Aging and its Distribution in Coarsening Processes

TL;DR

This paper analytically studies the age distribution in one-dimensional coarsening processes, revealing universal behavior and linear growth of average age across different models, with brief discussion on higher dimensions.

Contribution

It provides the first analytical determination of the age distribution function in specific coarsening models and shows its universality in the scaling limit.

Findings

P(tau,t) is identical for ballistic annihilation and Potts models in the scaling limit.

Average age grows linearly with observation time t.

Similar age growth behavior observed in 1D Ising model with zero temperature Glauber dynamics.

Abstract

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.