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Title: Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions

Abstract

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 labeled by a topological number N{sub v}=0,1,2,... . Mathematically, they can be interpreted as nontrivial 'vacuum' (N{sub v}=0) and static topological solitons (N{sub v}=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 (N{sub v}=0) and Josephson vortices (N{sub v}=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.

Authors:
;  [1]
  1. B. I. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Avenue, 61103 Kharkov (Ukraine)
Publication Date:
OSTI Identifier:
20787833
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevB.73.024513; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; ANALYTICAL SOLUTION; ELECTRIC CURRENTS; EQUILIBRIUM; FREE ENERGY; FREE ENTHALPY; JOSEPHSON EFFECT; JOSEPHSON JUNCTIONS; MAGNETIC FIELDS; SINE-GORDON EQUATION; SOLITONS; TOPOLOGY; VORTICES

Citation Formats

Kuplevakhsky, S. V., and Glukhov, A. M. Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions. United States: N. p., 2006. Web. doi:10.1103/PHYSREVB.73.0.
Kuplevakhsky, S. V., & Glukhov, A. M. Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions. United States. doi:10.1103/PHYSREVB.73.0.
Kuplevakhsky, S. V., and Glukhov, A. M. Sun . "Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions". United States. doi:10.1103/PHYSREVB.73.0.
@article{osti_20787833,
title = {Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions},
author = {Kuplevakhsky, S. V. and Glukhov, A. M.},
abstractNote = {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 labeled by a topological number N{sub v}=0,1,2,... . Mathematically, they can be interpreted as nontrivial 'vacuum' (N{sub v}=0) and static topological solitons (N{sub v}=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 (N{sub v}=0) and Josephson vortices (N{sub v}=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.},
doi = {10.1103/PHYSREVB.73.0},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 2,
volume = 73,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}
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