Diffusion equation for one-dimensional unbiased hopping

A computer simulation is presented of a one-dimensional particle migration by local hopping of Chandrasekhar type with no local bias but with hopping rates which vary with position in the system. Of the two possible diffusion equations to represent the process, one is clearly shown to be wrong while the other gives an accurate representation of the evolution of the system. The cases of both reflecting and absorbing boundaries are considered, and in the latter case a sum-rule previously derived for this type of random migration is verified. The concept of local particle traffic is introduced. Arguments are presented to show that the spatial traffic distribution gives a better insight into some aspects of particle activity than the probability distribution.