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We study relaxation dynamics of a three dimensional elastic manifold inrandom potential from a uniform initial condition by numerically solving theLangevin equation.We observe growth of roughness of the system up to largerwavelengths with time.We analyze structure factor in detail and find a compactscaling ansatz describing two distinct time regimes and crossover between them.We find short time regime corresponding to length scale smaller than the Larkinlength $L_c$ is well described by the Larkin model which predicts a power lawgrowth of domain size $L(t)$. Longer time behavior exhibits the random manifoldregime with slower growth of $L(t)$.

physical review. b, condensed matter and materials physics

Spatio-temporal scaling for out-of-equilibrium relaxation dynamics of an  elastic manifold in random media: crossover between the Larkin regime and  thermally activated regime