Inertial Dynamics of Run-and-Tumble Particle

We study the dynamics of a single inertial run-and-tumble particle on a straight line. The motion of this particle is characterized by two intrinsic time-scales, namely, an inertial and an active time-scale. We show that interplay of these two time-scales leads to the emergence of four distinct regimes, characterized by different dynamical behaviour of mean-squared displacement and survival probability. We analytically compute the position distributions in these regimes when the two time-scales are well separated. We show that in the large-time limit, the distribution has a large deviation form and compute the corresponding large deviation function analytically. We also find the persistence exponents in the different regimes theoretically. All our results are supported with numerical simulations.