Interavalanche correlations in the self-organized critical state of a multijunction superconducting quantum interference device

Abstract

A discrete-time model of a two-dimensional lattice of Josephson junctions [multijunction superconducting quantum interference device (SQUID)] equivalent to the Abelian sandpile model with currents as heights was studied by computer simulation. We use various methods of injection of current into the lattice: similar to the real experimental conditions and used previously in sandpile simulations, deterministic and stochastic. For most of these methods the probability density of voltage (an equivalent of avalanche size distribution) demonstrates a universal power-law behavior commonly accepted as the only indicator of self-organized criticality. We found that the characteristics specific for each method of injection are interavalanche correlators. They show quasiperiodic behavior (similar to the bulk-SQUID effect observed in real experiments) for deterministic injection, and ordinary exponential decay for strongly stochastic injection.