The sine-Gordon Equation in Josephson-Junction Arrays

Description of zero field steps on the potential energy surface of a Frenkel-Kontorova model for annular Josephson junction arrays

“…On the other hand, the example of an excitation with F dc = 25 is far over the symmetric SP All in all, we cannot see a resonant oscillation of the chain at the fin of the ZFS [6]. In contrast we detect no kind of vibration, but only a straight, stiff 'downhill' sliding of the chain.…”

“…Josephson junctions (JJs) are electronic superconducting devices. They are reported in the observation of different experiments [4][5][6]. We concentrate here on the emergence of ZFS in calculations with the Frenkel-Kontorova (FK) model with periodic boundary conditions (PBC) [7].…”

“…where φ(t) describes a high frequent phase difference (PD) between the two superconducting layers of the JJ [6,20], η is a damping factor, and F is the current through the JJ.…”

“…The chain has the equilibrium distance, a o = 0, and the φ i can change their order. An array of parallel JJs is described by a system of discrete SG equations [6,18]…”

Topology, defects, and topological defects

“…The solitary waves in this model can pass through one another while retaining their individual sizes and shapes [134], and for this reason they are named solitons. Solitons have found many applications including, for example, the analysis of seismic data [135], convecting nematic fluids [136], Josephson-junction arrays [137,138], and magnetic materials [139].…”