Phases and Dynamics of Disordered Condensed Matter Systems

0109164 Middleton该奖项支持理论研究，算法开发，数值模拟和淬火无序物理系统的广泛模型分析。使用经典自由度建模的样本系统包括随机磁体，如自旋玻璃，II型超导体，其中磁通量被无序钉扎，甚至生物学上重要的聚合物，如蛋白质和RNA。在过去几年中开发的优化算法已经扩大了可以精确研究的具有基态和平衡行为的模型系统的数量。在许多情况下，可以在系统大小的时间多项式中找到精确的基态或配分函数。 PI将扩展使用这种算法可以研究的模型的数量，并开发新的算法来产生激励和研究非平衡行为。一个应用将是更准确地确定临界指数，用于研究这些模型的缩放图像。此外，最近的工作已经直接解决了一些关于无序系统的更微妙的定性问题，例如近简并最优值的数量，热力学极限的性质，以及大的最低能量激发的性质。这些问题将在更多的模型中进行研究，目标是统一无序模型的描述。此外，将使用新的方法研究热活化和平衡的细节。 通过猝灭无序的集体输运发生在许多物理系统中，包括固体对固体的摩擦、流体流过粗糙表面、无序背景中移动的胶体晶体以及超导体中的磁通量运动。某些类型的运动，例如，通过无序驱动的过阻尼弹性介质是很好理解的。有许多模拟和实验缺乏对塑性流动的一般了解，其中颗粒可以彼此滑动并且传输是不均匀的。PI计划继续探索这种流动的模式。该模型介于弹性流动和塑性流动之间，可以在平均场水平上精确求解。该模型将被扩展到更现实的应用中，在有限的尺寸，潜在的普遍的临界行为，在从滞后到非滞后流的过渡，是服从实验研究的一些系统。PI将扩展金属点阵列中电荷输运的工作，这是一个有用的模型，用于研究通道流和普遍性问题。 该研究活动支持对学生进行最先进的计算和统计力学方法的培训。%该奖项支持理论和计算研究，以及统计力学和淬火无序扩展物理系统的驱动动力学教育。 这项工作涵盖了广泛的物理系统，例如，随机磁体，如自旋玻璃，II型超导体，其中磁通量被无序钉扎，甚至生物学上重要的聚合物，如蛋白质和RNA。 该研究是跨学科的，涉及影响计算机科学和计算凝聚态和材料物理的算法开发，以及统计物理和计算复杂性之间的界面活动。具体的研究活动主要集中在两个领域：（1）无序统计力学系统中的平衡和近平衡行为，包括记忆效应;（2）适用于超导体中磁通流和电荷密度波材料中输运的塑性流模型，以及电荷输运的新模型。这项工作的主旨是根本性的，旨在发现不同无序系统的普遍性质和物理联系，以及大量模型的特定物理性质，这些模型可以与实验进行比较，其中许多涉及对材料的日常使用很重要的现象。

0109164MiddletonThis award supports theoretical research, algorithm development, numerical simulations and analyses on a wide range of models for physical systems with quenched disorder. Sample systems modeled using classical degrees of freedom include random magnets, such as spin glasses, type-II superconductors, where magnetic flux is pinned by disorder, and even biologically important polymers, such as proteins and RNA. Optimization algorithms developed over the past few years have broadened the number of model systems with ground state and equilibrium behavior that can be studied with precision. In many cases, exact ground states or partition functions can be found in time polynomial in the system size. The PI will extend the number of models that can be studied using such algorithms and develop new algorithms to generate excitations and to study nonequilibrium behavior. One application will be to determine critical exponents more accurately, for studying scaling pictures for these models. In addition, recent work has directly addressed some of the more subtle, qualitative questions about disordered systems, such as the number of nearly degenerate optima, the nature of the thermodynamic limit, and the nature of large, lowest energy excitations. These questions will be studied for more models, with the goal of unifying the description of disordered models. In addition, the details of thermal activation and equilibration will be studied using new approaches. These will enable the study how memory effects take place in disordered magnets.Collective transport through quenched disorder occurs in a number of physical systems, including solid-on-solid friction, fluid flowing over rough surfaces, moving colloidal crystals in disordered backgrounds, and magnetic flux motion in superconductors. Some types of motion, e.g., overdamped elastic media driven through disorder, are well understood. There are many simulations and experiments for which a general understanding of plastic flow, where particles can slide by each other and the transport is inhomogeneous, is lacking. The PI plans to continue to explore a model for such flow. This model, which interpolates between well understood elastic flow and plastic flow, can be solved exactly at the mean field level. This model will be extended to more realistic applications in finite dimensions, where potentially universal critical behavior, at the transition from hysteretic to non-hysteretic flow, is amenable to experimental study in a number of systems. The PI will extend work on charge transport in arrays of metallic dots, which is a useful model for studying channel-like flow and questions of universality. The research activity supports the training of students in state of the art computational and statistical mechanical methods.%%%This award supports theoretical and computational research, and education on the statistical mechanics and driven dynamics of extended physical systems with quenched disorder. The work encompasses a wide range of physical systems, for example, random magnets, such as spin glasses, type-II superconductors, where magnetic flux is pinned by disorder, and even biologically important polymers, such as proteins and RNA. The research is interdisciplinary, involving algorithmic development that impacts both computer science and computational condensed matter and materials physics, and activities at the interface between statistical physics and computational complexity. Specific research activities lie in two general areas: (1) equilibrium and near equilibrium behavior, including memory effects, in disordered statistical mechanical systems, and (2) models for plastic flow, which are applicable to flux flow in superconductors and to transport in charge density wave materials, and a novel model for charge transport. The thrust of the work is fundamental, intended to discover universal properties of, and physical connections among, diverse disordered systems, as well as, specific physical properties of a large number of models which can be compared with experiments, many of which involve phenomena important to everyday uses of materials.***