Fluctuations & Broken Symmetries

这笔拨款支持凝聚态物理的理论研究。许多系统由基本元素组成，具有相对简单的交互作用；然而，它们的集体行为可能相当复杂和令人困惑。统计物理学利用强大的工具来描述物质的无数相是如何从原子的相互作用中出现的。这些方法还可以揭示生物和社会背景下的集体现象。这项研究旨在了解聚合物、细胞运动、视觉处理和润湿薄膜中各种现象的统计基础。起伏是本研究所述问题的内在组成部分，需要计算概率分布及其时间演化。采用场论的方法，在对称性和局域性等简单考虑的基础上，建立了适当的场和序参数在空间和时间中变化的方程。然后用微扰展开和重整化群等标准方法分析得到的集体行为。蒙特卡罗模拟等数值技术也是分析工具的重要补充。许多有趣的问题需要创造性地使用这些方法，并可能开发新的工具。在这项研究中提出的具体问题包括：氨基酸序列的疏水性在多大程度上决定了折叠蛋白质的结构；聚合物中的拓扑纠缠(如结)是真正的全球实体，还是由于物理限制而被迫形成容易定位的构型；肌动蛋白的聚合是如何推动细胞朝着特定方向前进的；自然图像中常见的定向片段的统计数据是什么，对视觉处理(人工或生物)有什么影响；变形(以及可能移动的)平板之间的电磁场的量子波动产生了什么力；表面起伏是氦薄膜变薄的原因吗？这项研究将涉及学生，并与课程密切相关。这笔助学金支持凝聚态物理的理论研究。许多系统由基本元素组成，具有相对简单的交互作用；然而，它们的集体行为可能相当复杂和令人困惑。统计物理学利用强大的工具来描述物质的无数相是如何从原子的相互作用中出现的。这些方法还可以揭示生物和社会背景下的集体现象。这项研究旨在了解聚合物、细胞运动、视觉处理和润湿薄膜中各种现象的统计基础。研究将涉及学生，并与课程密切相关。*

This grant supports theoretical research on condensed matter physics. Many systems are composed of basic elements with relatively simple interactions; yet their collective behavior can be quite complex and perplexing. Statistical physics utilizes powerful tools to describe how the myriad phases of matter emerge from the interactions of atoms. These methods may also shed light upon collective phenomena in biological and social contexts. This research aims at understanding the statistical basis of a diverse variety of phenomena in polymers, cell locomotion, visual processing, and wetting films.Fluctuations are an inherent component of the problems addressed in this research, necessitating the calculation of probability distributions and their time evolution. Adapting the methods of field theory, equations governing the variations of appropriate fields and order parameters in space and time are constructed on the basis of simple considerations such as symmetry and locality. The resulting collective behaviors are then analyzed by standard methods such as perturbation expansions and renormalization group. Numerical techniques, such as Monte Carlo simulations, are also an essential complement to analytical tools. Many problems of interest require creative use of these methods, and possible development of new tools.Specific questions asked in this research include: To what degree does the hydrophobicity of an amino acid sequence determine the structure of a folded protein; Are topological entanglements (such as knots) in polymers truly global entities, or forced to easily located configurations because of physical constraints; How does polymerization of actin propel a cell in a particular direction; What are the statistics of oriented segments common in natural images, and what are the implications for visual processing (artificial or biological); What are the forces that result from quantum fluctuations of the electromagnetic field between deformed (and possibly moving) plates; Are surface fluctuations responsible for the thinning of helium films as they become superfluid.The research will involve students and be closely linked to courses.%%%This grant supports theoretical research on condensed matter physics. Many systems are composed of basic elements with relatively simple interactions; yet their collective behavior can be quite complex and perplexing. Statistical physics utilizes powerful tools to describe how the myriad phases of matter emerge from the interactions of atoms. These methods may also shed light upon collective phenomena in biological and social contexts. This research aims at understanding the statistical basis of a diverse variety of phenomena in polymers, cell locomotion, visual processing, and wetting films. The research will involve students and be closely linked to courses.***