Optical activity in the Drude helix model

An old classical one-particle helix model for optical activity, first proposed by Drude, is reconsidered here. The quantum Drude model is very instructive because the optical activity can be calculated analytically without further approximations apart from the Rosenfeld long wavelength approximation. While it was generally believed that this model, when treated correctly, is optically inactive, we show that it leads to optical activity when the motion of the particle is quantum mechanically treated. We also find that optical activity arises even in the classical regime at non-zero energy, while for zero energy the model is inactive, in accordance with previous results. The model is compared with other one-electron models and it is shown that its predicted optical activity is qualitatively different from those of other one-electron systems. The vanishing of optical activity in the classical zero-energy limit for the Drude model is due to the localization of the particle at the equilibrium position, whereas in the analogous model of a particle moving freely on a helix without a definite equilibrium position, optical activity does not vanish but the spectrum is rescaled. The model under study leads to interesting predictions about the optical properties of, e.g., helicene derivatives.