Asymptotic states in long Josephson junctions are investigated in an external magnetic field. We show that a choice one of the solution of the stationary Ferrell-Prange equation can carry be out with use of an asymptotic solution of the sine-Gordon equation and that an evolution to that stable solution occurs by passing through metastable states, which is determined with a form of quickly damped initial perturbation. The boundary sine-Gordon and Ferrell-Prange problems were carried out with a numerical simulation. An approximated expression for the vortex and antivortex states is obtained in the case of large values of an external magnetic field.
A long Josephson junction in a constant external magnetic field and in the presence of a dc bias current is investigated. It is shown that the system, simulated by the sine-Gorgon equation, "remembers" a rapidly damping initial perturbation and final asymptotic states are determined exactly with this perturbation. Numerical solving of the boundary sine-Gordon problem and calculations of Lyapunov indices show that this system has a memory even when it is in a state of dynamical chaos, i.e. , dynamical chaos does not destroy initial information having a character of rapidly damping perturbation.Dynamical chaos is one of the most interesting phenomena in the theory of Josephson junctions. This phenomenon is not only of theoretical importance but also of practical importance, because many devices are founded on Josephson junctions, in particular, superconducting quantum interference devices (SQUID's). Dynamical chaos in these devices is another source of noise.Furthermore, a long Josephson junction (LJJ) serves as a very good system for studying nonlinear phenomena such as an excitation of Buxons and antifluxons, their propagation, interaction, scattering, and breakup. Investigations of the last few years showed that a LJJ detects deeper characteristics than had seemed. Even in the simplest case, when a bias current and an external oscillating field are absent, the presence only of a constant external magnetic field leads to the most interesting phenomenon connected with the selection of the solution of the stationary Ferrell-Prange equation. The fact is that this equation has not only provided one solution by given boundary conditions; the number of these solutions increases with the strength of the external magnetic field and the total length of the junction.Recently we have shown that the selection of a solution is carried out with the form of a small and rapidly damping initial perturbation in time in the nonstationary sine-Gordon equation and what is more surprising an asymptotic solution of this equation coincides with one of the stable solutions of the stationary Ferrell-Prange equation. Two circumstances are remarkable here: (1) A small perturbation inQuences very much the evolution of the system with t~oo; in a sense it defines the character of asymtotic solutions. (2) One can say that in spite of the fact that a small perturbation is a rapidly damping one, the stable asymptotic solution "remembers" the initial perturbation. In other words, the nonlinear system, i.e. , a LJJ, described with the sine-Gordon equation shows an effect of memory. However, in Ref. 12, the I JJ is studied solely under the infiuence of an external constant magnetic field. Therefore, it is of interest to investigate the LJJ Rom the point of view of the effect of memory not only in the presence of an external constant magnetic 6eld but also under the inBuence of a dc bias current through the junction causing an excitation of dynamical chaos. How will the effect of memory in the presence of a dc bias current be shown? Will this effect ...
Stationary and nonstationary, in particular, chaotic states in long Josephson junctions are investigated. Bifurcation lines on the parametric bias currentexternal 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 stationary states is given. 74.50+r, 05.45.+b Typeset using REVT E X 1
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