Voltage turbulence and vortex dynamics in dc-driven two-dimensional arrays of Josephson junctions

Abstract

Chaos and the role of vortices in turbulence are investigated in the context of a two-dimensional Josephson-junction-array model. A dc current is injected perpendicular to one edge of the array. The current varies linearly from Imax at one corner of the edge to I_min at the other corner. The two control parameters are Imax and the transverse gradient of the current ΔI=I_max-I_min that is equivalent to an injected vorticity. The kinetics, determined by current conservation, is in terms of phase angles, but vortices and their dynamic behavior can be monitored. The main results are the following: (a) a ΔI-vs-I_max phase diagram for the steady-state, periodic, quasiperiodic, and various spatially varying chaotic or "turbulent" regimes; (b) an identification of the voltage-spectrum frequencies with appearance rates of the vortex "collective variables"; (c) a physical picture of turbulence as a spatial rearrangement and mixing of positive and negative vortices at the drive edge, with irregular vortex appearances producing voltage chaos. The idea of collective variables for turbulence may have applications elsewhere.