VORTEX DYNAMICS IN CLASSICAL UNDERDAMPED JUNCTION ARRAYS

We study the response of an array of underdamped classical Josephson junctions when the phase configuration contains precisely one vortex. We first simulate the linear response of arrays to a small oscillating current and find, as a function of frequency, a well-defined resonance apart from the single-junction resonance. When a dc current is applied, in addition to the small ac current, the resonance is seen to split into two separate peaks. Next, we analyze the full set of evolution equations and show that the response of the array under these conditions is represented very well by a set of three linear equations. With zero dc current we obtain an analytical estimate of the resonance frequency. The reduced set also reflects, but underestimates, the splitting into two resonances, in an additional dc current. Finally, we extend the approach to nonlinear response to extract one differential equation for the motion of the vortex out of the complete set of equations describing the dynamics of the array.