Two-dimensional arrays of Josephson junctions in a magnetic field: A stability analysis of synchronized states

Trees, Brad; Stroud, D.

doi:10.1103/physrevb.59.7108

Cited by 9 publications

(5 citation statements)

References 34 publications

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“…Furthermore, such locking survives weak disorder in the critical currents. The effectiveness of a magnetic field in producing phase locking in square arrays has been discussed previously [21,22]. The present work provides additional evidence that a field f = 1/2 is effective in producing phase locking, even when the applied current has nonzero components parallel to both array axes [23].…”

Section: Discussionmentioning

confidence: 56%

Dynamical phase transition in a fully frustrated Josephson array on a square lattice

1999

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We study dynamical phase transitions at temperature T = 0 in a fully frustrated square Josephson junction array subject to a driving current density which has nonzero components ix, iy parallel to both axes of the lattice. Our numerical results show clear evidence for three dynamical phases: a pinned vortex lattice characterized by zero time-averaged voltages vx t and vy t, a "plastic" phase in which both vx t and vy t are nonzero, and a moving lattice phase in which only one of the timeaverage voltage components is nonzero. The last of these has a finite transverse critical current: if a current is applied in the x direction, a nonzero transverse current density iy is required before vy t becomes nonzero. The voltage traces in the moving lattice phase are periodic in time. By contrast, the voltages in the plastic phase have continuous power spectra which are weakly dependent on frequency. This phase diagram is found numerically to be qualitatively unchanged by the presence of weak disorder. We also describe two simple analytical models which recover some, but not all, the characteristics of the three dynamical phases, and of the phase diagram calculated numerically. 74.60.Ge,74.50.+r,74.60.Jg

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Section: Discussionmentioning

confidence: 56%

Dynamical phase transition in a fully frustrated Josephson array on a square lattice

1999

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“…It was shown in Ref. [37] that underdamped arrays in an external magnetic field perpendicular to the plane of the array could lift this degeneracy via the coupling of the junctions to the external magnetic field in the gauge-invariant phase difference. In the presence of critical current disorder, however, numerical simulations of the RSJ equations revealed that frequency synchronization was no longer possible.…”

Section: "Small-world" Connections In Two-dimensional Arraysmentioning

confidence: 99%

Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model

2005

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We study synchronization in disordered arrays of Josephson junctions. In the first half of the paper, we consider the relation between the coupled resistively and capacitively shunted junction ͑RCSJ͒ equations for such arrays and effective phase models of the Winfree type. We describe a multiple-time-scale analysis of the RCSJ equations for a ladder array of junctions with non-negligible capacitance in which we arrive at a second order phase model that captures well the synchronization physics of the RCSJ equations for that geometry. In the second half of the paper, motivated by recent work on small-world networks, we study the effect on synchronization of random, long-range connections between pairs of junctions. We consider the effects of such shortcuts on ladder arrays, finding that the shortcuts make it easier for the array of junctions in the nonzero voltage state to synchronize. In two-dimensional ͑2D͒ arrays we find that the additional shortcut junctions are only marginally effective at inducing synchronization of the active junctions. The differences in the effects of shortcut junctions in 1D and 2D can be partly understood in terms of an effective phase model.

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“…The relation between Cellular Neural Network (CNN) and the Josephson Transmission Line (JTL) array has been studied in many publications see for example [1], [5]. Two-dimensional array of Josephson Junctions is considered in [1].…”

Section: Cellular Neural Network Computing Of the Interaction Of Fluxonsmentioning

confidence: 99%

“…For this reason, fluxons have applications in information processing of electronic devices. In fact fluxons arise in the well known Josephson Junction (JJ) which is used in many applications in superconductor electronics [5].Recently, JJ have been considered as a source of THz radiation. Fluxons moving coherently in such junctions are a possible source of radiation.…”

Section: Introductionmentioning

confidence: 99%

CNN computing of the interaction of fluxons

Slavova

Tetzlaff

Markova³

2011

2011 XXXth URSI General Assembly and Scientific Symposium

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Two-dimensional arrays of Josephson junctions in a magnetic field: A stability analysis of synchronized states

Cited by 9 publications

References 34 publications

Dynamical phase transition in a fully frustrated Josephson array on a square lattice

Dynamical phase transition in a fully frustrated Josephson array on a square lattice

Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model

CNN computing of the interaction of fluxons

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