Single-file diffusion on self-similar substrates

.We study the single file diffusion problem on a one-dimensional lattice with a self-similar distribution of hopping rates. We find that the time dependence of the mean-square displacement of both a tagged particle and the center of mass of the system present anomalous power laws modulated by logarithmic periodic oscillations. The anomalous exponent of a tagged particle is one half of the exponent of the center of mass, and always smaller than 1/4. Using heuristic arguments, the exponents and the periods of oscillation are analytically obtained and confirmed by Monte Carlo simulations.