Spatiotemporal chaos in rf-driven Josephson junction series arrays

We study underdamped Josephson junction series arrays that are globally coupled through a resistive shunting load and driven by an rf bias current. They can be an experimental realization of many phenomena currently studied in globally coupled logistic maps. We study their spatiotemporal dynamics and we find coherent, ordered, partially ordered, turbulent, and quasiperiodic phases. The ordered phase corresponds to giant Shapiro steps in the IV characteristics. In the turbulent phase there is a saturation of the broad-band noise for a large number of junctions. This corresponds to a breakdown of the law of large numbers as seen in globally coupled maps. Coexisting with this phenomenon, we find an emergence of pseudosteps in the IV characteristics. This effect can be experimentally distinguished from the true Shapiro steps, which do not have broad-band noise emission. We study the stability of the breakdown of the law of large numbers against thermal fluctuations. We find that it is stable below a critical temperature Tc1. A measurement of the broad-band noise as a function of temperature T will show three different regimes: below Tc1 the broad-band noise decreases when increasing T, and there is turbulence and the breakdown of the law of large numbers. Between Tc1 and a second critical temperature Tc2 the broad-band noise is constant and the dynamics is dominated by the chaos of the individual junctions. Finally above Tc2 all the broad-band noise is due to thermal fluctuations, since it increases linearly with T