Crossover dynamics and non-Gaussian fluctuations in inertial active chains

TL;DR

This paper analyzes the complex dynamics of inertial active particles in a chain, revealing multiple crossover regimes and non-Gaussian fluctuations, with analytic expressions for key dynamical quantities.

Contribution

It provides a novel Green's function framework to analytically describe inertial active chains, capturing crossovers and non-Gaussian behavior in active matter.

Findings

Multiple crossover regimes identified in MSD and MSCV.

Non-Gaussian deviations characterized by excess kurtosis.

Scaling laws and data collapses confirmed across regimes.

Abstract

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 (MSD) and mean-squared change in velocity (MSCV), 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.