Random Walk with a Hop-Over Site: A Novel Approach to Tagged Diffusion and Its Applications

摘要

We study, on a $d$ dimensional hypercubic lattice, a random walk which ishomogeneous except for one site. Instead of visiting this site, the walker hopsover it with arbitrary rates. The probability distribution of this walk and thestatistics associated with the hop-overs are found exactly. This analysisprovides a simple approach to the problem of tagged diffusion, i.e., themovements of a tracer particle due to the diffusion of a vacancy. Applicationsto vacancy mediated disordering are given through two examples.