TY - JOUR

T1 - Generalisation of the Sinai anomalous diffusion law

AU - Stanley, H. E.

AU - Havlin, S.

PY - 1987

Y1 - 1987

N2 - Sinai has considered a novel one-dimensional walk with a random bias field E on each site. He has shown that when the field is taken with equal probability to be +E0 or -E0 the RMS displacement R identical to (( chi 2))1/2 increases with time t by the anomalously slow law R approximately (log t)2. Here the authors introduce long-range correlation between the random fields on each site by choosing a 'string' of k sites to a have the same value of E, where k is chosen from the power law distribution P(k)=k- beta. They find that the Sinai law is generalised to the form R approximately (log t)y, where y sticks at the Sinai value y=2 for beta >2. However, for 1< beta <2, y varies continuously with beta as t= beta /( beta -1). The authors interpret this result physically in terms of the novel crossover between the physics underlying the Sinai effect and the physics of biased diffusion.

AB - Sinai has considered a novel one-dimensional walk with a random bias field E on each site. He has shown that when the field is taken with equal probability to be +E0 or -E0 the RMS displacement R identical to (( chi 2))1/2 increases with time t by the anomalously slow law R approximately (log t)2. Here the authors introduce long-range correlation between the random fields on each site by choosing a 'string' of k sites to a have the same value of E, where k is chosen from the power law distribution P(k)=k- beta. They find that the Sinai law is generalised to the form R approximately (log t)y, where y sticks at the Sinai value y=2 for beta >2. However, for 1< beta <2, y varies continuously with beta as t= beta /( beta -1). The authors interpret this result physically in terms of the novel crossover between the physics underlying the Sinai effect and the physics of biased diffusion.

UR - http://www.scopus.com/inward/record.url?scp=36149037712&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/20/9/011

DO - 10.1088/0305-4470/20/9/011

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AN - SCOPUS:36149037712

SN - 0305-4470

VL - 20

SP - L615-L618

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 9

M1 - 011

ER -