Aging in Structural Changes of Amorphous Solids: A Study of First Passage Time and Persistence Time Distribution

The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(\mathrm{\Delta }t)$, and the persistence time, $p(\tau )$. In contrast to previous reports, both $p_1$ and $p$ are found to evolve with time upon aging. The age dependence of the persistence time distribution is shown to be sensitive to the details of the algorithm used to extract it from particle trajectories. By updating the reference point in event detection algorithm and accounting for the event specific aging time, we uncover age dependence of $p(\tau )$, hidden to previous studies. Moreover, the apparent age-dependence of $p_1$ in continuous time random walk with an age independent $p(\tau )$ is shown to result from an implicit synchronization of all the random walkers at the starting time.