Random walks on a fluctuating lattice: A renormalization group approach applied in one dimension

We study the problem of a random walk on a lattice in which bonds connecting nearest-neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with the dimensionality of the lattice.