Collective Excitations of Harmonically Trapped Ideal Gases

TL;DR

This paper provides an exact theoretical analysis of collective excitations in harmonically trapped ideal gases, extending solutions to multi-phase systems with interfaces, and clarifying the relation to the scaling ansatz method.

Contribution

It offers an exact solution to the Boltzmann-Vlasov equation for trapped ideal gases and generalizes to systems with phase interfaces, surpassing previous approximate methods.

Findings

Mode frequencies are integer multiples of trap frequency.

Scaling ansatz solutions are special cases of the exact solution.

Method applies to multi-phase systems with interfaces.

Abstract

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our findings, however, are most useful in case the trap contains more than one phase: we demonstrate how to obtain the oscillation frequencies in case an interface is present between the ideal gas and a different phase.