Josephson arrays

Josephson arrays Heart cell synchronization Neural networks Immune system Ecosystems... 

Reversibility and the in-phase periodic state of a Josephson array) Use a reversibility argument to prove that the in-phase periodic state of (8.7.1) is not attracting, even if the nonlinear terms are kept. 

Strogatz, S. H., and Mirollo, R. E. (1993) Splay states in globally coupled Josephson arrays analytical prediction of Floquet multipliers. Phys. Rev. E 47, 220. 

The most exciting property of these materials is that thin polycrystalline films can behave as two dimensional Josephson Tunnel Junction Arrays (110) displaying remarkably good electromagnetic coupling (111) both as emitters and receivers. Alternating current to direct current conversion has been observed in bulk samples (112), but the thin film geometry allows use of one film as a radiation emitter, and another film as the receiver (111). 

S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio. Josephson junction arrays with Bose-Einstein condensates. Science, 293(5531) 843-846(2001). 

POSSIBLE IMPLEMENTATION OF TOPOLOGICALLY PROTECTED QUBITS BY A NOVEL CLASS OF JOSEPHSON JUNCTION ARRAYS... 

Implementation of protected qubits by Josephson junction arrays... 

Figure 6. Left pane Location of the discrete degrees of freedom responsible for the dynamics of the Josephson junction array shown in Fig. 5. The spin degrees of freedom describing the state of the elementary rhombi are located on the bonds of the triangular lattice (shown in thick lines) while the constraints are defined on the sites of this lattice. The dashed line indicates the boundary condition imposed by a physical circuitry shown in Fig. 5 a. Contours 7 and 7 are used in the construction of topological order parameter and excitations. Right pane The lattice with K = 3 openings, the ground state of Josephson junction array on this lattice is 2fc = 8 fold degenerate.

Although quantum mechanics is required to explain the origin of the Josephson effect, we can nevertheless describe the dynamics of Josephson junctions in classical terms. Josephson junctions have been particularly useful for experimental studies of nonlinear dynamics, because the equation governing a single junction is the same as that for a pendulum In this section we will study the dynamics of a single junction in the overdamped limit. In later sections we will discuss underdamped junctions, as well as arrays of enormous numbers of junctions coupled together. 

Figure 1 shows an array of two identical overdamped Josephson junctions. 

N junctions, resistive load) Generalize Exercise 4.6.4 as follows. Instead of the two Josephson junctions in Figure 1, consider an array of N junctions in series. As before, assume the array is in parallel with a resistive load R, and that the junctions are identical, overdamped, and driven by a constant bias current 7. Show that the governing equations can be written in dimensionless form as... 

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