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Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments | | Daniel Fisher
; Pierre Le Doussal
; Cecile Monthus
; | | Date: |
24 Oct 1997 | | Journal: | Phys. Rev. Lett. {f 80} 3539 (1998). | | Subject: | cond-mat | | 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 "aging" 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. | | Source: | arXiv, cond-mat/9710270 | | Services: | Forum | Review | PDF | Favorites | |
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