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Fractional calculus approach for the phase dynamics of Josephson junction

Author

Listed:
  • Ali, Imtiaz
  • Rasheed, Amer
  • Anwar, Muhammad Shoaib
  • Irfan, Muhammad
  • Hussain, Zakir

Abstract

This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference between the macroscopic wave functions of the two superconductors across the junction. The governing non-linear partial differential equation is then solved using finite difference-finite element schemes. Other quantities of interest like Josephson current density and voltage across the junction are also computed. The effects of various parameters in the model on phase difference,Josephson current density and voltage are analyzed graphically with the help of numerical simulations.

Suggested Citation

  • Ali, Imtiaz & Rasheed, Amer & Anwar, Muhammad Shoaib & Irfan, Muhammad & Hussain, Zakir, 2021. "Fractional calculus approach for the phase dynamics of Josephson junction," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309632
    DOI: 10.1016/j.chaos.2020.110572
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    References listed on IDEAS

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    1. Chen, Ting & Wang, Derong, 2020. "Combined application of blockchain technology in fractional calculus model of supply chain financial system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Jean-Guy Caputo & Nikos Flytzanis & Emmanuel Vavalis, 1995. "A Semi-Linear Elliptic Pde Model For The Static Solution Of Josephson Junctions," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 241-262.
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