Bifurcations and a chaos strip in states of long Josephson junctions

Stationary and nonstationary, in particular, chaotic states in long Josephson junctions are investigated. Bifurcation lines on the parametric bias current-external magnetic field plane are calculated. The chaos strip along the bifurcation line is observed. It is shown that transitions between stationary states are the transitions from metastable to stable states and that the thermodynamical Gibbs potential of these stable states may be larger than for some metastable states. The definition of a dynamical critical magnetic field characterizing the stability of the stationaryComment: 13 pages, 6 Postscript figures, uses revtex.st

Static Solitons of the Sine-Gordon Equation and Equilibrium Vortex Structure in Josephson Junctions

The problem of vortex structure in a single Josephson junction in an external magnetic field, in the absence of transport currents, is reconsidered from a new mathematical point of view. In particular, we derive a complete set of exact analytical solutions representing all the stationary points (minima and saddle-points) of the relevant Gibbs free-energy functional. The type of these solutions is determined by explicit evaluation of the second variation of the Gibbs free-energy functional. The stable (physical) solutions minimizing the Gibbs free-energy functional form an infinite set and are labelled by a topological number Nv=0,1,2,... Mathematically, they can be interpreted as nontrivial ''vacuum'' (Nv=0) and static topological solitons (Nv=1,2,...) of the sine-Gordon equation for the phase difference in a finite spatial interval: solutions of this kind were not considered in previous literature. Physically, they represent the Meissner state (Nv=0) and Josephson vortices (Nv=1,2,...). Major properties of the new physical solutions are thoroughly discussed. An exact, closed-form analytical expression for the Gibbs free energy is derived and analyzed numerically. Unstable (saddle-point) solutions are also classified and discussed.Comment: 17 pages, 4 Postscript figure

Flux quantization in stationary and nonstationary states in long Josephson junctions

Dynamical chaos, states stability in long Josephson junctions are investigated from the point of view of the flux quantization. It is shown that the stationary Meissner and fluxon states having integer number of fluxons are stable. Stationary antifluxon states also having integer number of the flux quanta and all other states with half-integer number of flux quanta are unstable. The transitions between all states - Meissner, the states having the integer and half-integer number of the flux quanta - take place in the nonstationary case, and all these states are dynamically equivalent, but the number of the flux quanta is a nonregular time-dependent function for the chaotic states and regular for the regular ones