Interface Dynamics at the Depinning Transition

We study the local scaling properties of driven interfaces in disordered media modeled by the Edwards-Wilkinson equation with quenched noise. We find that, due to the super-rough character of the interface close to the depinning transition, the local width exhibits an anomalous temporal scaling. It does not saturate at a characteristic time ts(l)∼lz as expected, but suffers an anomalous temporal crossover to a different time regime tβ*, where β*≃0.21. This is associated with the existence of a local roughness exponent αloc≃1 that differs from the global one α≃1.2. The relevance of the typical size of pinned sites regions near the critical point investigated and the definition of the critical depinning is discussed.