Collective modes in quantum-dot arrays in magnetic fields

We study collective excitations in a model array of parabolically confined quantum dots in an applied magnetic field. Treating the interactions between electrons on the same dot exactly and those between electrons on different dots in a simple approximation, we find that the Hamiltonian separates into a term involving center-of-mass coordinates of the electrons on each dot and a term that depends on the relative coordinates on each dot. We diagonalize the center-of-mass Hamiltonian exactly and discuss retardation effects and interactions between the array and far-infrared radiation.