We consider quantum phase transitions with global symmetry breakings that result in the formation of topological defects. We evaluate the number densities of kinks, vortices, and monopoles that are produced in $d=1,2,3$ spatial dimensions respectively and find that they scale as $t^{-d/2}$ and evolve towards attractor solutions that are independent of the quench timescale. For $d=1$ our results apply in the region of parameters $\lambda \tau/m \ll 1$ where $\lambda$ is the quartic self-interaction of the order parameter, $\tau$ is the quench timescale, and $m$ the mass parameter.

中文翻译：

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拓扑缺陷的量子形成

我们考虑具有全局对称性破坏的量子相变，这导致拓扑缺陷的形成。我们评估了分别在 $d=1,2,3$ 空间维度中产生的扭结、涡旋和单极子的数量密度，发现它们按 $t^{-d/2}$ 缩放，并朝着吸引子解决方案发展与淬灭时间尺度无关。对于 $d=1$，我们的结果适用于参数 $\lambda \tau/m \ll 1$ 的区域，其中 $\lambda$ 是阶次参数的四次自相互作用，$\tau$ 是淬灭时间尺度，和 $m$ 质量参数。