Generalisation of the Sinai anomalous diffusion law

H. E. Stanley, S. Havlin

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Article number011
Pages (from-to)L615-L618
JournalJournal of Physics A: Mathematical and General
Issue number9
StatePublished - 1987


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