Numerical analysis of small charge solitons in 1D arrays of Josephson junctions

We investigate numerically a one-dimensional array of Josephson junctions in the regime of small charge solitons, ΛEJ > EC > EJ. Here EC and EJ are the charging and the Josephson energies of the junction, respectively, and Λ is the bare screening length (measured in number of junctions). Our investigation is based on a many-body tight binding approach. We have developed an efficient algebraic method which allowed us to take into account many charge states and confirm i) the flattening of the dispersion relation in the outer region of the Brillouin zone; ii) the broadening of the soliton in the flat band regime.