Nonequilibrium critical dynamics of a Kosterlitz-Thouless-transition

使用二维胶体系综，我们将通过连续的相变，研究当推动系统远离热平衡时，拓扑缺陷的形成。二维(2D)单晶的平衡熔化由著名的Kosterlitz-Thouless-Halperin-Nelson-Young情景(KTHNY理论)描述。在这个理论中，热激活的拓扑缺陷的解离破坏了位置和取向的顺序。对于KTHNY理论所预言的明确定义的连续相变，熔融和冻结应该是可逆的，并且与材料的历史无关。然而，情况并非如此，时间反转没有实现，正如我们最近在以前的工作中所展示的那样。各向同性的二维流体永远不会冻结成单晶，但如果以非零速率冷却，它会变成高度多晶的。我们观察到对称破缺并不是在全球范围内发生的，缺陷被冻结在内部。此外，我们的观测结果支持慢(线性)冷却速率的Kibble-Zurek机制(KZM)。Kibble-Zurek机制最初是由Tom Kibble发展起来的，用于描述原始希格斯场在大爆炸后不久被早期宇宙膨胀冷却时的缺陷密度。在空间中相隔足够远的区域，即使在光速下也无法交流，在自发对称破缺时，它们无法获得相同的序参数。W.Zurek将这个想法转移到了凝聚态物质和量子流体上。由于冷却过程中序参数涨落的临界减慢(关联时间趋于无穷大)，系统必然失去平衡，并且单极子和晶界等缺陷被合并到低温相中。我们将用微米级超顺磁性粒子的胶体单分子膜来研究这些现象，这些粒子执行布朗运动，并被限制在绝对平坦的界面上。与“真正的”原子不同，粒子足够大，速度也足够慢，可以很容易地在任何相关的时间尺度上用视频显微镜在单个粒子水平上进行监测。由于它们的超顺磁性，我们可以在时间尺度上猝灭我们的系综，比布朗时间(~秒)给出的最短内在时间尺度快几个数量级。在原子系统中，这一时间是&lt；10^-10秒，而且热流是有限的。对于胶体，在无与伦比的快速时间尺度上的冷却速率是可能的，进入在凝聚态物质中几乎不能到达的时间区域，在原始希格斯场中严格地不能到达的时间区域。对于超快猝灭，我建议磁区尺寸分布不依赖于猝灭后的过冷。相反，与形核形成强烈对比的是，它将取决于猝灭前的序参数涨落和局部对称性破缺的非常早期阶段。

Using a colloidal ensemble in two dimensions, we will investigate the formation of topological defects while pushing the system far from thermal equilibrium through a continuous phase transition.In equilibrium melting of two-dimensional (2D) mono-crystals is described by the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young scenario (KTHNY-Theory). In this theory the dissociation of thermally activated topological defects destroys positional and orientational order. For a well-defined continuous phase transitions as predicted by KTHNY-theory, melting and freezing should be reversible and independent of the history of the material. However, this is not the case and time reversal is not fulfilled as we demonstrated recently in previous work. An isotropic two-dimensional fluid never freezes into a mono-crystal but becomes highly poly-crystalline if cooled with a non-zero rate. We observed that symmetry breaking does not happen globally and defects are frozen in. Moreover, we showed that our observation support the Kibble-Zurek-mechanism (KZM) for slow (linear) cooling rates.The Kibble-Zurek mechanism was originally developed by Tom Kibble to describe the defect density of the primordial Higgs-field while cooled by expansion of the early universe shortly after Big Bang. Regions being separated far enough in space, such that they cannot communicate even with the speed of light, cannot gain the same order-parameter during spontaneous symmetry breaking. W. Zurek transferred the idea to condensed matter and quantum fluids. Due to critical slowing down of order parameter fluctuations during cooling (correlation times tend to infinity), the system must fall out of equilibrium and defects like monopoles and grain boundaries are incorporated into the low temperature phase.We will investigate those phenomena with a colloidal monolayer of micrometer sized super-paramagnetic particles, which perform Brownian motion and are confined to an absolutely flat interface. Unlike “real” atoms, particles are large AND slow enough that they can easily be monitored with video-microscopy on single particle level at any relevant time scale. Due to their super-paramagnetism we can quench our ensembles on times scales, orders of magnitudes faster than the shortest intrinsic time scale given by the Brownian time (~ sec). In atomic systems this time is < 10^-10sec and additionally the heat flux is limited. Cooling rates on unrivalled fast time scales are possible for colloids, entering a time region practically inaccessible in condensed matter and strictly inaccessible in the primordial Higgs-field.For ultrafast quenches I propose the domain-size distribution not to depend on the super-cooling after the quench. Instead, in strong contrast to nucleation, it will depend on the order-parameter fluctuations before the quench and the very early stage of local symmetry breaking.