Confinement effect on diffusion dynamics in active viscoelastic environments

Understanding the diffusion dynamics of active particles experiencing external potential in viscoelastic environments is key to understanding biological systems such as molecular motors which rarely move unbounded geometry. In this paper, we investigate the characteristics of motion governed by underdamped active generalized Langevin equation with harmonic potential. The effects of inertia, viscoelasticity, confinement, and active noise on the behavior of ensemble mean squared displacement (MSD) and time-averaged MSD (TAMSD), ergodicity, and velocity autocorrelation function (VAF) have been analyzed. We observe that confinement has significant effects on the long-term behavior of these observables. Finally, we numerically quantify the behavior of the first passage time statistics in a finite domain. Besides the slow viscoelastic environment, we find that the active force and confinement also reduce the mean first passage time (MFPT). In this context, these factors may play a constructive role in the search process in relevant systems such as living cells. Graphical abstract Schematic representation of the passive particles (red spheres) subject to external harmonic potential with force F in a viscoelastic environment including self-propelling particles (green spheres) by active noise $$\xi _{ac}$$ ξ ac