Band-gaps in long Josephson junctions with periodic phase-shifts
Ahmad, Saeed; Susanto, Hadi; Wattis, Jonathan A.D.
Jonathan A.D. Wattis Jonathan.Wattis@nottingham.ac.uk
We investigate analytically and numerically a long Josephson junction on an infnite domain, having arbitrary periodic phase shift of k, that is, the so-called 0-k long Josephson junction. The system is described by a one-dimensional sine-Gordon equation and has relatively recently been proposed as artificial atom lattices. We discuss the existence of periodic solutions of the system and investigate their stability both in the absence and presence of an applied bias current. We find critical values of the phase-discontinuity and the applied bias current beyond which a solution switches to its complementary counterpart. Due to the periodic discontinuity in the phase, the system admits regions of allowed and forbidden bands. We perturbatively investigate the Arnold tongues that separate the region of allowed and forbidden bands, and discuss the effect of an applied bias current on the band-gap structure. We present numerical simulations to support our analytical results.
|Journal Article Type||Article|
|Publication Date||Apr 4, 2017|
|Journal||Physics Letters A|
|Peer Reviewed||Peer Reviewed|
|APA6 Citation||Ahmad, S., Susanto, H., & Wattis, J. A. (2017). Band-gaps in long Josephson junctions with periodic phase-shifts. Physics Letters A, 381(13), doi:10.1016/j.physleta.2017.01.062|
|Keywords||Long Josephson junctions; Sine-Gordon equation; Band-gaps; Arnold tongues|
|Copyright Statement||Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0|
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0
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