Using the method developed by Bogolyubov et al., we find analytically a steady-state solution for the resistively shunted junction (RSJ) model of the Josephson junction that is driven by a constant current source. This solution explains how the relative amplitude of the voltage oscillation depends on the junction parameters such as I 0 (the critical current), R (the resistance), C (the capacitance), and the external current I e . The validity of the analytical solution is assessed by comparing it with numerical results. We find that this solution is useful for normal tunnel junction with I e /I 0 of order 1 or larger, and for any other weak links with I e /I 0 much larger than 1.
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References
W. C. Stewart, Appl. Phys. Lett. 12, 277 (1968).
D. E. McCumber, J. Appl. Phys. 39, 3113 (1968).
H. H. Zappe, J. Appl. Phys. 44, 1371 (1973).
V. N. Belykh, N. F. Pedersen, and O. H. Soerensen, Phys. Rev. B 16, 4853 (1977).
D. N. Langenberg, D. J. Scalapino, B. N. Taylor, and R. E. Eck, Phys. Lett. 20, 563 (1966).
E. E. Shin and B. B. Schwartz, Phys. Rev. 152, 207 (1966).
D. B. Sullivan, R. L. Peterson, V. E. Kose, and J. E. Zimmerman, J. Appl. Phys. 41, 4865 (1970).
D. E. Sullivan and J. E. Zimmerman, AJP, 39, 1504 (1971).
N. Minorsky, Nonlinear Oscillations (Van Nostrand, Princeton, New Jersey, 1962), Chapter 3.
P. S. Lee, Y. C. Lee, C. T. Chang, and D. S. Chu, Phys. Rev. Lett. 30, 538 (1973).
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Liu, I., Lee, Y.C. An asymptotic solution for the resistively shunted junction (RSJ) model of the Josephson junction. J Low Temp Phys 44, 11–21 (1981). https://doi.org/10.1007/BF00115072
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DOI: https://doi.org/10.1007/BF00115072