Quench dynamics of the three-dimensional U(1) complex field theory: Geometric and scaling characterizations of the vortex tangle.
Quench dynamics of the three-dimensional U(1) complex field theory: Geometric and scaling characterizations of the vortex tangle.
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三维 U(1) 复场论的淬灭动力学：涡旋缠结的几何和尺度表征。
DOI：
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发表时间：
2016
影响因子：
2.4
通讯作者：
L. Cugliandolo
中科院分区：
文献类型：
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作者：
Michikazu Kobayashi;L. Cugliandolo
我们详细研究了三维U(1)不变相对论复场理论的平衡性质和随机动态演化。这个模型已经被用来在不同的极限下描述有限化学势的相对论玻色子的性质、第二类超导体、磁性材料和宇宙学的各个方面。我们用不同的方法表征了热力学二阶相变。我们研究了平衡涡的构型及其在所有温度下的统计和几何性质。结果表明，在很高的温度下，细丝的统计为全填充环模型。我们确定了在有序相中，涡长的数密度以代数方式下降的温度，并将其与几何渗流转变联系在一起，我们用各种方法表征了这一转变。在此阈值下，我们测量了涡旋缠绕的分维性质。接下来，我们从无序相中的平衡开始，穿过热力学临界点，深入有序相，执行无限速率淬火。我们发现可以区分三个时间域：第一种方法是在数值精度上与渗流阈值下的状态有许多相同的特征；第二种是粗化过程，它在足够低的温度下不会改变长涡环的分形性质；以及最后一种方法是达到平衡。这些特征与用于构建涡线的重连规则无关。在这些区域中的每一个区域，我们确定了系统中涡旋的不同长度尺度。我们还研究了有序化过程的标度性质和拓扑缺陷的渐近湮灭，证明了随时间演化的涡旋纠缠可以在动态标度框架内描述。
We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II superconductors, magnetic materials, and aspects of cosmology. We characterize the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls off algebraically and we associate it to a geometric percolation transition that we characterize in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermodynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach toward a state that, within numerical accuracy, shares many features with the one at the percolation threshold; a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops; and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.
影响因子：
8.6
作者：
P. Walmsley;A. Golov
通讯作者：
P. Walmsley;A. Golov
随机量化可以避免符号问题吗？
影响因子：
8.6
作者：
Aarts G
通讯作者：
Aarts G