Steady state correlations and induced trapping of an inertial AOUP particle

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