Journal Articles Physical Review Letters Year : 1998

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.

Dates and versions

hal-00003998 , version 1 (25-01-2005)

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Daniel Fisher, Pierre Le Doussal, Cécile Monthus. Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments. Physical Review Letters, 1998, 80, pp.3539-3542. ⟨hal-00003998⟩
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