Influence of the shape of quantum dots on their far-infrared absorption

We investigate the effects of the shape of quantum dots on their far-infrared absorption in an external magnetic field by a model calculation. We focus our attention on dots with a parabolic confinement potential deviating from the common circular symmetry, and dots having a circular doughnut shape. For a confinement where the generalized Kohn theorem does not hold, we are able to interpret the results in terms of a mixture of a center-of-mass mode and collective modes reflecting an excitation of relative motion of the electrons. The calculations are performed within the time-dependent Hartree approximation, and the results are compared to available experimental results.