Self-organized criticality in the Kardar-Parisi-Zhang equation

Kardar-Parisi-Zhang interface depinning with quenched noise is studied in an ensemble that leads to self-organized criticality in the quenched Edwards-Wilkinson (QEW) universality class and related sandpile models. An interface is pinned at the boundaries, and a slowly increasing external drive is added to compensate for the pinning. The ensuing interface behavior describes the integrated toppling activity history of a QKPZ cellular automaton. The avalanche picture consists of several phases depending on the relative importance of the terms in the interface equation. The SOC state is more complicated than in the QEW case and it is not related to the properties of the bulk depinning transition.