  We study single-file diffusion on a one-dimensional lattice with a random
fractal distribution of hopping rates. For finite lattices, this problem shows
three clearly different regimes, namely, nearly independent particles, highly
interacting particles, and saturation. The mean-square displacement of a tagged
particle as a function of 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. The other crossover time $t_l$, between the second and the
third regime, depends on the lattice length. We find analytic expressions for
these dependencies and show how the general behavior can be characterized by an
universal form. We also show that the mean-square displacement of the center of
mass presents two regimes; anomalous diffusion for times shorter than $t_l$,
and normal diffusion for times longer than $t_l$. We study single-file
diffusion on a one-dimensional lattice with a random fractal distribution of
hopping rates. For finite lattices, this problem shows three clearly different
regimes, namely, nearly independent particles, highly interacting particles,
and saturation. The mean-square displacement of a tagged particle as a function
of 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. The
other crossover time $t_l$, between the second and the third regime, depends on
the lattice length. We find analytic expressions for these dependencies and
show how the general behavior can be characterized by an universal form. We
also show that the mean-square displacement of the center of mass presents two
regimes; anomalous diffusion for times shorter than $t_l$, and normal diffusion
for times longer than $t_l$.
