Interface motion in random media at finite temperature

We have studied numerically the dynamics of a one-dimensional driven elastic interface in a random medium, focusing on the thermal rounding of the depinning transition and on the behavior in the T=0 pinned phase. Thermal effects are quantitatively more important than expected from simple dimensional estimates. For a sufficiently low temperature, the creep velocity at a driving force equal to the T=0 depinning force exhibits a power-law dependence on T, in agreement with earlier theoretical and numerical predictions for charge-density waves. We have also examined the dynamics in the T=0 pinned phase resulting from slowly increasing the driving force towards threshold. The distribution of avalanche sizes S_∥ decays as S_∥^-1-κ, with {κ}=0.05±{}0.05, in agreement with recent theoretical conjectures.