Static solitons of the sineGordon 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 saddlepoints) of the relevant Gibbs freeenergy functional. The type of these solutions is determined by explicit evaluation of the second variation of the Gibbs freeenergy functional. The stable (physical) solutions minimizing the Gibbs freeenergy 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 sineGordon 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, closedform analytical expression for the Gibbs free energy is derived and analyzed numerically. Unstable (saddlepoint) solutions are also classified and discussed.
 Authors:
 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; SINEGORDON EQUATION; SOLITONS; TOPOLOGY; VORTICES
Citation Formats
Kuplevakhsky, S. V., and Glukhov, A. M. Static solitons of the sineGordon 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 sineGordon 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 sineGordon equation and equilibrium vortex structure in Josephson junctions". United States.
doi:10.1103/PHYSREVB.73.0.
@article{osti_20787833,
title = {Static solitons of the sineGordon 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 saddlepoints) of the relevant Gibbs freeenergy functional. The type of these solutions is determined by explicit evaluation of the second variation of the Gibbs freeenergy functional. The stable (physical) solutions minimizing the Gibbs freeenergy 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 sineGordon 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, closedform analytical expression for the Gibbs free energy is derived and analyzed numerically. Unstable (saddlepoint) 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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