DYNAMICS OF AN UNDERDAMPED JOSEPHSON-JUNCTION LADDER

We show analytically that the dynamical equations for an underdamped l adder of coupled small Josephson junctions can be approximately reduce d to the discrete sine-Gordon equation. As numerical confirmation, we solve the coupled Josephson equations for such a ladder in a magnetic field. We obtain discrete-sine-Gordon-Like IV characteristics, includi ng a flux how and a ''whirling'' regime at low and high currents, and voltage steps that represent a lock-in between the vortex motion and l inear ''phasons,'' and which are quantitatively predicted by a simple formula. At sufficiently high anisotropy, the fluxons on the steps pro pagate ballistically.