Holographic superfluid ring with a weak link

We explore the generation of topological defects in the course of a dynamical phase transition in a ring with a weak link, i.e., a SSS Josephson junction, from the AdS/CFT correspondence. By setting different parameters of the junction (width, steepness, depth) and the final temperature of the quench, the configurations of the charge density and condensate of the order parameters of the dual field theory are presented. Meanwhile, we observe that in the final equilibrium state, variations in parameters of the junctions only affect the configurations of the charge density and condensate of the order parameters, without altering their values outside the junction. However, variations in the final temperature will directly affect the values of the charge density and condensate of the order parameters outside of the junction. Moreover, in the final equilibrium state, we propose an analytic relation between the gauge-invariant velocity in the two superconducting states in the SSS Josephson junction, which agrees well with the numerical results.