Hierarchical diffusion, aging and multifractality

We study toy aging processes in hierarchically decomposed phase spaces where the equilibrium probability distributions are multifractal. We found that the auto-correlation function, survival-return probability, shows crossover behaviour from a power law t(-x) in the quasi-equilibrium regime (t << t(w)) to another power law t(-lambda) (lambda greater than or equal to x) in the off-equilibrium regime (t >> t(w)) obeying a simple t/t(w) scaling law. The exponents x and lambda are related with the so-called moss exponents which characterize the multifractality.