Title: Scarce defects induce anomalous deterministic diffusion
Author: Mario Hidalgo-Soria
We introduce a model of deterministic particles in disordered media which exhibits a transition from normal to anomalous diffusion. The model consists of a set of non-interacting overdamped particles moving on a disordered potential. The disordered potential can be thought as a substrate having some “defects” scattered along a one-dimensional line. The distance between two contiguous defects is assumed to have a heavy-tailed distribution with its respective parameter. Depending of the value of this parameter, we identify three distinct scenarios: a normal diffusive phase, a superdiffusive phase and a subdiffusive. The transition from normal to anomalous diffusion happens when the defects become scarcer.
We also prove that the transport is normal independently of the diffusion regime (normal, subdiffusive, or superdiffusive).
We give analytical expressions for the effective diffusion coefficient for the normal diffusive phase and analytical expressions for the diffusion exponent in the case of anomalous diffusion. We test all these predictions by means of numerical simulations.