Study of Fluxons in Josephson Junctions by Considering Dissipation and Scattering

Gharaati, Abdolrasoul; Forozani, Ghasem; Khosravani, Sara

doi:10.30473/jphys.2026.77643.1298

Document Type : Research

Authors

¹ Professor, Department of Physics, Payame Noor University, Tehran, Iran.

² Associate Professor, Payame Noor University, Tehran, Iran.

³ Ph.D. Student, Department of Physics, Payame Noor University, Tehran, Iran.

https://doi.org/10.30473/jphys.2026.77643.1298

Abstract

This paper investigates the structure of Josephson junctions, which, as one of the most fundamental elements in superconductivity, play a key role in the advancement of condensed matter physics, quantum field theory, and modern quantum technologies. The governing equation for the phase of such a system in the absence of dissipation and dispersion is the ordinary sine-Gordon equation, which describes fluxon propagation without considering the effects of dissipation and dispersion. However, in real physical system, the constituent materials of Josephson junctions always accompanied by dissipation and dispersion, which can significantly affect the dynamical behavior of fluxons. Here, by generalizing the sine-Gordon equation and including terms corresponding to dissipation and dispersion, and also considering the normalized bias current as a control parameter, the dynamics of fluxons in Josephson junctions have been studied. The result of this study show that the effects of dissipation and dispersion, especially in the presence of a normalized bias current, play a decisive role in the stability, propagation velocity of fluxons. The findings of this research confirm that considering dissipation and dispersion coefficients is essential and cannot be neglected in most cases. According to the calculations and simulations performed, it is observed that the effect of loss and dispersion can be compensated with the help of bias current. Therfore, the studies presented in this paper can be considered an effective step towards more realistic simulation of fluxon dynamics in parctical superconducting system.

Keywords

References

[1] W. Perold, “Superconducting Quantum Interference Device (SQUID) Mangnetometers: Principles, Fabrication and Applications”, Stellenbosch University, (2010).

[2] R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectures on physics, Addison_Wesley, Reading, Massachusetts, Vol. III, (1966).

[3] R. Rajaraman, “Solitons and Instantons”, Elsevier, North Holland, (1996).

[4] A. Wallraff aus Bonn, “Fluxon Dynamics in Annular Josephson Junction from Relativistic strings to Quantum particles”, (2000).

[5] G. Grosso, “Solid state physics”, University of Pavia, Academic Press, (2000).

[6] A. Garaati, N. Fathi, S. Johnson, A. Biswas, “Analytical solution of fluxons in a nonhomogenous Josephson junction”, Wave in Random and Complex Media, (2012).

[7] H. Kooiker, “Fluxon Dynamics of the State in a Two-Fold Stack of Long Josephson Junctions”, University of Twente, Enschede, (2005).

[8] A. V. Ustinov “Solitons in Josephson junction” Physica D 123, 315, 329 (1998)

[9] D. Mares-Rincon, S. Macias, J.E. Macias-Diaz, J. A. Guerrero-Diaz-de-Leon, T. Bountis “A Discrete Model to Solve a Bifractional Dissipative Sin-Gordon Equation:Theorical Analysis and Simulations”, Fractal and fractional, (2025).

[10] Y. Wang, M. N. Raihen, E. Ilhan, H. M. Baskonus, “On the new sine-Gordon solitons the generalized Korteweg-de Vries and modified Kortewg-de Vries models via beta operator”, Mathematcs, (2025).

[11] J. Guo, M. Li, “The dynamics of some exact solution to a (3+1)-dimensional sine-Gordon equation”, Wave Motion, (2024).

[12] J. Clarke and A. I. Braginski, the SQUID Handbook: Fundamentals and Technology of SQUIDS and SQUID System, Vol.1. Weinheim, Germany: Wiley-VCH, (2004)

[13] R. L. Fagaly, “Superconducting Quantum Instruments and Applications”, Rev. Sci. nstrum., Vol. 77, no. 10, P. 101101, Oct. (2006)

[14] M. Tinkham, Introduction to Superconductivity, 2nd ed. Mineola, NY, USA: Dover Publications, (2004)

[15] H. K. Chang et al., “SQUID-based geophysical survey techniques and their applications,” J. Appl. Geophys., vol. 168, pp. 1-12, Sep. (2019)

[16] J. H. Hinken and S. K. G. Kater, “Nondestructive testing with HTS SQUIDs,” IEEE Trans. Appl. Geophys., vol. 168, pp. 3841-3844, Jun. (1999)

[17] T. R. Madden, “Review of electrical and magnetic fields accompanying seismic and volcanic activity,” Surv. Geophys, vol. 15, no. 4, pp. 441-475, Jul. (1994)

[18] T. Visser, “Modelling and Analysis of Long Josephson junction”, PhD thesis, University of Twente, (2002).

[19] N. Riazi, “Dynamics of Salitons in Inhomogeneous Josephson Junctions”, Int. J. Theo. Phys., Vol. 35, No. 1, (1996).

[20] A. Wallraff, “Fluxon Dynamics and Radiation Emission in Two Fold Long Josephson Junction Stacks”, American Institute of Physics, (1996).

[21] A. Abdumalikov, “Vortex Dynamics in Ultra-Narrow Josephson Junctions”, Lehrstuhl für Mikrocharakterisierung, Friedrich-Alexander-Univ., (2005).

[22] N. Riazi & A.R. Gharaati, “Dynamics of sine-Gordon Solitons”, Int. J. Theor. Phys., Vol.37, No.1, (1998).

[23] A.V. Ustinov,“Long Josephson Junctions and Stacks”,Physikalisches Institute III,Universitat Erlangen-Nurnberg D-91054, Erlangen, Germany, (1998).

[24] M. Remoissent, “Wave called Solitons”, Springer Verlag Berlin, 2^ndedition, (1996).

[25] J. J. Mazo and A. V. Ustinov, “The Sine-Gordon Equation in Josephson-Junction Arrays,” in The Sine-Gordon Model and its and High-Energy Physics, Eds. Cham, Switzerland: Springer International Publishing, pp.115-139, (2014)

[26] A.C. Scott, F.Y.F. Chu, and S.A. Reible, “Magnetically propagation on a Josephson transmission line,” J. Appl. Phys., vol. 47, no. 7, pp. 3272-3286, Jul. (1976).

Quarterly Journal of Optoelectronic

Study of Fluxons in Josephson Junctions by Considering Dissipation and Scattering

References

References

Volume 8, Issue 3 - Serial Number 24
May 2026
Pages 9-18

Study of Fluxons in Josephson Junctions by Considering Dissipation and Scattering

References

References

Volume 8, Issue 3 - Serial Number 24May 2026Pages 9-18

Volume 8, Issue 3 - Serial Number 24
May 2026
Pages 9-18