Aging and its Distribution in Coarsening Processes

Details Aging and its Distribution in Coarsening Processes Aging and its Distribution in Coarsening Processes

1996-09-19

arxiv.org/abs/cond-mat/9609192v1

Phys. Rev. E 55, 6684 (1997).

Physics

Condensed Matter

7 pages, RevTeX, 4 ps files included, to be submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.55.6684

We investigate the age distribution function P(tau,t) in prototypical one-dimensional coarsening processes. Here P(tau,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 tau. We determine P(tau,t) analytically for two cases, 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(tau,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 briefly the age distribution in dimension d greater than or equal to 2.

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