TY - JOUR

T1 - Diffusion in the presence of random fields and transition rates

T2 - Effect of the hard-core interaction

AU - Koscielny-Bunde, Eva

AU - Bunde, Armin

AU - Havlin, Shlomo

AU - Stanley, H. Eugene

PY - 1988

Y1 - 1988

N2 - We study diffusion of hard-core particles in linear chains where disorder arises from two distinct sources, (i) random bias fields and (ii) random transition rates. In the case of random bias fields, the step probability to the left and right is randomly chosen to be (1+E)/2 and (1-E)/2 with equal probability. Using Monte Carlo simulations and scaling arguments we find that the mean-square displacement is given by x2(t)[A(c)(lnt)]4, and the probability density P(x,t) scales as P(x,t)-1/2G(x/x2(t)>1/2). Here c is the concentration of particles; for c0 x2(t) reduces to the Sinai result for noninteracting particles. We find that the scaling function G(u) has the form G(u)exp(-u), with =1.5, a value distinctly different from the value for noninteracting particles (=1.25) and from the value for zero-bias field (=2). In contrast, in the case of random transition rates with a power-law distribution, we find that the asymptotic behavior of x2(t) as well as P(x,t) is changed by the hard-core interaction.

AB - We study diffusion of hard-core particles in linear chains where disorder arises from two distinct sources, (i) random bias fields and (ii) random transition rates. In the case of random bias fields, the step probability to the left and right is randomly chosen to be (1+E)/2 and (1-E)/2 with equal probability. Using Monte Carlo simulations and scaling arguments we find that the mean-square displacement is given by x2(t)[A(c)(lnt)]4, and the probability density P(x,t) scales as P(x,t)-1/2G(x/x2(t)>1/2). Here c is the concentration of particles; for c0 x2(t) reduces to the Sinai result for noninteracting particles. We find that the scaling function G(u) has the form G(u)exp(-u), with =1.5, a value distinctly different from the value for noninteracting particles (=1.25) and from the value for zero-bias field (=2). In contrast, in the case of random transition rates with a power-law distribution, we find that the asymptotic behavior of x2(t) as well as P(x,t) is changed by the hard-core interaction.

UR - http://www.scopus.com/inward/record.url?scp=0001406245&partnerID=8YFLogxK

U2 - 10.1103/physreva.37.1821

DO - 10.1103/physreva.37.1821

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AN - SCOPUS:0001406245

SN - 1050-2947

VL - 37

SP - 1821

EP - 1823

JO - Physical Review A

JF - Physical Review A

IS - 5

ER -