Time-dependent propulsion of noninteracting inertial active stochastic particles*

In most of the works reported so far on active matter, inertia is neglected and its self-propulsion speed is assumed constant. In this work, we propose a model in which active particles have non-negligible inertia (mass and moment of inertia) and a time-dependent periodic propulsion speed. We study the most general propulsion using Fourier series and address some particular cases such as a square wave signal for the propulsion speed. The effect of inertia and time-dependent propulsion on the system’s mean-square displacement, is found theoretically following a Langevin formalism. Langevin dynamics simulations are also employed to corroborate our theoretical findings.