Kibble-Zurek mechanism and current-phase relation in a holographic Josephson junction

We present a comprehensive study of the current-phase relation of the Josephson junction in a holographic superfluid ring, realized from the stochastic and non-equilibrium dynamics according to the Kibble-Zurek mechanism. By employing a spatially modulated charge density to engineer a weak link, the current-phase relation is investigated in a range of geometric and thermodynamic parameters. The seminal sinusoidal relation between the current and the phase emerges periodically due to the compact shape of the geometry. We also identify the relations between the critical current and the geometric parameters of the junction: the width, steepness and depth. Furthermore, we demonstrate that the critical current exhibits a characteristic exponential decaying against the final temperature, reflecting the thermal degradation of the order parameter in a strong-coupling regime. Our results establish a robust framework for holographic Josephson devices, offering experimentally testable predictions for the non-equilibrium dynamics of high-T_c superconductors.