubbed ``weltering'' motions -- in cross-dimensional rethermalization experiments via Monte Carlo simulations, where we find stark differences from the dilute regime. These observations are interpreted within a semi-empirical theory of viscous hydrodynamics for gases confined to anisotropic harmonic potentials. The derived equations of motion provide a simple effective theory that show favorable agreement with full numerical solutions. To do so, the theory must carefully account for the size and shape of the effective volume within which the gas' behavior is hydrodynamic. Although formulated for dipolar molecules, our theoretical framework retains a flexibility to accommodate arbitrary elastic cross sections.
We consider collective motion and damping of dipolar Fermi gases in the hydrodynamic regime. We investigate the trajectories of collective oscillations---here dubbed ``weltering'' motions---in cross-dimensional rethermalization experiments via Monte Carlo simulations, where we find stark differences from the dilute regime. These observations are interpreted within a semiempirical theory of viscous hydrodynamics for gases confined to anisotropic harmonic potentials. The derived equations of motion provide a simple effective theory that show favorable agreement with full numerical solutions. To do so, the theory must carefully account for the size and shape of the effective volume within which the gas's behavior is hydrodynamic. Although formulated for close-to-threshold dipolar collisions, our theoretical framework can be repurposed for other elastic cross sections in future studies.
In a recent theoretical effort, a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar gases has been derived. Within this model, the dipolar scattering results in an anisotropic viscosity tensor. Effects of the anisotropy have been predicted to be observable in the weltering motion, i.e., the collective oscillations of a dipolar Fermi gas, as well as in its acoustic behavior. In this contribution, we approach dipolar fluids from a computational fluid dynamics (CFD) perspective. To this end, previously derived analytic expressions of the anisotropic viscosity tensor are implemented in the finite-element software COMSOL Multiphysics. This allows us to investigate a whole spectrum of fluid flow situations but now including the inherent anisotropy of dipolar scattering. We present first results of such CFD simulations with an emphasis on effects attributable to the special characteristics of the anisotropic viscosity tensor.
In a recent theoretical effort, a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar gases has been derived. Within this model, the dipolar scattering results in an anisotropic viscosity tensor. Effects of the anisotropy have been predicted to be observable in the weltering motion, i.e., the collective oscillations of a dipolar Fermi gas, as well as in its acoustic behavior. In this contribution, we approach dipolar fluids from a computational fluid dynamics (CFD) perspective. To this end, previously derived analytic expressions of the anisotropic viscosity tensor are implemented in COMSOL Multiphysics®. This allows us to investigate a whole spectrum of fluid flow situations but now including the inherent anisotropy of dipolar scattering.
By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.
By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.
In this thesis we present fully nonlinear dissipative hydrodynamics simulations using the lattice Boltzmann method which we have developed to study hydrodynamics in cold atomic gases. We motivate and derive the specifics of the lattice Boltzmann implementation for this system, and then use our simulations to study collective oscillations in two-dimensional Fermi gases. We show that all dominant frequencies and damping rates of the breathing and quadrupole oscillatory modes agree quantitatively with analytic solutions in the hydrodynamic limit for a gas with ideal equation of state in a harmonic trap. We suggest improvements to our numerical methods which we expect to improve the quantitative agreement of the quadrupole mode frequency with the expected value outside of the hydrodynamic limit. We also suggest techniques for extracting the non-dominant (non-hydrodynamic) damping rate of the quadrupole mode in the hydrodynamic regime with higher precision. Additionally, we propose that the observed non-hydrodynamic damping of the quadrupole mode would be interesting to study experimentally for applications to collective oscillations in the quark-gluon plasma.