论文标题
边界条件在跨越连续过渡后的拓扑缺陷的完整计数统计中的作用
Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition
论文作者
论文摘要
在有限时间内自发对称性破裂的情况下，拓扑缺陷以密度生成，并根据Kibble-Zurek机构（KZM）随着驾驶时间的规模而定。超出KZM以外的通用性的签名最近已揭幕：拓扑缺陷的数量分布已显示出二项式分布，其中所有累积物都以淬火率继承了通用的幂律缩放，而累积的口粮是恒定的。在这项工作中，我们分析了边界条件在拓扑缺陷统计中的作用。特别是，我们考虑了一个晶格系统，该晶格系统具有最近的邻居相互作用，受到了由能量惩罚项实施的软抗周期，开放和周期性的边界条件。我们表明，对于快速和中等的淬火，扭结数分布的累积物具有一个通用缩放，除了通过添加剂术语以外，它独立于边界条件，这在慢速淬灭的极限中变得突出，从而导致幂律行为的破坏。我们使用晶格上的一维标量理论来测试理论预测。
In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft anti-periodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except by an additive term, that becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.
