Hierarchical Diffusion, Aging and Multifractality

Abstract

We study toy aging processes in hierarchically decomposed phase spaces where the equilibrium probability distributions are multifractal. We found that the an auto-correlation function, survival-return probability, shows crossover behavior from a power law $t^{-x}$ in the quasi-equilibrium regime ($t\ll\tw$) to another power law $t^{-\lambda }$ ($\lambda \ge x$) in the off-equilibrium regime ($t\gg\tw$) obeying a simple $t/\tw$ scaling law. The exponents $x$ and $\lambda$ are related with the so called mass exponents which characterize the multifractality.

28 pages, LaTex, 6 PostScript figures. To appear in Journal of Physics A

References in corpus (3)

• Nonequilibrium Dynamics and Aging in the Three--Dimensional Ising Spin Glass Model
• Nonequilibrium Dynamics and Aging in the Three--Dimensional Ising Spin Glass Model
• Off-Equilibrium Dynamics of 1+1 dimensional Directed Polymer in Random Media

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