Phase retrapping in a pointlike $\phi$ Josephson junction: the Butterfly effect

Abstract

We consider a $\phi$ Josephson junction, which has a bistable zero-voltage state with the stationary phases $\psi =\pm \phi$. In the non-zero voltage state the phase "moves" viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well ($-\phi$ or $+\phi$) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to zero-voltage state. In the limit of low damping the $\phi$ Josephson junction exhibits a butterfly effect --- extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

References in corpus (3)

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