Periodic driving controls random motion of Brownian steppers

We study the motion of Brownian steppers, which are objects moving unidirectionally by discrete steps. A single step is composed of two processes. An activation process describing the random attachment of a fuel molecule is followed by a conformational change of the stepper, leading to the forward motion. Whereas activation is given by a Markovian rate process, the forward motion is defined by a gamma distribution. In this paper we propose a periodic modulation of the fuel concentration in order to control the random motion of the stepper. We show that the driving may reduce the fluctuations of the stepper. Corresponding minima of the diffusion coefficient and maxima of the Péclet number prove the regularity of the motion.