Nonequilibrium critical dynamics of a Kosterlitz-Thouless-transition

Kosterlitz-Thouless 转变的非平衡临界动力学

• 批准号: 408261333
• 负责人: Dr. Peter Keim
• 金额: --
• 依托单位: Abteilung Dynamik komplexer Fluide
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/408261333?language=en
• 关键词: Nonequilibrium; critical; dynamics; Kosterlitz; Thouless

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.

使用二维胶体系综，我们将研究拓扑缺陷的形成，同时通过连续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-Thouless-Halperin-Nelson-Young 情景（KTHNY 理论）描述。在该理论中，热激活拓扑缺陷的解离破坏了位置和方向顺序。对于 KTHNY 理论预测的明确的连续相变，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，正如我们最近在之前的工作中所证明的那样，时间反转并未实现。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，对称性破缺不会全局发生，并且缺陷被冻结。此外，我们的观察结果支持缓慢（线性）冷却速率的基布尔-祖雷克机制（KZM）。基布尔-祖雷克机制最初由汤姆基布尔开发，用于描述大爆炸后不久因早期宇宙膨胀而冷却的原始希格斯场的缺陷密度。在空间中分离得足够远的区域，即使以光速也无法通信，在自发对称破缺期间无法获得相同的有序参数。 W. Zurek 将这个想法转移到凝聚态物质和量子流体上。由于冷却过程中有序参数波动的严重减慢（相关时间趋于无穷大），系统必须失去平衡，并且单极子和晶界等缺陷会被纳入低温相中。我们将使用微米级超顺磁颗粒的胶体单层来研究这些现象，这些颗粒执行布朗运动并被限制在绝对平坦的界面中。与“真实”原子不同，粒子很大且速度足够慢，可以在任何相关时间尺度上轻松地通过视频显微镜在单粒子水平上监测它们。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（〜秒）给出的最短内在时间尺度快几个数量级。在原子系统中，这个时间< 10^-10秒，而且热通量受到限制。对于胶体来说，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，并且在原始希格斯场中严格无法进入。对于超快淬火，我建议域尺寸分布不依赖于淬火后的过冷。相反，与成核形成强烈对比的是，它将取决于淬火之前的有序参数波动和局部对称性破缺的早期阶段。