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

¹ Helsinki University of Technology, Laboratory of Physics 02105 HUT, Helsinki, Finland
² Budapest University of Technology, Department of Theoretical Physics H-1111 Hungary

Corresponding author: mja@fyslab.hut.fi

Received: 16 October 2001
Accepted: 14 December 2001

Abstract

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.