Electrodynamic response of a harmonic atom in an external magnetic field

We consider theoretically the long-wavelength magneto-optical response of an electron system, harmonically confined in two (quantum wire) or three (quantum dot or disk) spatial dimensions by external parabolic potentials. In particular, we prove explicitly that the resonance frequencies of such systems are independent of electron number and exactly the same as the corresponding bare resonance frequencies. This is the generalization of Kohn's theorem to harmonically confined structures. We discuss a number of recent experimental results in light of this exact result.