Phys. Rev. E 55, 71–78 (1997)Random walk on a linear chain with a quenched distribution of jump lengths
We study the random walk of a particle on a linear chain, where a jump length 1 or 2 is assigned randomly to each lattice site with probability p1 and p2=1-p1, respectively. We find that the probability p1eff for the particle to be at a site with jump length 1 is different from p1, which causes the diffusion coefficient D to differ from the mean-field result. A theory is developed that allows us to calculate p1eff and D for all values of p1. In the limit p1→0, the theory yields a nonanalytic dependence of p1eff on p1,p1eff∼-p12ln p1. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.55.71
DOI:
10.1103/PhysRevE.55.71
PACS:
05.40.+j, 66.10.Cb, 66.30.Jt, 66.30.Lw
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