Structures and Dynamics in Disordered Systems

该奖项支持分层结构系统老化和玻璃老化的理论和计算研究。等级结构在许多环境中普遍存在，例如生物网络、社会和经济组织。具有分层特性的定制材料可能会产生普通物质所没有的复杂但控制良好的功能。它们的递归设计有助于严格的分析以及高效的工程设计。应用凝聚态物理的古老工具，如重整化群，可以获得对此类结构上的传输和关键现象的深刻新见解，有利于设计可调谐相变或量子计算设备等应用。在由重整化群产生的强大的普适性概念的精神下，应用于常规格上的系统，PI正在为分层网络上的关键现象制定一个重整化群分类方案。层次网络表现出许多罕见的临界现象，这些现象在实际材料中很少发现，如倒立Kosterlitz-Thouless转变，无限顺序或不连续转变，以及具有可调临界指数的非普适转变。理解和控制这种转变最终为工程材料和纳米结构提供了可能，这些材料和纳米结构具有普通材料不具备的自定义特性。这些概念将在广泛的凝聚态系统中得到发展。在此过程中，PI将研究和推进RG方法在处理全局约束中的应用，并为网络上的非平衡和量子输运现象设计新的RG方案。例如，PI将研究递归晶格中的量子计算问题，用严格的方法分析量子干涉如何影响高维结构中量子搜索的Grover算法，以建议在量子计算机中有效实现内存。第二个关于玻璃弛豫的项目的中心假设是，老化通常与记录的波动有关，这意味着间歇性事件或“地震”驱动了许多玻璃材料的动力学，导致淬火或结构紊乱，而与具体的微观细节无关。具体来说，这个项目旨在研究一个新的真实空间模型，为唱片动力学提供相关的现象学。将对该模型进行广泛的模拟，以揭示其与已知老化现象的一致性，包括各种热力学测量的再现。探索和检验新措施的实验效果。根据记录动力学的理论描述将被设计出来，并与最近的实验结果相匹配。虽然有理论捕捉到玻璃材料老化行为的各种特征，但它们之间很少有统一的概念。模式耦合理论不适用于玻璃化转变以下，动力学约束模型很少有转变，平均场理论的有效温度概念缺乏波动来捕捉老化现象的完全非平衡性质。一般来说，热力学描述提供了有用的指标，然而，模糊了激活动力学的真正亚广泛特征。PI将通过设计和分析一个基于记录动力学的模型，并通过对广泛的老化现象提供定量见解，研究间歇性极端波动作为松弛过程的控制动力的重要性。从长远来看，可能会出现对复杂松弛的更统一的描述，从而加强对无序材料的使用和设计的控制。将探讨对复杂能源景观的理解，在材料设计以及生物进化和组合优化中有用的含义。该奖项支持分层结构系统老化和玻璃材料老化的理论和计算研究。在过去十年中，对复杂网络的研究彻底改变了我们对许多人造和自然结构的理解。特别是，等级结构已经成为复杂材料设计以及生物网络、社会和经济组织研究的中心问题。PI对分层网络中传输过程动力学的研究，以及对颗粒材料或电子流动的建模，揭示了全新的模式，与在普通材料中观察到的典型行为截然不同。该项目的一个目标是使用传统凝聚态物理工具来理解和分类这些新特性，并适当地适应这些结构。这种见解可以用于设计具有定制和可控特征的超材料。另一种表现出复杂动力学的系统是由胶体和类似无序的材料提供的。在高密度和/或低温下，这些非晶材料达到玻璃态，其特征是极慢的弛豫动力学，这本身取决于过程的历史。在无序系统中，慢弛缓存在于许多层面，无论好坏：我们希望更快地“解开”交通堵塞，更快地通过漏斗运输谷物，或者更密集地包装物体，但我们也希望真正的玻璃——原则上是一种流体材料——能长时间保持其形状。一种称为“老化”的统一现象学已被用来描述这种松弛动力学在广泛的其他不相关的材料上的表现。然而，需要一个通用的机制来证明这种全面的推广是难以捉摸的。在第二个项目中，PI将深入研究一个有希望的理论和数值机制，并与实验证据密切相关。

TECHNICAL SUMMARYThis award supports theoretical and computational research and aging on hierarchically structured systems and aging in glasses. Hierarchical structures are pervasive in many environments, such as biological networks, and social and economical organizations. Custom-made materials that exhibit hierarchical properties may lead to complex yet well-controlled functionalities not found in ordinary matter. Their recursive design lends itself to rigorous analysis as well as to efficient engineering. Applying venerable tools from condensed matter physics, such as the renormalization group, deep new insight can be gained for transport and critical phenomena on such structures, benefiting applications such as the design of tunable phase transitions or of quantum computing devices.In the spirit of the powerful concept of universality arising from renormalization group, as applied to systems on conventional lattices, the PI is formulating a renormalization group-classification scheme for critical phenomena on hierarchical networks. Hierarchical networks exhibit a number of uncommon critical phenomena that are rare to find in real materials, such as inverted Kosterlitz-Thouless transitions, infinite-order or discontinuous transitions, and non-universal transitions with tunable critical exponents. Understanding and controlling such transitions ultimately provides the possibility to engineer materials and nanostructures with custom properties not available in ordinary materials. These notions will be developed for a broad range of condensed matter systems. In the process, the PI will investigate and advance the application of RG methods to handle global constraint, and novel RG schemes will be devised for non-equilibrium and quantum transport phenomena on networks. For example, the PI will investigate problems in quantum computing in recursive lattices to analyze with rigorous methods how quantum interference affects Grover's algorithm for quantum search in higher-dimensional structures to suggest efficient realizations of memory in a quantum computer.The central hypothesis of the second project on glassy relaxation is that aging generally is connected with record fluctuations, implying that intermittent events or "quakes" drive the dynamics in many glassy materials, with quenched or structural disorder, irrespective of specific microscopic details. Specifically, this project aims to study a new real-space model that provides the relevant phenomenology for record dynamics. Extensive simulations of this model will be conducted to reveal its consistency with known aging phenomena, including the reproduction of various thermodynamic measures. New measures will be explored and tested for their experimental efficacy. Theoretical descriptions in terms of record dynamics will be devised and matched to recent experimental results.While there are theories that capture various features of aging behavior in glassy materials, there are few unifying concepts among them. Mode-coupling theory does not apply below the glass transition, kinetically constrained models rarely have a transition, and effective temperature concepts from mean field theories lack fluctuations to capture the full non-equilibrium nature of the aging phenomenon. In general, thermodynamic descriptions provide useful indicators, yet, blur the true sub-extensive character of activated dynamics. The PI will examine the significance of the importance of intermittent, extremal fluctuations as a controlling impetus for the relaxation process by devising and analyzing a model based on record dynamics and by providing quantitative insights into a broad spectrum of aging phenomena. In the long run, a more unified description of complex relaxation may emerge, enhancing control in the use and design of disordered materials. Implications for the understanding of complex energy-landscapes, useful in materials design as well as for biological evolution and combinatorial optimization, will be explored.NON-TECHNICAL SUMMARYThis award supports theoretical and computational research and aging on hierarchically structured systems and aging in glassy materials. The study of complex networks has revolutionized our understanding of many man-made and natural structures in the last decade. Hierarchical structures, in particular, have become a central issue in the design of complex materials as well as in the study of biological networks, social and economical organizations. The PI's research on the dynamics of transport processes within hierarchical networks and modeling the flow of granular materials or electrons, reveals entirely new patterns, very distinct from the typical behaviors observed in ordinary materials. One goal of this project is to understand and classify these novel properties using the tools of traditional condensed matter physics, appropriately adapted to these structures. Such insight can be exploited to engineer meta-materials with custom-made and controllable features.Another system exhibiting complex dynamics is provided by colloidal and similarly disordered materials. At high density and/or low temperature these amorphous materials attain a glassy state characterized by extremely slow relaxation dynamics, which itself depends on the history of the process. Slow relaxation in disordered systems arises at many levels, for better or for worse: We desire to "unpack" traffic jams faster, to transport grains through hoppers more quickly, or to pack objects more densely, but we also hope that actual glass - in principle a fluid material - retains it shape for long times. A unifying phenomenology referred to as "aging" has been used to describe manifestations of this relaxation dynamics over a wide class of otherwise unrelated materials. Yet, a generic mechanism needed to justify such a sweeping generalization has been elusive. In this second project, the PI will investigate in depth a promising mechanism theoretically and numerically, and in close connection with the experimental evidence.