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 {ital 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 {ital 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 {ital T}{sub {ital c}1}. A measurement of the broad-band noise as a function of temperature {ital T} will show three different regimes: below {ital T}{sub {ital c}1} the broad-band noise decreases when increasing {ital T}, and there ismore » turbulence and the breakdown of the law of large numbers. Between {ital T}{sub {ital c}1} and a second critical temperature {ital T}{sub {ital c}2} the broad-band noise is constant and the dynamics is dominated by the chaos of the individual junctions. Finally above {ital T}{sub {ital c}2} all the broad-band noise is due to thermal fluctuations, since it increases linearly with {ital T}.« less