Fractional Fluxon Dynamics in Long Josephson Junctions

In this thesis, I investigate the dynamics of fractional fluxons in two-gap Long Josephson Junctions (LJJs). Due to time reversal symmetry (TRS) breaking within the LJJ, a single fluxon may split into a bound pair of fractional fluxons, behaving as a sort of quasi-molecule. While fractionated, the fluxon pair is bound together by an interaction potential, which is repulsive at short distances, but attractive at longer distances, relatively speaking. In order to induce TRS breaking, an external bias potential and a pinning potential is introduced, representing an external current and a micro-resistance, into the initial equation of motion, the Double Sine-Gordon Equation (DSG). Using a software called freefem++, I simulate a LJJ with experimental parameters that allow for broken TRS, and so has fractional fluxon dynamics. After confirming fractional fluxons were present, I calculate the tunneling rate through the potential barrier for each fluxon. The tunneling rate was found to be in agreement with previous results for a single fluxon for the large fluxon, and not for the smaller fluxon.