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We study diffusion on topologically linear fractal structures under the influence of a uniform external field. Due to the fractal nature of the chain, the uniform field acts on a random walker like random correlated (local) fields in a one-dimensional chain. We find that the mean square displacement of the walker is universal and depends logarithmically on time t as ⟨ r 2 ⟩ ∼ ln 2 t , independent of the fractal dimension of the chain.
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Roman et al. (1988) studied this question.
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