The large area Josephson junction is considered. On the basis of Maxwell equations the influence of the magnetic field on fluxion dynamics is considered. The presented studies show that assumptions ...presumed in the literature do not restrict experimental settings adopted in the considerations of the fluxion movement in the Josephson junction. It is shown that the particular orientation of the magnetic fields is not needed in order to study physical effects of curvature and therefore they do not restrict the experimental arrangements.
In the framework of the two-dimensional field model the influence of the curvature on kink width is discussed. Breading of the kink width in a curved region of the manifold is observed. Examples of ...kinks on curved manifolds are studied analytically and numerically as well. The deformation of the kink front in the form of the travelling waves propagating along the curved surfaces are found. Enlarging of the travelling wave speed in a curved regions of the manifold is predicted.
The influence of curvature on kink creation during continuous phase transition in a long Josephson junction is considered. An example of a Josephson junction with constant curvature shows that the ...number density of kinks produced in this system is reduced in the curved regions of the junction.
The complex scalar field models which possess, in the spectra of solutions, the vortices with cylindrical symmetry are considered. The rigorous construction of the curved, constant width, vortices is ...presented. In the framework of the used formalism an example of the curved vortex of constant width is discussed in detail.
A Josephson junction is a device made of two superconducting electrodes separated by a very thin layer of isolator or normal metal. This relatively simple device has found a variety of technical ...applications in the form of Superconducting Quantum Interference Devices (SQUIDs) and Single Electron Transistors (SETs). One can expect that in the near future the Josephson junction will find applications in digital electronics technology RSFQ (Rapid Single Flux Quantum) and in the more distant future in construction of quantum computers. Here we concentrate on the relation of the curvature of the Josephson junction with its inductance. We apply a simple Capacitively Shunted Junction (CSJ) model in order to find condition which guarantees consistency of this model with prediction based on the Maxwell and London equations with Landau-Ginzburg current of Cooper pairs. This condition can find direct experimental verification.
The kink solution in the long Josephson junction is studied. The perturbation scheme of constructing the fluxon solution in curved junction is formulated. The prediction from the perturbation scheme ...is compared with the prediction that follows from the numerical studies of the complete field model.
The impact of thermal noise on kink motion through the curved region of the long Josephson junction is studied. On the basis of the Fokker–Planck equation the analytical formula that describes the ...probability of transmission of the kink over the potential barrier is proposed. The analytical results are compared with the simulations based on the field model. It has been numerically shown that above one Kelvin the probabilities of crossing the barrier are correctly described by the formula proposed in the paper.
•The formula that describes the probability of transmission of the kink is proposed.•The analytical results are compared with the simulations based on the field model.•Above one Kelvin the probabilities of crossing the barrier are correctly described.
The modification of the sine–Gordon model with explicitly broken translational invariance is studied. Different simplified descriptions of the kink motion are applied and compared. The main problem ...of the collective coordinate descriptions is identified and a solution is proposed. Some modification of the known collective coordinate approaches is proposed and a new treatment is suggested. The results are compared with the results of the exact field model.
•The field model with position dependent dispersive term is physically motivated.•It is shown that the inhomogeneities act on the kink as potential barriers.•Two modifications of the collective coordinate approaches are proposed.•For small inhomogeneities new methods better reproduce results of the field model.
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