标题： 四维量子涡旋与湍流的非平衡动力学和普适性 显示英文标题

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

摘要： 量子涡旋的研究为理解不同物理系统中的非平衡动力学提供了关键见解。 虽然先前的研究集中在二维点状涡旋和三维线状涡旋上，但四维空间中的量子涡旋预计会呈现扩展的涡旋面形式，从而从根本上丰富动力学。 在这里，我们对四维量子涡旋和湍流进行了全面的数值研究。 使用一种特殊的可视化方法，我们发现了在低维度中不存在的拓扑数衰减现象，以及涡旋重新连接过程的高维对应物。 我们进一步探索了四维相变中的淬火动力学，并验证了高维Kibble-Zurek机制的适用性。 我们的模拟为四维量子湍流提供了数值证据，其特征是普遍幂律行为。 这些发现揭示了高维拓扑缺陷所遵循的普遍原则，为未来利用合成维度的实验实现提供了见解。 显示英文摘要

摘要： 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.