Nonequilibrium critical dynamics of a Kosterlitz-Thouless-transition

利用二维的胶体系综，我们将研究拓扑缺陷的形成，同时通过连续的相变使系统远离热平衡。二维（2D）单晶的平衡熔化由著名的kosterlitz - thoulless - 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秩序。对于kthny理论预测的定义明确的连续相变，熔化和冻结应该是可逆的，并且与材料的历史无关。然而，事实并非如此，正如我们最近在以前的工作中所证明的那样，时间反转并没有实现。各向同性二维流体永远不会冻结成单晶，但如果以非零速率冷却，则会变成高度多晶。我们观察到对称性破缺不会在全局发生，缺陷被冻结。此外，我们表明我们的观察支持慢（线性）冷却速率的kibble - zurek机制（KZM）。基布尔-祖雷克机制最初是由汤姆·基布尔提出的，用来描述在大爆炸后不久由于早期宇宙膨胀而冷却的原始希格斯场的缺陷密度。在空间中距离足够远的区域，它们甚至不能以光速通信，也不能在自发对称性破缺时获得相同的序参量。W. Zurek把这个想法转移到凝聚态物质和量子流体上。由于冷却过程中序参量波动的临界慢化（相关时间趋于无穷大），系统必须脱离平衡，单极子和晶界等缺陷被纳入低温相。我们将用微米大小的超顺磁粒子的胶体单层来研究这些现象，这些粒子进行布朗运动并且被限制在一个绝对平坦的界面上。与“真实的”原子不同，粒子足够大，速度足够慢，可以很容易地用视频显微镜在任何相关的时间尺度上对单个粒子水平进行监测。由于它们的超顺磁性，我们可以在时间尺度上淬灭我们的系综，比布朗时间（~ sec）给出的最短内在时间尺度快几个数量级。在原子系统中，这个时间小于10^-10秒，另外，热通量是有限的。胶体在无与伦比的快速时间尺度上的冷却速率是可能的，进入一个在凝聚态物质中几乎无法进入的时间区域，而在原始希格斯场中则严格无法进入。对于超快淬火，我提出了不依赖于淬火后过冷的畴尺寸分布。相反，与成核形成强烈对比的是，它将取决于淬火前的序参量波动和局部对称性破缺的早期阶段。

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.