Stability analysis of Shapiro steps in Josephson-junction arrays

Abstract

The coupled set of evolution equations of the individual resistively shunted junctions in an array is written in a form that directly reveals the existence of a single-junction solution (SJS) for specific values of the external magnetic 6eld. We formulate a condition that determines these field strengths in terms of the corresponding ground-state configurations.By studying the linearized evolution equations, around this coherent-phase solution, we show that the array is phase locked to the external source when the S3S is stable. Only in this case does it have relevance in practice. Our analysis clearly indicates that there are only regular Shapiro steps in the regions of stability, and in between these regions our simulations confirm the absence of fractional steps, reported earlier. Furthermore, simulations, also in fields with no SjS, demonstrate a degree of insensitivity to the field strength, which is only partly understood.

On the locked dynamical states of an overdamped Josephson junction array

“…As a first step we have considered the effect of the temperature. Temperature fluctuations may cause the erasing of some dynamical attractors [14], and one may wonder whether or not this is the case for the states that we have observed at T = 0. The effect of the temperature on equation ( 1) can be taken into account by adding a white-noise current term, n ij , such that [15] n ij (t) = 0 (4)…”

Non-Equilibrium Coherent Vortex States and Subharmonic Giant Shapiro Steps in Josephson Junction Arrays

“…These steps can not be explained within the context of the non-inductive RSJ model, which proved successful in providing an understanding of the f = p/q Shapiro steps. 7,8,9,11,12 In this review we will show that these extra subharmonic steps can be produced by breaking the translational invariance in the arrays.…”

“…This interpretation was successfully verified in numerical simulation modelling of the arrays by a resistively shunted junction (RSJ) model 7,8 , as well as from analytic studies 9 . There have also been some experimental 10 and theoretical studies 11,12,13 of the relevance of the geometry of the arrays and the direction of the input current on the generation of fractional GSS. Moreover, the experiments in GSS have encouraged investigations of JJA as coherent radiation sources 14 .…”

Clustering Bifurcation and Spatiotemporal Intermittency in RF-Driven Josephson Junction Series Arrays

“…They arise naturally in studies of Josephson junctions arrays, multimode laser, charge-density wave, oscillatory neuronal system, and so on. Some rather surprising and novel features, such as clustering, splay state, collective behavior, and violation of the law of large numbers are revealed in these continuous and discrete globally coupled models Bhattacharya et al, 1987;Chernikov & Schmidt, 1995;Domínguez et al, 1991;Domínguez & Cerdeira, 1995;Eikmans & van Himbergen, 1991;Fisher, 1983;Free et al, 1990;Hadley & Beasley, 1987;Hadley et al, 1988;Kaneko, 1989;Kvale & Hebboul, 1991;Lee et al, 1992;Middleton et al, 1992;Strogatz & Mirollo, 1993;Tchiastiakov, 1996;Tsang et al, 1991;Tsang & Schwartz, 1992;Watanabe & Strogatz, 1993;Wiesenfeld et al, 1996].…”

“…Equation (1) exhibits rich spatiotemporal behavior, including phase locking, bifurcations, chaos, solitonic excitation, and pattern formation, breaking the law of large numbers and novel pseudo-Shapiro steps emerge in turbulence Domínguez et al, 1991;Domínguez & Cerdeira, 1995;Eikmans & van Himbergen, 1991;Free et al, 1990;Kvale & Hebboul, 1991;Lee et al, 1992]. However, to the best of our knowledge, the mechanism of the transitions among these dynamical phases, specially the transition from coherence to turbulence, has never been discussed.…”