拓扑缺陷、内在结构和超一致性
Topological Defects, Inherent Structures, and Hyperuniformity
摘要：
无序超均匀系统是一种奇异的物质状态，它完全抑制了像晶体一样的大尺度密度波动，但没有像液体或玻璃那样的布拉格峰。这类系统已经在各种平衡和非平衡物理和生物系统中被发现，并且通常被赋予新的物理性质。与非平衡系统中无序超均匀性的出现相关的机制，特别是固有结构，往往没有得到很好的理解，我们将在这项工作中从拓扑的角度来解决。具体来说，我们考虑一类具有代表性的无序的固有结构，它是通过不断引入随机分布的拓扑缺陷（位错和向错）经常看到在胶体系统和原子尺度的二维材料。我们证明，这些固有的结构可以被看作是拓扑变体的有序超均匀状态（如晶体）连接通过连续的拓扑变换路径，显着保持超均匀性。此外，我们开发了一个连续介质理论来证明，这些固有结构中的大尺度密度波动主要是由拓扑缺陷，在低缺陷浓度下，可以近似为与每个单独的缺陷（应变源）相关的位移场的叠加导致的弹性位移场占主导地位。我们严格证明，超均匀性，只要与位移场的某些条件得到满足。我们的研究结果还突出了解耦的位置自由度的振动自由度时，寻找无序超均匀性的重要性，因为超均匀性往往掩盖了热波动。
英文摘要：
Disordered hyperuniform systems are exotic states of matter that completely suppress large-scale density fluctuations like crystals, and yet possess no Bragg peaks similar to liquids or glasses. Such systems have been discovered in a variety of equilibrium and non-equilibrium physical and biological systems, and are often endowed with novel physical properties. The mechanisms associated with the emergence of disordered hyperuniformity in nonequilibrium systems, in particular inherent structures are often not well understood, which we will address from a topological perspective in this work. Specifically, we consider a representative class of disordered inherent structures which are constructed by continuously introducing randomly distributed topological defects (dislocations and disclinations) often seen in colloidal systems and atomic-scale two-dimensional materials. We demonstrate that these inherent structures can be viewed as topological variants of ordered hyperuniform states (such as crystals) linked through continuous topological transformation pathways, which remarkably preserve hyperuniformity. Moreover, we develop a continuum theory to demonstrate that the large-scale density fluctuations in these inherent structures are mainly dominated by the elastic displacement fields resulted from the topological defects, which at low defect concentrations can be approximated as superposition of the displacement fields associated with each individual defect (strain source). We rigorously demonstrate that hyperuniformity is preserved as long as certain conditions associated with the displacement fields are met. Our results also highlight the importance of decoupling the positional degrees of freedom from the vibrational degrees of freedom when looking for disordered hyperuniformity, since the hyperuniformity property is often cloaked by thermal fluctuations.
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