Interface dynamics at the depinning transition

TL;DR

This paper investigates the local scaling behavior of driven interfaces near the depinning transition, revealing anomalous temporal scaling and differences between local and global roughness exponents in disordered media.

Contribution

It introduces the concept of anomalous temporal crossover in local width scaling and distinguishes local and global roughness exponents near depinning.

Findings

Local width exhibits anomalous temporal scaling near depinning.

Local roughness exponent differs from the global one, with values approximately 1 and 1.2 respectively.

Identifies a crossover time regime characterized by an exponent around 0.21.

Abstract

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 $t_s(l) \sim l^z$ as expected, but suffers an anomalous temporal crossover to a different time regime $t^{\beta_*}$, where $\beta_* \simeq 0.21 $. This is associated with the existence of a local roughness exponent $\alpha_{loc} \simeq 1$ that differs from the global one $\alpha \simeq 1.2$. The relevance of the typical size of pinned sites regions near the critical point is investigated and the definition of the critical depinning is dicussed.