Dynamics of harmonically confined systems: some rigorous results

In this paper we consider the dynamics of harmonically-confined atomic gases. We present various general results which are independent of particle statistics, interatomic interactions and dimensionality. Of particular interest is the response of the system to external perturbations having either a static or dynamic nature. We prove an extended Harmonic Potential Theorem which is useful in determining the damping of the centre of mass motion for some initially prepared nonequilibrium state. We also study the response of the gas to a dynamic perturbation in which the external potential oscillates at an arbitrary frequency. We show in this case that either the energy absorption rate or the centre of mass dynamics can serve as a probe of the optical conductivity of the system.