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Band-gaps in long Josephson junctions with periodic phase-shifts

Ahmad, Saeed; Susanto, Hadi; Wattis, Jonathan A.D.

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Saeed Ahmad

Hadi Susanto

Professor of Applied Mathematics


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.


Ahmad, S., Susanto, H., & Wattis, J. A. (2017). Band-gaps in long Josephson junctions with periodic phase-shifts. Physics Letters A, 381(13),

Journal Article Type Article
Acceptance Date Jan 30, 2017
Online Publication Date Feb 7, 2017
Publication Date Apr 4, 2017
Deposit Date Mar 2, 2017
Publicly Available Date Mar 2, 2017
Journal Physics Letters A
Print ISSN 0375-9601
Electronic ISSN 0375-9601
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 381
Issue 13
Keywords Long Josephson junctions; Sine-Gordon equation; Band-gaps; Arnold tongues
Public URL
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