DIFFUSION OF WALKERS WITH PERSISTENT VELOCITIES

We describe some properties for a phenomenological model of superdiffusion based on a generalization of the persistent random walk in one dimension to continuous time. The time spent moving to either increasing or decreasing x is characterized by a fractal-time pausing time density, psi(t) approximately T-alpha/t-alpha + 1, with 1 < alpha < 2. For this system it is shown that asymptotically p(0,t) approximately 1/t1/alpha. The form of the profile is shown to be Gaussian near the peak and to fall off like tx-(1 + alpha) near the tails, and the survival probability is asymptotically proportional to exp(- Bt/L-alpha). These results are confirmed by numerical calculations based on the method of exact enumeration.