Collaborative Research: Unified Field Theory of Soft Amorphous Solids

非技术概述从谷物的集合到蛋白质、胶体或聚合物的聚集体，软固体具有各种结构并表现出广泛的物理响应。它们往往存在于机械稳定性的边缘，这导致了它们在应用中的适应性。例子包括玻璃、水泥、压实沙，甚至酸奶或巧克力慕斯。该奖项支持专注于软固体物理学的理论和计算研究和教育，目的是开发和测试软固体动力学的新理论框架。与晶体不同，软固体的结构一般不表现出任何有序性。因此，它们的机械响应不能用定义晶体行为的对称性破坏和长程有序的传统范式来描述。传统的弹性理论建立在动量(力学平衡)和能量守恒原理的基础上，由此产生了图案的对称性、序参数、几何和拓扑。边缘软固体中没有能量守恒，在那里耗散或活跃的过程可以发挥作用，使这些理论无效。在这里提出的新框架中，守恒原理就是从力学平衡的约束中产生的。这种方法提供了一种自然的方法，结合了软固体固有的应力和结构重排之间的耦合，这在现有的理论中是缺失的，以构建具有应力场和变形场中的非均匀的非晶态材料的有效场论。PI将作为榜样，通过促进宣传活动，交流和讨论理论是如何建立的，它们如何与现象和实验相联系，以及理论家发展哪些具体技能，来激励更多不同的学生学习理论凝聚态物理。推广活动还将向K-12学生和普通公众传播凝聚态物理的兴奋。技术总结该奖项支持旨在了解无定形软固体(如果酱颗粒、凝胶，甚至生物组织)中结构与功能关系的研究和教育。越来越清楚的是，从力学平衡的约束中出现的局域化的、次维的应力模式，决定了广泛的软物质的非平衡力学响应。次维激发也出现在张量规范理论中，张量规范理论是最近发展起来的一类用于量子自旋液体的场论。最近发现的张量规范理论到无定形固体力学的严格映射构成了拟议研究的基础。这种映射有可能解决应力如何传递以及为什么它们在柔软的无定形固体中局部化的问题。在非晶态系统中，一个突出的挑战是识别区分不同应力承载状态的序参数。值得注意的是，序参数的缺乏也是量子自旋液体的一个特征，在量子自旋液体中，诸如缠绕数之类的拓扑指数可以区分状态。对于机械结构，拓扑力学提供了一个可以准确做到这一点的索引。有趣的是，软物质的弹性理论和量子自旋液体的张量规范理论是出现在某种粗粒化水平上的场论，而拓扑力学明确地考虑了机械约束在其中运行的网络结构，这表明拓扑力学可能是建立起软非晶材料中起作用的微观力学约束和适当的张量规范理论框架之间联系的正确工具。理论和数值模拟的结合将被用来探索张量规范理论产生的新范式对软非晶材料的影响，并建立这种连续统理论和拓扑力学之间的联系，拓扑力学提供了非晶态固体在外部应力下维持和演化的能力的网络特有的描述。考虑到软无定形固体的普遍存在，其力学响应的统一场论将对软凝聚态物理以及与之相关的材料科学、化学和结构工程的应用学科产生变革。这项合作将开发新的计算工具来补充和告知理论，并确定新的实验测试。理论和仿真之间的反馈将体现在博士后、研究生和本科生的研究培训中。通过张量规范理论的共享框架在软硬凝聚态物理之间建立的桥梁为软硬凝聚态物理之间的界面培训提供了新的机会。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical summaryFrom collections of grains to aggregates of proteins, colloids or polymers, soft solids have a variety of structures and exhibit a broad range of physical response. They often exist at the margin of mechanical stability, which leads to the adaptability exploited in their applications. Examples include glass, cement, compacted sand, and even yogurt or chocolate mousse. This award supports theoretical and computational research and education focused on the physics of soft solids, with the objective to develop and test a new theoretical framework for their dynamics. Distinct from crystals, the structures of soft solids, generically, do not exhibit any order. Therefore, their mechanical response cannot be described by the conventional paradigm of broken symmetry and long-range order that define the behavior of crystals. Conventional elasticity theories are built on principles of momentum (mechanical equilibrium) and energy conservation, from which symmetries, order parameters, geometry and topology of patterns emerge. The absence of energy conservation in marginal soft solids, where dissipative or active processes can be at play, invalidates these theories. In the new framework proposed here, conservation principles emerge from just the constraints of mechanical equilibrium. This approach provides a natural way of incorporating the coupling between stress and structural rearrangements inherent in soft solids, which is missing in existing theories, to construct an effective field theory for amorphous materials with heterogeneities in stress and deformation fields. The PIs will engage as role models to inspire a more diverse population of students to theoretical condensed matter physics by promoting outreach activities that communicate and discuss how theories are built, how they connect to phenomena and experiments, and what specific skills theorists develop. Outreach activities will also disseminate the excitement of condensed matter physics to K-12 students and the general public.Technical SummaryThis award supports research and education aimed at understanding the structure-function relationship in amorphous soft solids such as jammed grains, gels, and even biological tissues. It has become increasingly clear that localized, sub-dimensional, stress patterns emerging from the constraints of mechanical equilibrium, determine the non-equilibrium mechanical response of a wide range of soft matter. Sub-dimensional excitations have also emerged in tensor gauge theories, a class of field theories recently developed for quantum spin liquids. A recently discovered rigorous mapping of such a tensor gauge theory to mechanics of amorphous solids forms the basis of the proposed research. This mapping has the potential to solve the problem of how stresses get transmitted and why they localize in soft, amorphous solids. An outstanding challenge in amorphous systems is identifying an order parameter that distinguishes between different stress-carrying states. Remarkably, the absence of an order parameter is also a feature of quantum spin liquids, where topological indices such as winding numbers can distinguish between the states. For mechanical structures, topological mechanics provides an index that can do precisely that. Interestingly enough, the elasticity theories of soft matter and tensor gauge theories for quantum spin liquids are field theories that emerge at some level of coarse-graining, whereas topological mechanics explicitly takes into account the network architecture in which the mechanical constraints operate, suggesting that topological mechanics may be the right tool to establish the connection between the microscopic mechanical constraints at play in soft amorphous materials and the appropriate tensor gauge theory framework. A combination of theory and numerical simulations will be used to explore the implications of a new paradigm emerging from tensor gauge theory for soft amorphous materials, and establish connections between this continuum theory and topological mechanics, which provides a network-specific description of the ability of amorphous solids to sustain and evolve under external stresses. Given the ubiquitous presence of soft amorphous solids, a unified field theory of their mechanical response will be transformative for soft condensed matter physics, and the associated applied disciplines of materials science, chemical and structural engineering. The collaboration will develop new computational tools to complement and inform theory and identify new experimental tests. The feedback between theory and simulations will be reflected in the research training of postdocs, graduate and undergraduate students. The bridge created between soft and hard condensed matter physics through the shared framework of tensor gauge theories offers new opportunities for training at the interface between soft and hard condensed matter physics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.