Abstract
Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or −E. The probability density¯P(x, t) is found to scale asymptotically as
withA(E)=ln[(1+E)/(1-E)],β=4.25, and α=1.25. The mean square displacement scales as\(\langle x^2 \rangle \sim [A(E)]^{ - \beta } F[tA^\beta (E)]\), where F(u)∼ln4 u asymptotically.
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Bunde, A., Havlin, S., Roman, H.E. et al. On the field dependence of random walks in the presence of random fields. J Stat Phys 50, 1271–1276 (1988). https://doi.org/10.1007/BF01019166
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DOI: https://doi.org/10.1007/BF01019166