A mean-field model of intermittent particle transport and its quasi-steady-state approximation

We propose a mean-field model of intermittent particle transport, where a particle may be in one of two phases: the first is an active (ballistic) phase, when a particle runs with constant velocity in some direction, and the second is a passive (diffusive) phase, when the particle diffuses freely. The particle can instantly change the phase of motion. When the particle is in the active phase the rate of transition to the passive phase depends, in general, on time from the beginning of the run, so the distribution of the free path is not exponential. When the particle is in the passive phase the transition rate is constant, and diffusion is non-anomalous Brownian.