Transport dynamics with alternate Cooper-pair and quasiparticle tunnelings in one-dimensional charge Josephson arrays

For a single weak-coupled Josephson junction, stochastic Cooper-pair tunnelings drive the superconducting current on low voltage biases, while quasiparticle tunnelings stimulate the normal current on high biases above the superconducting gap voltage. Considering these interactive dynamics simultaneously in one-dimensional weak-coupled Josephson arrays in electrodynamic environments, the theoretical work by rate equations is structured herein, and the charge transport associated with short-range (Cooper pair and quasiparticle) and long-range (Cooper-pair soliton and quasiparticle soliton) behaviors is analyzed.