Crossover dynamics and non-Gaussian fluctuations in inertial active chains

Inertial effects in active matter, although often neglected in overdamped descriptions, can play an important role in shaping the dynamics of interacting self-propelled particles. We study the dynamics of inertial active particles in a one-dimensional chain with harmonic nearest-neighbor interactions, highlighting the interplay of persistence, interaction, and inertial timescales. Using a Green's function approach, we derive the mean-squared displacement and mean-squared change in velocity, revealing multiple crossovers between ballistic, diffusive, and subdiffusive regimes and providing analytic expressions for scaling coefficients and crossover times. Non-Gaussian deviations in active Brownian particles are captured through excess kurtosis, reflecting heavy-tailed, finite-support, or bimodal distributions that evolve systematically over time. Time-dependent probability distributions exhibit distinct data collapses within different temporal regimes, confirming the robustness of the scaling behavior. Overall, this framework connects multiparticle interactions to microscopic dynamics, revealing experimentally accessible signatures of inertia in active matter.