Hopping dynamics of a tracer particle confined in a fluctuating lattice

We investigate the hopping dynamics of a tracer particle in a two-dimensional fluctuating lattice using Brownian dynamics simulations. Conventional analyses based on the mean square displacement and the self-intermediate scattering function reveal subdiffusive behavior characteristic of hopping transport, but these averaged quantities cannot resolve individual hopping events. To overcome this limitation, we apply hop functions originally developed for glassy and supercooled liquids, which enable the identification of discrete hopping events and provide microscopic insight into tracer dynamics. In this fluctuating lattice, direct tracking of tracer trajectories between interstitial sites offers a clear reference for validating hop-function definitions. We systematically evaluate different formulations by assessing their accuracy in identifying hopping events, reproducing residence-time distributions, and predicting free-energy barriers from hop-function probability distributions. Our results demonstrate that, among the tested formulations, the newly proposed h₂(t) yields the most accurate identification of hopping events and achieves excellent quantitative agreement with both direct trajectory tracking and umbrella-sampling free-energy barriers across a wide range of fluctuation regimes. These findings establish hop-function analysis as a robust and quantitatively reliable tool for characterizing tracer dynamics in confined, thermally fluctuating environments.