Vortex dynamics in classical Josephson junction arrays: models and recent experimental developments

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Abstract
This review deals with the recent progress achieved in the understanding of vortex dynamics in discrete arrays of classical Josephson junctions, JJAs. We first give an up-to-date overview of the discrete models currently used to describe the physics of JJAs: the `JJ array formalism', the discretized version of the sine-Gordon equation and the Frenkel-Kontorova model. Special emphasis is put on the recent reformulation of the screening term that makes use of the full-inductance matrix. The relationship between the phase and the vortex-particle dynamics is also discussed. An overview of the `state of the art' in the understanding of the single-vortex dynamics in overdamped JJAs follows; the dependence of the motion of the vortex on its size (i.e. on the screening strength, the sample geometry and the coupling anisotropy, ) and, also, on the bias current is pointed out and discussed. A peculiar phenomenon, alternate-vortex motion, is also briefly illustrated. Subsequently, we review the single-vortex dynamics in underdamped JJAs. A short description of the conditions that lead to the observation of anomalous dissipation, vortex reflection, ballistic vortex motion, resonances, instabilities and row switching is given. To conclude, we discuss open problems and future perspectives of the research on JJAs.

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