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We study single-file diffusion on a one-dimensional lattice with a randomfractal distribution of hopping rates. For finite lattices, this problem showsthree clearly different regimes, namely, nearly independent particles, highlyinteracting particles, and saturation. The mean-square displacement of a taggedparticle as a function of time follows a power law in each regime. The firstcrossover time $t_s$, between the first and the second regime, depends on theparticle density. The other crossover time $t_l$, between the second and thethird regime, depends on the lattice length. We find analytic expressions forthese dependencies and show how the general behavior can be characterized by anuniversal form. We also show that the mean-square displacement of the center ofmass presents two regimes; anomalous diffusion for times shorter than $t_l$,and normal diffusion for times longer than $t_l$. We study single-filediffusion on a one-dimensional lattice with a random fractal distribution ofhopping rates. For finite lattices, this problem shows three clearly differentregimes, namely, nearly independent particles, highly interacting particles,and saturation. The mean-square displacement of a tagged particle as a functionof time follows a power law in each regime. The first crossover time $t_s$,between the first and the second regime, depends on the particle density. Theother crossover time $t_l$, between the second and the third regime, depends onthe lattice length. We find analytic expressions for these dependencies andshow how the general behavior can be characterized by an universal form. Wealso show that the mean-square displacement of the center of mass presents tworegimes; anomalous diffusion for times shorter than $t_l$, and normal diffusionfor times longer than $t_l$.

Universal behavior for single-file diffusion on a disordered fractal