Eur. Phys. J. B 42, 407-414 (2004)
https://doi.org/10.1140/epjb/e2004-00397-0

Local waiting times in critical systems

Helsinki University of Technology, Laboratory of Physics, P.O. Box 1100, FIN-02015 HUT, Finland

Corresponding author: ^a mja@fyslab.hut.fi

Received: 24 December 2003
Revised: 13 September 2004
Published online: 23 December 2004

Abstract

The quiet times at a fixed point in space are investigated in a system close to or at a non-equilibrium phase transition. The statistics for such first-return times follow from the universality class of the dynamics and the ensemble: for a power-law waiting time distribution the exponent depends on the dimension and the underlying model. We study the two-dimensional Manna sandpile, with both the continously driven self-organized version and the tuned one. The latter has an absorbing state or depinning phase transition at a critical value of the control parameter. The connection to a driven interface in a random medium gives the exponent of the waiting time distribution. In the open ensemble, differences ensue due to the spatial inhomogeneity and the properties of the driving signal. For both ensembles, the waiting time distributions are found to exhibit logarithmic corrections to scaling.