1997/10/31 by Daniel Fisher, Pierre Le Doussal, Cecile Monthus · 1 citation
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1103/physrevlett.80.3539
published as Phys. Rev. Lett. {\bf 80} 3539 (1998). · 5 pages, 1 figures, RevTex
arxiv created 1997/12/12 · arxiv updated 2009/11/30
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 "aging" with (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.