Fluxon trapping by inhomogeneities in long Josephson junctions

Following the approach of collective coordinates for the location X(t), and speed U(t), of a fluxon travelling in a long Josephson junction (LJJ), we show that the conditions of fluxon trapping by an array of N point-like inhomogeneities are determined by the relative location of the separatrices of N unstable fixed points in the U,X phase plane. In the particular case of experimental interest in which the inhomogeneities are “microresistors” , we find specific parameter values and initial conditions such that each “microresistor” will trap one fluxon thus turning the LJJ into a quantum flux ‘shuttle’. We also solve for the same parameter values, the corresponding PDE numerically and verify the validity of the results obtained by the ODE's of the collective coordinate approach.