Slow dynamics of an elastic string in a random potential

We study the slow dynamics of an elastic string in a two dimensional pinning landscape by means of Langevin dynamics simulations. We find that the Velocity-Force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. However, at strong disorder, the creep exponent $\mu$ and the roughness $\zeta$ of the string display a clear deviation from the values $\mu \approx 1/4$ and $\zeta \approx 2/3$ expected assuming a quasi-equilibrium-nucleation picture of the creep motion. We also analyzed the non-stationary relaxation of the string towards the steady state. We identify a slowly growing length $L(T,F,t)$ separating equilibrated and non-equilibrated length scales during the relaxation. For equilibrated lengths, $l < L$, we find a roughness $\zeta \approx 2/3$ at $F=0$ while for small $F > 0$ an ``excess'' of roughness $\zeta > 2/3$ is always observed.