Inertial self-propelled particles

TL;DR

This paper investigates how inertia affects the behavior of active particles driven by active Ornstein-Uhlenbeck dynamics, analyzing their trajectories, correlations, and active pressure in different confinement scenarios.

Contribution

It provides a detailed analytical study of inertial effects on active particles, including correlation functions and pressure, in both free and confined conditions.

Findings

Inertia influences particle velocity and active force correlations.

Inertia affects the mean square displacement and time-correlation functions.

Active pressure is significantly impacted by inertial effects.

Abstract

We study a self-propelled particle moving in a solvent with the active Ornstein Uhlenbeck dynamics in the underdamped regime to evaluate the influence of the inertia. We focus on the properties of potential-free and harmonically confined underdamped active particles, studying how the single-particle trajectories modify for different values of the drag coefficient. In both cases, we solve the dynamics in terms of correlation matrices and steady-state probability distribution functions revealing the explicit correlations between velocity and active force. We also evaluate the influence of the inertia on the time-dependent properties of the system, discussing the mean square displacement and the time-correlations of particle positions and velocities. Particular attention is devoted to the study of the Virial active pressure unveiling the role of the inertia on this observable.