Dynamical Simulation On The Josephson-junction Array With Random Phase-shift

In this thesis, using dynamic scaling theory, we numerically investigate the two-dimensional XY model with random phase-shift. First, we have analyzed the direct-current Josephson affection, alternating-current Josephson affection and the interaction between Josephson affection and magnetic field. And then we have analyzed the transition in JJA model with uniform disorder. What's more, we have compared those results with earlier works. Finally, we have investigated the transition JJA model with random phase-shift. In the random phase-shift system, we have simplified it into the resistively shunted junction (RSJ) form. Under the fluctuation twist boundary condition, we have investigated the dynamic transition with different disorder strengths by the dynamic scaling theory and also we turn to the depinning transition at zero temperature and creep motion of various at low temperature for different disorder strengths. By the scaling analysis, we can obtain more accurate critical force and dynamic critical exponent.The main results of each part are as follows:(1) For the two-dimensional Josephson arrays exposed to the uniform disorder. In the weak disorder region, the system undergoes a KTB phase transition type. In the stronger disorder region, it follows the non-KTB phase transition type. We used the scaling theory, providing further evidence for existence of non-KTB phase, possibly glass phase. What's more, the dynamic exponents are close to previous results for simulation of Monte Carlo, verifying our methods and model are correct. And then, we studied the two-dimensional Josephson arrays dynamic simulation with Gauss disorder type. The results are similar with the uniform type. In weak disorder region, the system exposed to the KTB transition type and a non-KTB transition is also observed in the stronger disorder region. By the scaling theory, the critical current decrease as the disorder strength by dynamic scaling theory.(2) For the two-dimensional Josephson arrays with random phase-shift, we turn to the depinning transition at zero temperature and the creep motion of vortices at low temperatures. By the dynamic scaling, we can get to the dynamic exponents and critical currents. Whether the disorder is weal or strong, a continuous depinning transition is found at zero temperature and creeping law is observed at low temperatures. What's more, the critical currents decrease as the disorder strength, illustrating the disorder affection the vortices'motion. In the medium strong disorder region, the scaling type meet the non-Arrhenius creeping law at low temperature, but in strong disorder region Arrhenius creeping law. However, all of those creeping equation satisfied with the exponent type, which are close to the previous result.