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

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dc.creatorKuplevakhsky, S. V.
dc.creatorGlukhov, A. M.
dc.date2006-02-21
dc.date.accessioned2026-07-07T07:01:51Z
dc.date.available2026-07-07T07:01:51Z
dc.descriptionThe 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.
dc.description17 pages, 4 Postscript figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0602485
dc.identifierhttp://arxiv.org/abs/cond-mat/0602485
dc.identifierPhys. Rev. B 73, 024513 (2006)
dc.identifierdoi:10.1103/PhysRevB.73.024513
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/108402
dc.subjectSuperconductivity
dc.subjectPattern Formation and Solitons
dc.titleStatic Solitons of the Sine-Gordon Equation and Equilibrium Vortex Structure in Josephson Junctions
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