L. Frachebourg et al., AGING AND ITS DISTRIBUTION IN COARSENING PROCESSES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(6), 1997, pp. 6684-6689
We investigate the age distribution function P(tau,t) in prototypical
coarsening processes. Here P(tau,t) is the probability density that in
a time interval (0,r) a given site was last crossed by an interface i
n the coarsening process at time tau. We determine P(tau,t) exactly in
one dimension for the (deterministic) two-velocity ballistic annihila
tion process and the !stochastic) infinite-state Potts model with zero
-temperature Glauber dynamics. Surprisingly, we find that in the scali
ng limit, P(tau,t) is identical for these two models, We also show tha
t the average age, i.e., the average time since a site was last visite
d by an interface, grows linearly with the observation time t. This la
tter property is also found in the one-dimensional Ising model with ze
ro-temperature Glauber dynamics. We also discuss the age distribution
in dimension d greater than or equal to 2 and find similar qualitative
features to those in one dimension.