Active Ornstein-Uhlenbeck model for self-propelled particles with inertia

TL;DR

This paper extends the active Ornstein-Uhlenbeck model to include inertia, analyzing how inertial effects influence the dynamics of self-propelled particles under various conditions, revealing regimes where inertia dominates or enhances motion.

Contribution

It introduces an inertial extension of the active Ornstein-Uhlenbeck model and provides analytical solutions for particle dynamics in different potentials and coupling scenarios.

Findings

Inertia causes superdiffusive behavior in active particles.

Displacement is enhanced by inertia in harmonic confinement.

Large mass accumulation leads to inertia-dominated superdiffusive motion.

Abstract

Self-propelled particles, which convert energy into mechanical motion, exhibit inertia if they have a macroscopic size or move inside a gaseous medium, in contrast to micron-sized overdamped particles immersed in a viscous fluid. Here we study an extension of the active Ornstein-Uhlenbeck model, in which self-propulsion is described by colored noise, to access these inertial effects. We summarize and discuss analytical solutions of the particle's mean-squared displacement and velocity autocorrelation function for several settings ranging from a free particle to various external influences, like a linear or harmonic potential and coupling to another particle via a harmonic spring. Taking into account the particular role of the initial particle velocity in a nonstationary setup, we observe all dynamical exponents between zero and four. After the typical intertial time, determined by the particle's mass, the results inherently revert to the behavior of an overdamped particle with the exception of the harmonically confined systems, in which the overall displacement is enhanced by inertia. We further consider an underdamped model for an active particle with a time-dependent mass, which critically affects the displacement in the intermediate time-regime. Most strikingly, for a sufficiently large rate of mass accumulation, the particle's motion is completely governed by inertial effects as it remains superdiffusive for all times.