Kink propagation and trapping in a two-dimensional curved Josephson junction

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    Abstract

    Sine-Gordon kink propagation in a curved planar waveguide is considered. The waveguide consists of two rectangular regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. The latter models an energy-providing mechanism for Josephson junctions of overlap type. A collective variable approach based on the kink position and the kink width depending on the transversal coordinate is developed. The latter allows to take into account both longitudinal and centrifugal forces which act on the nonlinear excitation moving in a region with finite curvature and to obtain a qualitatively good agreement with the numerical simulations. The region with finite curvature acts as a potential barrier whose height and width depend on the radius of curvature of the waveguide. The kink transmission, reflection, and trapping are investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink.
    Original languageEnglish
    JournalPhysical Review B Condensed Matter
    Volume69
    Issue number13
    Pages (from-to)134506
    Number of pages10
    ISSN0163-1829
    DOIs
    Publication statusPublished - 2004

    Bibliographical note

    Copyright (2004) American Physical Society.

    Keywords

    • Collective coordinates
    • Josephson junctions
    • sine-Gordon equation
    • Curved space
    • Solitons

    Cite this

    @article{892d61f7d06b4e85851da8b0e5bce66d,
    title = "Kink propagation and trapping in a two-dimensional curved Josephson junction",
    abstract = "Sine-Gordon kink propagation in a curved planar waveguide is considered. The waveguide consists of two rectangular regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. The latter models an energy-providing mechanism for Josephson junctions of overlap type. A collective variable approach based on the kink position and the kink width depending on the transversal coordinate is developed. The latter allows to take into account both longitudinal and centrifugal forces which act on the nonlinear excitation moving in a region with finite curvature and to obtain a qualitatively good agreement with the numerical simulations. The region with finite curvature acts as a potential barrier whose height and width depend on the radius of curvature of the waveguide. The kink transmission, reflection, and trapping are investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink.",
    keywords = "Collective coordinates, Josephson junctions, sine-Gordon equation, Curved space, Solitons",
    author = "Carlos Gorria and Gaididei, {Yuri Borisovich} and S{\o}rensen, {Mads Peter} and Christiansen, {Peter Leth} and Caputo, {Jean Guy}",
    note = "Copyright (2004) American Physical Society.",
    year = "2004",
    doi = "10.1103/PhysRevB.69.134506",
    language = "English",
    volume = "69",
    pages = "134506",
    journal = "Physical Review B (Condensed Matter and Materials Physics)",
    issn = "1098-0121",
    publisher = "American Physical Society",
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    }

    Kink propagation and trapping in a two-dimensional curved Josephson junction. / Gorria, Carlos; Gaididei, Yuri Borisovich; Sørensen, Mads Peter; Christiansen, Peter Leth; Caputo, Jean Guy.

    In: Physical Review B Condensed Matter, Vol. 69, No. 13, 2004, p. 134506.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Kink propagation and trapping in a two-dimensional curved Josephson junction

    AU - Gorria, Carlos

    AU - Gaididei, Yuri Borisovich

    AU - Sørensen, Mads Peter

    AU - Christiansen, Peter Leth

    AU - Caputo, Jean Guy

    N1 - Copyright (2004) American Physical Society.

    PY - 2004

    Y1 - 2004

    N2 - Sine-Gordon kink propagation in a curved planar waveguide is considered. The waveguide consists of two rectangular regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. The latter models an energy-providing mechanism for Josephson junctions of overlap type. A collective variable approach based on the kink position and the kink width depending on the transversal coordinate is developed. The latter allows to take into account both longitudinal and centrifugal forces which act on the nonlinear excitation moving in a region with finite curvature and to obtain a qualitatively good agreement with the numerical simulations. The region with finite curvature acts as a potential barrier whose height and width depend on the radius of curvature of the waveguide. The kink transmission, reflection, and trapping are investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink.

    AB - Sine-Gordon kink propagation in a curved planar waveguide is considered. The waveguide consists of two rectangular regions joined by a bent section of constant curvature. Transverse homogeneous and inhomogeneous Neumann boundary conditions are used. The latter models an energy-providing mechanism for Josephson junctions of overlap type. A collective variable approach based on the kink position and the kink width depending on the transversal coordinate is developed. The latter allows to take into account both longitudinal and centrifugal forces which act on the nonlinear excitation moving in a region with finite curvature and to obtain a qualitatively good agreement with the numerical simulations. The region with finite curvature acts as a potential barrier whose height and width depend on the radius of curvature of the waveguide. The kink transmission, reflection, and trapping are investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink.

    KW - Collective coordinates

    KW - Josephson junctions

    KW - sine-Gordon equation

    KW - Curved space

    KW - Solitons

    U2 - 10.1103/PhysRevB.69.134506

    DO - 10.1103/PhysRevB.69.134506

    M3 - Journal article

    VL - 69

    SP - 134506

    JO - Physical Review B (Condensed Matter and Materials Physics)

    JF - Physical Review B (Condensed Matter and Materials Physics)

    SN - 1098-0121

    IS - 13

    ER -