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Pinned fluxons in a Josephson junction with a finite length inhomogeneity

Derks, G, Doelman, A, Knight, CJK and Susanto, H (2010) Pinned fluxons in a Josephson junction with a finite length inhomogeneity European Journal of Applied Mathematics. pp. 1-44.

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We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or - for instance by varying the length of the inhomogeneity - may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity - a relation we determine explicitly. In combination with continuation arguments and Sturm-Liouville theory, we determine the stability of all constructed pinned fluxons. It follows that if a given system is able to sustain at least one pinned fluxon, there is exactly one stable pinned fluxon, i.e. the system selects one unique stable pinned configuration. Moreover, it is shown that both for microresistors and microresonators this stable pinned configuration may be non-monotonic - something which is not possible in the homogeneous case. Finally, it is shown that results in the literature on localised inhomogeneities can be recovered as limits of our results on microresonators.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Doelman, A
Knight, CJK
Susanto, H
Date : 26 August 2010
DOI : 10.1017/S0956792511000301
Related URLs :
Additional Information : Copyright 2007 Cambridge University Press.
Depositing User : Symplectic Elements
Date Deposited : 26 Jan 2012 10:46
Last Modified : 06 Jul 2019 05:09

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