Non-equilibrium Dynamics and Universality of 4D Quantum Vortices and Turbulence

The study of quantum vortices provides critical insights into non-equilibrium dynamics across diverse physical systems. While previous research has focused on point-like vortices in two dimensions and line-like vortices in three dimensions, quantum vortices in four spatial dimensions are expected to take the form of extended vortex surfaces, thereby fundamentally enriching dynamics. Here, we conduct a comprehensive numerical study of 4D quantum vortices and turbulence. Using a special visualization method, we discovered the decay of topological numbers that does not exist in low dimensions, as well as the high-dimensional counterpart of the vortex reconnection process. We further explore quench dynamics across phase transitions in four dimensions and verify the applicability of the higher-dimensional Kibble-Zurek mechanism. Our simulations provide numerical evidence of 4D quantum turbulence, characterized by universal power-law behavior. These findings reveal universal principles governing topological defects in higher dimensions, offering insights for future experimental realizations using synthetic dimensions.