Collective oscillations of a classical gas confined in harmonic traps

TL;DR

This paper derives the frequency and damping of collective oscillations in a classical gas within harmonic traps, bridging hydrodynamic and collisionless regimes using Boltzmann equation analysis.

Contribution

It provides an explicit analytical approach to describe collective oscillations in classical gases, including transition regimes and trap geometries.

Findings

Good agreement with numerical simulations

Explicit formulas for oscillation frequencies and damping

Transition behavior between regimes accurately modeled

Abstract

Starting from the Boltzmann equation we calculate the frequency and the damping of the monopole and quadrupole oscillations of a classical gas confined in an harmonic potential. The collisional term is treated in the relaxation time approximation and a gaussian ansatz is used for its evaluation. Our approach provides an explicit description of the transition between the hydrodynamic and collisionless regimes in both spherical and deformed traps. The predictions are compared with the results of a numerical simulation.