Steady state correlations and induced trapping of an inertial AOUP particle

TL;DR

This paper analyzes the dynamics of an inertial active Ornstein-Uhlenbeck particle in a harmonic trap, revealing how inertia and activity influence correlations, mean square displacement, and trapping behavior.

Contribution

It provides exact calculations of steady state correlations and MSD for inertial AOUPs, highlighting the effects of inertia and activity on trapping and dynamical regimes.

Findings

Initial ballistic motion transitions to diffusive or non-diffusive regimes.

Increased activity leads to stronger confinement and eventual trapping.

Velocity decorrelation depends on the interplay between inertial and activity time scales.

Abstract

We study the dynamics of an inertial active Ornstein-Uhnlenbeck particle self-propelling in a confined harmonic well. The transport behaviour of the particle is investigated by analyzing the particle trajectories, steady state correlations, and mean square displacement (MSD). The steady state correlation functions for the position as well as velocity are exactly calculated using different methods. We explore how the inertia affects the dynamical behaviour, when the particle is confined in a harmonic trap as well as when it is set free. From the exact calculation of MSD, it is observed that the initial time regimes are ballistic for both harmonically confined particle and free particle, whereas the long time regimes are diffusive for a free particle and non diffusive for a harmonically confined particle. One of our interesting observation is that the harmonically confined particle gets more and more confined with increase in the self propulsion time or activity time of the dynamics and finally it gets trapped for very large self propulsion time. For a free particle, the velocity correlation decays by the complex interplay between the inertial time scale and the self propulsion time scale of the dynamics. Moreover, decorrelation in velocity happens only when these two time scales are of equal order.