Collaborative Research: Unified Field Theory of Soft Amorphous Solids

从颗粒的集合到蛋白质、胶体或聚合物的聚集体，软固体具有多种结构，并表现出广泛的物理反应。它们通常存在于机械稳定的边缘，这导致了它们在应用中被利用的适应性。例如玻璃、水泥、压实的沙子，甚至酸奶或巧克力慕斯。该奖项支持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，软固体的结构通常没有任何秩序。因此，它们的力学响应不能用定义晶体行为的破缺对称性和长程有序的传统范式来描述。传统的弹性理论是建立在动量（力学平衡）和能量守恒原理的基础上的，从中产生了图案的对称性、有序参数、几何和拓扑。在边缘软固体中，能量守恒的缺失，耗散或活性过程可以发挥作用，使这些理论无效。在这里提出的新框架中，守恒原理仅仅是从力学平衡的约束中产生的。该方法提供了一种结合现有理论所缺失的软固体中固有的应力和结构重排之间耦合的自然方法，以构建具有非均质应力场和变形场的非晶态材料的有效场理论。pi将作为榜样，通过促进交流和讨论理论是如何建立的，它们如何与现象和实验联系起来，以及理论家发展的具体技能，来激励更多不同群体的学生学习理论凝聚态物理。外展活动还将向K-12学生和公众传播凝聚态物理的兴奋。该奖项支持旨在理解非晶软固体（如堵塞颗粒、凝胶甚至生物组织）中结构-功能关系的研究和教育。越来越清楚的是，局部的、次维的、从力学平衡约束中出现的应力模式，决定了广泛软物质的非平衡力学响应。次维激励也出现在张量规范理论中，这是最近为量子自旋液体发展起来的一类场论。最近发现的这种张量规范理论到非晶固体力学的严格映射形成了提出的研究的基础。这种映射有可能解决应力是如何传播的问题，以及它们为什么会在柔软的无定形固体中定位。在非晶系统中，一个突出的挑战是确定区分不同应力承载状态的有序参数。值得注意的是，序参数的缺失也是量子自旋液体的一个特征，其中拓扑指标如圈数可以区分状态。对于机械结构，拓扑力学提供了一个可以精确做到这一点的指标。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在某种程度上出现的粗粒化的场论，而拓扑力学明确地考虑了机械约束运行的网络结构，这表明拓扑力学可能是建立软非晶材料微观力学约束与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用于探索从张量规范理论中出现的软非晶材料新范式的含义，并建立这种连续统理论与拓扑力学之间的联系，该理论提供了非晶固体在外部应力下维持和演化能力的网络特定描述。鉴于软非晶固体的普遍存在，其力学响应的统一场论将对软凝聚态物理以及相关的材料科学、化学和结构工程应用学科产生革命性的影响。这项合作将开发新的计算工具，以补充理论并为理论提供信息，并确定新的实验测试。理论与模拟之间的反馈将反映在博士后、研究生和本科生的研究训练中。通过张量规范理论的共享框架，在软硬凝聚态物理之间架起了一座桥梁，为软硬凝聚态物理的界面训练提供了新的机会。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.