Intermittent Kac's flights with resetting.

Abstract

A generalized telegrapher equation associated with intermittent changes in the sign velocity of Kac's flights has been studied in the presence of the resetting mechanism. To solve this problem, we used the fluctuation-dissipation theorem to write a memorylike master equation approach to obtain the solution for the evolution of a normalized positive distribution. This distribution is associated with an intermittent hyperbolic diffusionlike process. We studied the time-dependent propagator and its stationary distribution. The variance for the evolution of the profile has been studied as a function of the resetting time. An approach is presented to tackle the problem of the mean first passage time for the intermittent telegrapher equation with resetting. The limiting cases of ordinary diffusion and ordinary telegrapher equations with resetting are also studied.