Exploration of fractional effects and a non-sinusoidal current-phase relation in Josephson junction arrays
Marissa CondonPurpose
The paper aims to provide a numerical exploration of the effect of fractional spatial derivatives and a non-sinusoidal current-phase relation for systems modelled using sine-Gordon equations and, in particular, Josephson junction parallel arrays.
Design/methodology/approach
The effect of fractional derivatives is examined for single, double and triple sine-Gordon equations. This is then extended to the Josephson junction array model. In addition, the effect of a non-sinusoidal current-phase model is examined. The effect on an initial spatial distribution with no input is considered and subsequently analysis with an input current is examined.
Findings
The findings indicate that higher-order harmonics can result in non-monotonic behaviour or an oscillation for the case of an initial spatial distribution. Similarly, fractional spatial derivatives introduce an oscillation and result in non-monotonic behaviour. The incorporation of additional harmonics affects the response of the Josephson array system, which can have consequences in relation to signal detection. Fractional derivatives affect the damping of the response of the system.
Originality/value
The paper is original in investigating the combination of fractional spatial derivatives and a non-sinusoidal current-phase relation for a Josephson junction parallel array.