Vortex dynamics in a Josephson junction array by using the time-dependent vorticity-vorticity correlation function

We have studied numerically the motion of vortices in an underdamped Josephson junction array, especially in the presence of a magnetic field of 1/5 flux quantum per plaquette. Such a magnetic field density provides a square vortex lattice that has a lattice constant of √(5)a, where a is the plaquette length of the array. For a ratchet array, we use both alternate critical currents and alternate inter-capacitances along the direction of vortex flow. To analyze the dynamics of several vortices around a mid row of the array, we use the time-dependent vorticity-vorticity correlation function as well as the time-dependent vorticity. The vortices on a fractional Shapiro n/5-step are found to move through n plaquettes transversely to the direction of the applied current during a single ac cycle.