High Precision Numerically Assisted Diagrammatic Calculation of Transport on Lattices.

In diffusion on a lattice with equal rates between sites, the solution can be modeled by a random walker by taking the number of ways the hopper can go to each site divided by the total different ways it can go in n hops and summing that over n from 0 to infinity, with each term weighted by the probability to make n hops. By introducing self-hops, where the walker returns to its initial site, this method can be applied to heterogeneous lattices having different rates between sites, as well as lattices with unusual boundary conditions. Due to the similar structure of the differential equations for diffusion and masses attached by springs in the Laplace domain, this method can also be applied to the latter situation.