Landau Damping of Spin Waves in Trapped Boltzmann Gases

TL;DR

This paper presents a semiclassical numerical method to analyze Landau damping of spin waves in trapped ultracold gases, reproducing known results and providing new insights into damping mechanisms and rates for different modes.

Contribution

It introduces a semiclassical approach to study Landau damping in trapped gases, extending previous unbounded system results to inhomogeneous traps and calculating damping rates for specific modes.

Findings

Landau damping occurs due to resonant phase space trajectories.

Damping rates depend on interaction strength and mode type.

The method agrees with previous kinetic equation solutions.

Abstract

A semiclassical method is used to study Landau damping of transverse pseudo-spin waves in harmonically trapped ultracold gases in the collisionless Boltzmann limit. In this approach, the time evolution of a spin is calculated numerically as it travels in a classical orbit through a spatially dependent mean field. This method reproduces the Landau damping results for spin-waves in unbounded systems obtained with a dielectric formalism. In trapped systems, the simulations indicate that Landau damping occurs for a given spin-wave mode because of resonant phase space trajectories in which spins are "kicked out" of the mode (in spin space). A perturbative analysis of the resonant and nearly resonant trajectories gives the Landau damping rate, which is calculated for the dipole and quadrupole modes as a function of the interaction strength. The results are compared to a numerical solution of the kinetic equation by Nikuni et al.