Relaxation dynamics of an elastic string in random media

Jae Dong Noh, Hyunggyu Park

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13 Scopus citations


We investigate numerically the relaxation dynamics of an elastic string in two-dimensional random media by thermal fluctuations starting from a flat configuration. Measuring spatial fluctuations of its mean position, we find that the correlation length grows in time asymptotically as ξ∼ (lnt) 1/ χ∼. This implies that the relaxation dynamics is driven by thermal activations over random energy barriers which scale as EB (ℓ) ∼ ℓ χ∼ with a length scale ℓ. Numerical data strongly suggest that the energy barrier exponent χ∼ is identical to the energy fluctuation exponent χ=1/3. We also find that there exists a long transient regime, where the correlation length follows a power-law dynamics as ξ∼ t1/z with a nonuniversal dynamic exponent z. The origin of the transient scaling behavior is discussed in the context of the relaxation dynamics on finite ramified clusters of disorder.

Original languageEnglish
Article number040102
JournalPhysical Review E
Issue number4
StatePublished - 8 Oct 2009


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