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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Doelman, A. van Heijster, P. and Xie, F. 2016. A Geometric Approach to Stationary Defect Solutions in One Space Dimension. SIAM Journal on Applied Dynamical Systems, Vol. 15, Issue. 2, p. 655.


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    SEMERDJIEVA, E. G. and TODOROV, M. D. 2013. NUMERICAL INVESTIGATION OF BIFURCATIONS AND TRANSITIONS OF JOSEPHSON VORTICES IN INHOMOGENEOUS JUNCTIONS. International Journal of Bifurcation and Chaos, Vol. 23, Issue. 12, p. 1350192.


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  • European Journal of Applied Mathematics, Volume 23, Issue 2
  • April 2012, pp. 201-244

Pinned fluxons in a Josephson junction with a finite-length inhomogeneity

  • GIANNE DERKS (a1), ARJEN DOELMAN (a2), CHRISTOPHER J. K. KNIGHT (a1) and HADI SUSANTO (a3)
  • DOI: http://dx.doi.org/10.1017/S0956792511000301
  • Published online: 26 August 2011
Abstract

We consider a Josephson junction system installed with a finite length inhomogeneity, either of micro-resistor or micro-resonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or – for instance by varying the length of the inhomogeneity – may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity – a relation we determine explicitly. In combination with continuation arguments and Sturm–Liouville theory, we determine the stability of all constructed pinned fluxons. It follows that if a given system is able to sustain at least one pinned fluxon, a microresistor has exactly one pinned fluxon, i.e. the system selects one unique pinned stable pinned configuration, and a microresonator has at least one stable pinned configuration. Moreover, it is shown that both for micro-resistors and micro-resonators this stable pinned configuration may be non-monotonic – something which is not possible in the homogeneous case. Finally, it is shown that results in the literature on localised inhomogeneities can be recovered as limits of our results on micro-resonators.

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[1]M. J. Ablowitz , D. J. Kaup , A. C. Newell & H. Segur (1973) Method for solving the sine-Gordon equation. Phys. Rev. Lett. 30, 12621264.

[2]H. Akoh , S. Sakai , A. Yagi & H. Hayakawa (1985) Real time fluxon dynamics in Josephson transmission line. IEEE Trans. Magn. 21, 737740.

[4]A. Benabdallah , J. G. Caputo & N. Flytzanis (2002) The window Josephson junction: A coupled linear nonlinear system. Physica D 161, 79101.

[5]A. Benabdallah & J. G. Caputo (2002), Influence of the passive region on zero field steps for window Josephson junctions. J. Appl. Phys. 92, 38533862.

[7]T. L. Boyadjiev , O. Yu. Andreeva , E. G. Semerdjieva & Yu. M. Shukrinov (2008) Created by current states in long Josephson junctions. Europhys. Lett. 83, 47008.

[8]J. G. Caputo , N. Efraimidis , N. Flytzanis , N. Lazaridis , Y. Gaididei , I. Moulitsa & E. Vavalis (2000) Static properties and waveguide modes of a wide lateral window Josephson junction. Int. J. Mod. Phys. C 11, 493518.

[9]L. D. Carr , K. W. Mahmud & W. P. Reinhardt (2001) Tunable tunneling: An application of stationary states of Bose–Einstein condensates in traps of finite depth. Phys. Rev. A 64, 033603.

[10]G. Derks , A. Doelman , van Gils, S. A. & H. Susanto (2007) Stability analysis of π-kinks in a 0-π Josephson junction. SIAM J. Appl. Dyn. Syst. 6, 99141.

[11]G. Derks , A. Doelman , S. A. van Gils & T. Visser (2003) Travelling waves in a singularly perturbed sine-Gordon equation. Physica D 180, 4070.

[12]E. Goldobin , K. Vogel , O. Crasser , R. Walser , W. P. Schleich , D. Koelle & R. Kleiner (2005) Quantum tunneling of semifluxons in a 0-π-0 long Josephson junction. Phys. Rev. B 72, 054527.

[13]R. H. Goodman & R. Haberman (2007) Chaotic Scattering and the n-Bounce Resonance in Solitary-Wave Interactions Phys. Rev. Lett. 98, 104103.

[14]R. H. Goodman & M. I. Weinstein (2008), Stability and instability of nonlinear defect states in the coupled mode equations – Analytical and numerical study. Physica D 237, 27312760.

[15]P. J. A. van Heijster , A. Doelman , T. J. Kaper , Y. Nishiura , K.-I. Ueda (2011) Pinned fronts in heterogeneous media of jump type. Nonlinearity 24, 127157.

[16]H. Hilgenkamp (2008) π-phase shift Josephson structures. Supercond. Sci. Technol. 21, 034011.

[17]Yu. S. Kivshar , A. M. Kosevich & O. A. Chubykalo (1988) Finite-size effects in fluxon scattering by an inhomogeneity. Phys. Lett. A 129, 449452.

[18]Y. S. Kivshar & B. A. Malomed (1989) Dynamics of solitons in nearly integrable systems. Rev. Mod. Phys. 61, 763915; (1991) 63, 211 (Addendum).

[19]Y. S. Kivshar , Z. Fei & L. Vázquez (1991) Resonant soliton-impurity interactions Phys. Rev. Lett. 67, 11771180.

[22]T. Kontos , M. Aprili , J. Lesueur , F. Genet , B. Stephanidis & R. Boursier (2002) Josephson junction through a thin ferromagnetic layer: Negative coupling. Phys. Rev. Lett. 89, 137007.

[23]E. Mann (1997) Systematic perturbation theory for sine-Gordon solitons without use of inverse scattering methods. J. Phys. A: Math. Gen. 30, 12271241.

[24]R. Marangell , C. K. R. Jones T. & H. Susanto (2010) Localized standing waves in inhomogeneous Schrödinger equations. Nonlinearity 23, 2059.

[25]D. W. McLaughlin & A. C. Scott (1978) Perturbation analysis of fluxon dynamics. Phys. Rev. A 18, 16521679.

[26]T. Ortlepp , Mielke, O. Ariando , C. J. M. Verwijs , K. F. K. Foo , H. Rogalla , F. H. Uhlmann & H. Hilgenkamp (2006) Flip-flopping fractional flux quanta. Science 312, 14951497.

[28]C. M. Pegrum (2006) Can a fraction of a quantum be better than a whole one? Science 312, 14831484.

[29]B. Piette , W. J. Zakrzewski & J. Brand (2005) Scattering of topological solitons on holes and barriers. J. Phys. A 38, 1040310412.

[30]B. Piette & W. J. Zakrzewski (2007) Scattering of sine-Gordon kinks on potential wells. J. Phys. A 40, 59956010.

[31]S. Sakai , H. Akoh & H. Hayakawa (1985) Fluxon transfer devices. Japan. J. Appl. Phys. 24, L771L773.

[32]S. Scharinger , C. Gürlich , R. G. Mints , M. Weides , Kohlstedt, H., Goldobin, E., Koelle, D. & R. Kleiner (2010) Interference patterns of multifacet 20 × (0-π) Josephson junctions with ferromagnetic barrier. Phys. Rev. B 81, 174535.

[34]H. Susanto , S. A. van Gils , T. P. P. Visser , H. J. H. Smilde & H. Hilgenkamp (2003) Static semifluxons in a long Josephson junction with π-discontinuity points. Phys. Rev. B 68, 104501104508.

[35]H. Susanto , E. Goldobin , D. Koelle , R. Kleiner & S. A. van Gils (2005) Controllable plasma energy bands in a one-dimensional crystal of fractional Josephson vortices. Phys. Rev. B 71, 174510.

[38]M. Weides , M. Kemmler , E. Goldobin , D. Koelle , R. Kleiner , H. Kohlstedt & A. Buzdin (2006) High quality ferromagnetic 0 and π Josephson tunnel junctions. Appl. Phys. Lett. 89, 122511.

[39]M. Weides , M. Kemmler , E. Goldobin , H. Kohlstedt , R. Waser , D. Koelle & R. Kleiner (2006) 0-π Josephson tunnel junctions with ferromagnetic barrier. Phys. Rev. Lett. 97, 247001.

[40]M. Weides , H. Kohlstedt , R. Waser , M. Kemmler , J. Pfeiffer , D. Koelle , R. Kleiner & E. Goldobin (2007) Ferromagnetic 0-π Josephson junctions. App. Phys. A 89, 613617.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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