标题： 三维O(2)模型中拓扑缺陷的非平衡动力学 显示英文标题

标题： Non-equilibrium dynamics of topological defects in the 3d O(2) model

摘要： 我们研究了三维格点上的 O(2) 非线性 $\sigma$-模型，该模型以涡旋的形式表现出拓扑缺陷。 这些缺陷倾向于组织成类似全局宇宙弦的涡旋线。因此，此模型用作研究拓扑缺陷动力学的测试平台。 它经历的是二阶相变，因此适用于研究 Kibble-Zurek 机制。 在此背景下，我们探讨当温度从临界温度以上快速降低到以下时拓扑缺陷的持久性；这种冷却（或“淬火”）过程使系统脱离平衡。 我们通过广泛的逆冷却速率 $\tau_{\rm Q}$和最终温度，使用不同的蒙特卡洛算法进行探测。 结果一致表明，持久拓扑缺陷的密度遵循 $\tau_{\rm Q}$的幂律，与 Zurek 的猜想一致。 另一方面，目前我们的结果并未证实此幂律中指数的 Zurek 预测值，但对其最终检验仍在进行中。 显示英文摘要

摘要： We present a study of the 3d O(2) non-linear $\sigma$-model on the lattice, which exhibits topological defects in the form of vortices. They tend to organize into vortex lines that bear close analogies with global cosmic strings. Therefore, this model serves as a testbed for studying the dynamics of topological defects. It undergoes a second order phase transition, hence it is appropriate for investigating the Kibble-Zurek mechanism. In this regard, we explore the persistence of topological defects when the temperature is rapidly reduced from above to below the critical temperature; this cooling (or "quenching") process takes the system out of equilibrium. We probe a wide range of inverse cooling rates $\tau_{\rm Q}$ and final temperatures, employing distinct Monte Carlo algorithms. The results consistently show that the density of persisting topological defects follows a power-law in $\tau_{\rm Q}$, in agreement with Zurek's conjecture. On the other hand, at this point our results do not confirm Zurek's prediction for the exponent in this power-law, but its final test is still under investigation.