ISSN:
1572-9613
Keywords:
Random walks
;
random fields
;
density distribution
;
fluctuations
;
anomalous diffusion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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 $$\left\{ {[A(E)]^{\beta /2} /\ln ^2 t} \right\}\exp \left( { - \left\{ {x[A(E)]^{\beta /2} /\ln ^2 t} \right\}^\alpha } \right)$$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01019166
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