Dynamics of charge solitons in 1-D arrays of Josephson junctions

A 1-D array of Josephson coupled superconducting grains whose kinetic inductance dominates over the Josephson inductance is studied. We show that in this limit excess Cooper pairs in the array give rise to charge solitons via polarization of the grains. We analyze the dynamics of these macroscopic topological excitations, and find that their classical relativistic motion leads to saturation branches in the I-V characteristic of the array. When the dephasing length of the charge soliton is larger than the length of the array, we expect that it behaves quantum mechanically. We study the dynamics of quantum charge solitons in a ring-shaped array biased by an external flux, and show that they can exhibit phenomena like persistent current and coherent current oscillations.