Fast Algorithms For Josephson Junction Arrays : Bus--bars and Defects

No abstract. It's a review article beginning with introduction.

In this work, we use supratransmission and infratransmission in the mathematical modeling of the propagation of digital signals in weakly damped, discrete Josephson-junction arrays, using energy-based detection criteria. Our results show an efficient and reliable transmission of binary information.

Mathematical models related to some Josephson junctions are pointed out and attention is drawn to the solutions of certain initial boundary problems and to some of their estimates. In addition, results of rigorous analysis of the behaviour of these solutions when the time tends to infinity and when the small parameter tends to zero are cited. These analyses lead us to mention some of the open problems.

Discrete arrays of Josephson junction elements differ from their continuum counterparts in two essential ways: i) localized dynamic states in discrete arrays, which are not present in the corresponding continuum system, can interact with other excitations that are present; ii) fluxoid quantization for the non-superconducting `holes' provides a constraint for discrete arrays that is not present in the corresponding continuum system. The consequences of these effects in one-dim...

The effects of finite size and of finite current on the current-voltage characteristics of Josephson junction arrays is studied both theoretically and by numerical simulations. The cross-over from non-linear to linear behavior at low temperature is shown to be a finite size effect and the non-linear behavior at higher temperature, $T>T_{KT}$, is shown to be a finite current effect. These are argued to result from competition between the three length scales characterizing the ...

We study how the addition of defects in an otherwise uniform Josehpson junction array modifies the critical current of the array, by numerically solving the system of coupled Josephson equations. Our results confirm the existence of two different regimes, depending on the normalized maximum Josephson current of each junction, $i_{\rm max}$: for large $i_{\rm max}$, the defects deteriorate partially the critical state of the uniform array and so decrease the critical current, ...

In this note I survey the extensive literature on the dynamics of large series arrays of identical current biased Josephson junctions coupled through various shared loads. The equations describing the dynamics are invariant under permutation of the junctions so that in addition to the usual dynamical systems and numerical methods, group theoretic methods can be applied. In practice it is desirable to operate these circuits at a stable in-phase oscillation. The works summarize...

In this work we study the magnetic remanence exhibited by Josephson junction arrays in response to an excitation with an AC magnetic field. The effect, predicted by numerical simulations to occur in a range of temperatures, is clearly seen in our tridimensional disordered arrays. We also discuss the influence of the critical current distribution on the temperature interval within which the array develops a magnetic remanence. This effect can be used to determine the critical ...

We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase relationships (I$\Phi$). We present results for a three-junction system in the vicinity of charge degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I$\Phi$ at phase $\pi$ persist and that, at maximum ...

Various properties of mesoscopic two-dimensional Josephson junction arrays are reviewed. Particular attention is paid to structure of the topological excitations, charges and vortices, which are shown to be dual to each other. This duality persists in the presence of external magnetic fields and offset charges, which influence vortices and charges in an equivalent way. A double-layer junction array is also considered, where an even further reaching duality is discovered.