Devil's Staircases and Continued Fractions in the Josephson Junctions
arXiv:1309.1277 · doi:10.1103/PhysRevB.88.214515
Abstract
The detailed numerical simulations of the IV-characteristics of Josephson junction under external electromagnetic radiation show devil's staircases within different bias current intervals. We have found that the observed steps form very precisely continued fractions. Increasing of the amplitude of radiation shifts the devil's staircases to higher Shapiro steps. The algorithm of appearing and detection of the subharmonics with increasing radiation amplitude is proposed. We demonstrate that subharmonic steps registered in the famous experiments by A. H. Dayem and J. J. Wiegand [Phys. Rev 155, 419 (1967)] and J. Clarke [Phys. Rev. B 4, 2963 (1971)] also form continued fractions.
4 pages, 4 figures
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Cited by in corpus (9)
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- Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces
- Complexity of Shapiro steps
- The largest Lyapunov exponent as a tool for detecting relative changes in the particle positions
- All fractional Shapiro steps in the RSJ model with two Josephson harmonics