Relaxation dynamics of an elastic string in random media

Abstract

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 $\xi \sim (\ln t{)}^{1/\tilde{\chi }}$. This implies that the relaxation dynamics is driven by thermal activations over random energy barriers which scale as $E_B(\ell )\sim {\ell }^{\tilde{\chi }}$ with a length scale $\ell$. Numerical data strongly suggest that the energy barrier exponent $\tilde{\chi }$ is identical to the energy fluctuation exponent $\chi =1/3$. We also find that there exists a long transient regime, where the correlation length follows a power-law dynamics as $\xi \sim t^{1/z}$ 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.

References in corpus (5)

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• Superuniversality in phase-ordering disordered ferromagnets
• Dynamic fluctuations of elastic lines in random environments
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