Role of aperiodic order for fluxon dynamics in Josephson junction arrays

Erik Lennholm; Michael Hörnquist

doi:10.1103/PhysRevE.59.381

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Role of aperiodic order for fluxon dynamics in Josephson junction arrays

Erik Lennholm, Michael Hörnquist

DOI 10.1103/PhysRevE.59.381 · Physical Review E

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Abstract

We perform numerical simulations of a kink-shaped soliton, a fluxon, propagating in arrays of Josephson junctions ordered according to the period-doubling sequence, the Fibonacci sequence, the paper-folding sequence, the Rudin-Shapiro sequence, and the Thue-Morse sequence. The equation of motion is the discrete sine-Gordon equation with additional terms describing dissipation and an injected bias current. With the use of an effective potential we explain the behavior of the fluxon when it gets pinned in different arrays. The potential also gives a qualitative understanding of the deviation of the velocity of a propagating fluxon compared with an earlier obtained formula. It turns out that the self-similarity of the underlying sequences is important for the detailed dynamics, but not for the speed of a propagating fluxon. Finally, we show how this effective potential can be used to arrange an array to have some desired properties.