Mean first passage time for anomalous diffusion

When the random force acting on a particle diffusing in an interval [0,L] and subjected to a constant external force is a Gaussian white noise, the “Brownian” mean-squared displacement is described by the seminal relation 〈x²〉=2Dt^γ with γ=1. However, for more complicated random forces the diffusion may be slower (γ<1, “subdiffusion”) or faster (γ>1, “superdiffusion”) than the “normal” diffusion. For both these cases we calculated the mean free passage time (MFPT)—the time needed to reach one of the traps at boundaries. The simple formulas for the different diffusive regimes are compared quantitatively for the simplest case of the absence of an external field and for an initial position in the middle of the interval. It turns out that the MFPT’s for anomalous diffusion can be both larger or smaller than that for normal diffusion depending on the values of the length of the interval and the diffusion coefficient. Moreover, the MFPT can show nonmonotonic changes with the degree of departure from normal diffusion.