Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments
Abstract
Sinai\'s model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of it not returning to the origin are obtained, as well as the two-time distribution which exhibits äging\" with $\\frac{\\ln t}{\\ln t\'}$ scaling and a singularity at $\\ln t =\\ln t\'$. The effects of a small uniform force are also studied. Extension to motion of many domain walls yields non-equilibrium time dependent correlations for the 1D random field Ising model with Glauber dynamics and \"persistence\" exponents of 1D reaction-diffusion models with random forces.