Dynamics of an underdamped Josephson-junction ladder.

We show analytically that the dynamical equations for an underdamped ladder of coupled small Josephson junctions can be approximately reduced 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, including a flux flow and a “whirling” regime at low and high currents, and voltage steps which represent a lock-in between the vortex motion and linear “phasons”, and which are quantitatively predicted by a simple formula. At sufficiently high anisotropy, the fluxons on the steps propagate ballistically. PACS numbers:74.40.+k, 74.50.+r, 03.20.+i, 05.45.+b, 85.25.C Typeset using REVTEX