Anomalous statistics of particle spreading in quenched random velocity field

Abstract

We study the motion of a random walker in two dimensional randomly oriented Manhattan lattice where each horizontal and vertical link in a regular square lattice is assigned a random direction. This model describes the anomalous diffusion properties of the tracer particles that are driven by a random unidirectional zero mean velocity field. By means of numerical analysis and with the use of qth order moment 〈xq(t)〉∼tqβ, we find the anomalous scaling exponent β=2∕3 that perfectly agrees with previous studies. We develop some precise results to understand the anomalous nature of random motion in random environments. This is done by the study of non-Gaussian properties of the probability density function, logarithmic scaling of the diffusion entropy and weak ergodicity analysis. It is also found that the mean exit times from a bounded domain is related to the fractal nature of the process.