The diffusion behavior of a simple map with periodic quenched disorder

To explore the effect of quenched disorder on chaotic diffusion, we investigate the diffusion properties of a simple map with periodic quenched disorder. As the period T approaches infinity, the map will exhibit sublinear diffusion behavior, the same as that revealed by Radons [Phys. Rev. Lett. 77 (1996) 4748], such that the corresponding diffusion coefficient D vanishes. For T=140, we find, the system varies with the configuration of disorder to exhibit a great diversity of diffusion behavior, including normal diffusion with diminished D (about less than two or three orders of magnitude), the crossover from large D diffusion to very small D diffusion, and the crossover from normal diffusion to completely suppressed diffusion. Based on the decomposition formalism [H.C. Tseng, H.J. Chen, Int. J. Mod. Phys. 13 (1999) 83], we find that the correlation behavior of the sequences of +1 or −1, which are determined by the kinds of disorder (represented by +1 or −1) visited by the trajectories of the map, is responsible for the different diffusion processes. We also show that the connection between the diffusion behavior and the disorder configuration is dominated by the variance and the power spectrum of the associated potential.