Aging and its distribution in coarsening processes

We investigate the age distribution function P(t ,t) in prototypical coarsening processes. Here P(t ,t) is the probability density that in a time interval (0,t) a given site was last crossed by an interface in the coarsening process at time t . We determine P(t ,t) exactly in one dimension for the ~deterministic! two-velocity ballistic annihilation process and the ~stochastic! infinite-state Potts model with zero-temperature Glauber dynamics. Surprisingly, we find that in the scaling limit, P(t ,t) is identical for these two models. We also show that the average age, i.e., the average time since a site was last visited by an interface, grows linearly with the observation time t . This latter property is also found in the one-dimensional Ising model with zero-temperature Glauber dynamics. We also discuss the age distribution in dimension d>2 and find similar qualitative features to those in one dimension. @S1063-651X~97!09406-3#