Stability analysis of static solutions in a Josephson junction

We present all the possible solutions of a Josephson junction with bias current and magnetic field with both inline and overlap geometry, and examine their stability. We follow the bifurcation of new solutions as we increase the junction length. The analytical results, in terms of elliptic functions in the case of inline geometry, are in agreement with the numerical calculations and explain the strong hysteretic phenomena typically seen in the calculation of the maximum tunneling current. This suggests a different experimental approach based on the use, instead of the external magnetic field the modulus of the elliptic function or the related quantity the total magnetic flux to avoid hysteretic behavior and unfold the overlapping $I_{max}(H)$ curves.Comment: 36 pages with 17 figure

A Semi-Linear Elliptic Pde Model For The Static Solution Of Josephson Junctions

In this study we derive a semi-linear Elliptic Partial Differential Equation (PDE) problem that models the static (zero voltage) behavior of a Josephson window junction. Iterative methods for solving this problem are proposed and their computer implementation is discussed. The preliminary computational results that are given, show the modeling power of our approach and exhibit its computational efficiency. Keywords: Josephson Junctions, Numerical Analysis, Partial Differential Equations, Solitons. 1. Introduction A Josephson junction consists of two superconducting materials weakly linked through a thin oxide layer allowing for the tunneling of Cooper electron pairs and quasiparticles (dressed electrons) (see Ref. [1-3]). Specifically, in Ref. [1] Josephson described the electrodynamics of such a device not by current and voltage but by their integrals, charge and flux, which are related to the phase difference OE(x; y) of the macroscopic wave functions (order parameters) of the elec..

Effect Of Geometry On Fluxon Width In A Josephson Junction

this paper we used an efficient numerical procedure for the calculation of the time independent magnetic flux structures in a window Josephson junction. Compared to previously used energy minimization technique

Split Mode Method For The Elliptic 2d Sine-Gordon Equation: Application To Josephson Junction In Overlap Geometry

this paper so far one can conclude that we have two basic techniques to simulate an overlap 2D window Josephson junction. The first one is to solve the 2D PDE mathematical problem and the second one is to solve the system o