Dynamics of the Josephson junction
Authors:
M. Levi, F. C. Hoppensteadt and W. L. Miranker
Journal:
Quart. Appl. Math. 36 (1978), 167-198
MSC:
Primary 78.35; Secondary 80.35
DOI:
https://doi.org/10.1090/qam/484023
MathSciNet review:
484023
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Abstract: We study the sine-Gordon equation and systems of discrete approximations to it which are respectively a model of the Josephson junction and models of coupled-point Josephson junctions. We do this in the so-called current-driven case. The voltage response of these devices is the average of the time derivative of the solution of these equations and we demonstrate the existence of running periodic solutions for which the average exists. Static solutions are also studied. These together with the running solutions explain the multiple-valuedness in the response of a Josephson junction in several cases. The stability of the various solutions is described in some of the cases. Numerical results are displayed which give details of structure of solution types in the case of a single point junction and of the one-dimensional distributed junction.
Y. Imry and P. Marcus, Nonlinear effects in coupled Josephson devices, Proceedings of the 1975 Stanford Applied Superconductivity Conference.
Y. Imry and L. S. Schulman, Qalitative theory of nonlinear behavior of coupled Josephson junction, to appear.
D. N. Landberg, D. J. Scalapino and B. N. Taylor, The Josephson effects, Scientific American, 21, 30–39 (May 1966).
W. Liniger and F. Odeh, Perturbation solutions of the Josephson phase equation, to appear.
J. Matisoo, Josephson-type superconductive tunnel junctions and applications, IEEE Transactions on Magnetics, 5, 848–873 (1969).
F. Odeh, On existence, uniqueness and stability of solutions of the Josephson phase equation, to appear.
C. S. Owen and D. J. Scalapino, Vortex structure and critical currents in Josephson junctions, Pht. Rev., 164, 538–544 (1967).
J. M. Rowell, Phys. Rev. Letters 11, 200 (1963).
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
F. Tricomi, Integrazione di un’equazione differenzale presentasi in elettrotecnica, Ann. Sc. Norm. Sup. Pisa 2 (1933)
Y. Imry and P. Marcus, Nonlinear effects in coupled Josephson devices, Proceedings of the 1975 Stanford Applied Superconductivity Conference.
Y. Imry and L. S. Schulman, Qalitative theory of nonlinear behavior of coupled Josephson junction, to appear.
D. N. Landberg, D. J. Scalapino and B. N. Taylor, The Josephson effects, Scientific American, 21, 30–39 (May 1966).
W. Liniger and F. Odeh, Perturbation solutions of the Josephson phase equation, to appear.
J. Matisoo, Josephson-type superconductive tunnel junctions and applications, IEEE Transactions on Magnetics, 5, 848–873 (1969).
F. Odeh, On existence, uniqueness and stability of solutions of the Josephson phase equation, to appear.
C. S. Owen and D. J. Scalapino, Vortex structure and critical currents in Josephson junctions, Pht. Rev., 164, 538–544 (1967).
J. M. Rowell, Phys. Rev. Letters 11, 200 (1963).
J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience, N.Y., 1950
F. Tricomi, Integrazione di un’equazione differenzale presentasi in elettrotecnica, Ann. Sc. Norm. Sup. Pisa 2 (1933)
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Article copyright:
© Copyright 1978
American Mathematical Society
