ANALYTIC CALCULATION OF THE DIFFUSION-COEFFICIENT FOR RANDOM-WALKS ONSTRIPS OF FINITE WIDTH - DEPENDENCE ON SIZE AND NATURE OF BOUNDARIES

We study unbiased random walks in discrete time n on a square lattice, in the form of a strip of finite width N in the y direction, with a f amily of boundary conditions parametrized by a stay probability GAMMA per time step at the edge sites. The diffusion coefficient K = lim(n - -> infinity)[X(n)2]/n is computed analytically to exhibit its dependen ce on N and GAMMA. The result is generalized to the case of a strip wi th side branches attached to the boundary sites to simulate the effect of rough edges. A further generalization is made to obtain K for a ra ndom walk in d dimensions on a lattice bounded in one of the direction s. Thus, K serves as a probe of both the transverse size of the region in which diffusion takes place and the nature of the bounding surface s.