Gigantic dynamical spreading and anomalous diffusion of jerky active particles

Jerky active particles are Brownian self-propelled particles which are dominated by "jerk," the change in acceleration. They represent a generalization of inertial active particles. In order to describe jerky active particles, a linear jerk equation of motion which involves a third-order derivative in time, Stokes friction, and a spring force is combined with activity modeled by an active Ornstein-Uhlenbeck process. This equation of motion is solved analytically and the associated mean-square displacement (MSD) is extracted as a function of time. For small damping and small spring constants, the MSD shows an enormous superballistic spreading with different scaling regimes characterized by anomalous high dynamical exponents 6, 5, 4, or 3 arising from a competition among jerk, inertia, and activity. When exposed to a harmonic potential, the gigantic spreading tendency induced by jerk gives rise to an enormous increase of the kinetic temperature and even to a sharp localization-delocalization transition, i.e., a jerky particle can escape from harmonic confinement. The transition can be either first or second order as a function of jerkiness. Finally it is shown that self-propelled jerky particles governed by the basic equation of motion can be realized experimentally both in feedback-controlled macroscopic particles and in active colloids governed by friction with memory.