Chaos, noise, and tails on the I-V curve steps of rf-driven Josephson junctions

Structured chaos in a devil's staircase of the Josephson junction

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Transient chaos induces anomalous transport properties of an underdamped Brownian particle

For an underdamped Brownian particle in a one-dimensional periodic potential we theoretically predict three unusual transport properties: (i) A static bias force (of either sign) generates an average particle motion in the opposite direction. (ii) A small bias leads to a particle transport in the direction of the bias, but upon increasing the bias the particle velocity reverses direction. (iii) For a given bias force, the particle motion follows the direction of the force for low temperatures, but upon increasing the temperature reverses its direction. The considered model is shown to be minimal for the occurrence of these phenomena. A detailed analysis of its deterministic properties and the influence of thermal noise is carried out with numerical simulations that are complemented by analytical approximations. Intuitive explanations of the basic mechanism behind the three effects are provided; their origin is attributed to a subtle interplay between the stability of coexisting attractors, noise induced metastability, and transient chaos. An experimental system for the realization of the predicted effects is given within the Stewart-McCumber model for Josephson junctions. Suitable parameter values for which these effects can be observed are quite realistic experimentally.