Anomalous diffusion in periodic potentials under self-similar colored noise

We present numerical studies of anomalous diffusion in periodic potentials by simulating a generalized Langevin equation. It is proved that the particle driven by a thermal colored noise with the spectral density vanishing at zero frequency allows superdiffusive motion. It is found that the system subjected to sub- or superohmic damping exhibits two motion modes in a corrugated plane: running oscillated state and mixed running and oscillating states, respectively. Induced, the anomalous power can be enhanced up twice for the latter case and thus a wide range of diffusive regimes is observed with changing titled force.