Statistical Field Theories and Collective Phenomena

9805833 Kardar Complex现象通常来自简单的潜在实体的集体相互作用，例如晶体中的原子或大脑中的神经元。 统计力学为量化集体现象提供了强大的工具，无论是平均行为还是平均波动。 本研究旨在了解聚合物、通量线、表面、网络和复杂流体中的静态和动态波动现象。 提取相互作用系统的普遍特征的主要分析工具是场论。 控制相关场在空间和时间中变化的方程是根据各种参数（对称性，局部性等）构建的。然后通过公知的技术如微扰展开和重整化群进行分析。 数值方法也被用来模拟复杂系统。 本研究也将探讨一些不太传统的方法：（i）标准场论可以被视为波动线性对象（世界线）的描述。 本文给出了描述一类具有任意内部维数的波动流形（具有固定连通性）的推广。(ii)引入路径积分方法来研究复杂流体中扩展物体引入的边界效应。 即使是一个简单的系统，如真空中的移动镜子，也会改变电磁场的量子涨落，从而产生可以用这种方法计算的力和辐射现象。 具体的研究课题包括：（一）第二类超导体中的通量相：通过热涨落、无序钉扎和不稳定纵向电流的综合效应对相图的修改。(ii)具有随机相互作用和交联的聚合物和凝胶的构型。(iii)在生物系统中形成的非线性模式（皮质映射或微管组装）。(iv)生长系统和漂移聚集体中的非平衡涨落的描述。(v)一个单一的电荷（带电聚合物）的波动和几个扩展的带电物体之间的相互作用。 复杂的现象通常来自简单的潜在实体的集体相互作用，例如晶体中的原子或大脑中的神经元。 统计力学为量化集体现象提供了强大的工具，无论是平均行为还是平均波动。 本研究旨在了解聚合物、通量线、表面、网络和复杂流体中的静态和动态波动现象。 具体的研究课题包括：（一）第二类超导体中的通量相：通过热涨落、无序钉扎和不稳定纵向电流的综合效应对相图的修改。(ii)具有随机相互作用和交联的聚合物和凝胶的构型。(iii)在生物系统中形成的非线性模式（皮质映射或微管组装）。(iv)描述生长系统和漂移聚集体中的非平衡涨落。(v)一个单一的电荷（带电聚合物）的波动和几个扩展的带电物体之间的相互作用。 ***

9805833 Kardar Complex phenomena often emerge from the collective interactions of simple underlying entities, such as atoms in a crystal, or neurons in the brain. Statistical mechanics provides powerful tools for quantifying collective phenomena, in both average behavior, and fluctuations around average. This research is aimed at understanding static and dynamic fluctuation phenomena in polymers, flux lines, surfaces, networks, and complex fluids. The chief analytical tool for extracting universal features of interacting systems is field theory. Equations governing the variation of a relevant field in space and time are constructed on the basis of various arguments (symmetry, locality, etc.) and then analyzed by well known techniques such as perturbation expansions and renormalization group. Numerical methods are also employed to simulate complex systems. Some less conventional approaches will also be explored in this research: (i) standard field theory can be regarded as a description of fluctuating linear objects (world-lines). A generalization to describe a class of fluctuating manifolds (with fixed connectivity) of arbitrary internal dimensions will be formulated. (ii) Path integral methods are introduced to study boundary effects introduced by extended objects immersed in a complex fluid. Even a simple system such as a moving mirror in vacuum modifies the quantum fluctuations of the electromagnetic field, leading to forces and radiation phenomena that can be calculated by this method. Specific topics of study include: (i) flux phases in type II superconductors: the modification of the phase diagram by the combined effects of thermal fluctuations, pinning by disorder, and destabilizing longitudinal currents. (ii) configurations of polymers and gels with random interactions and crosslinks. (iii) nonlinear patterns formed in biological systems (cortical maps or microtubule assemblies). (iv) description of nonequilibrium fluctuations in growing sys tems and drifting aggregates. (v) fluctuations of a single polyelectrolyte (charged polymer) and interactions between several extended charged objects. %%% Complex phenomena often emerge from the collective interactions of simple underlying entities, such as atoms in a crystal, or neurons in the brain. Statistical mechanics provides powerful tools for quantifying collective phenomena, in both average behavior, and fluctuations around average. This research is aimed at understanding static and dynamic fluctuation phenomena in polymers, flux lines, surfaces, networks, and complex fluids. Specific topics of study include: (i) flux phases in type II superconductors: the modification of the phase diagram by the combined effects of thermal fluctuations, pinning by disorder, and destabilizing longitudinal currents. (ii) configurations of polymers and gels with random interactions and crosslinks. (iii) nonlinear patterns formed in biological systems (cortical maps or microtubule assemblies). (iv) description of nonequilibrium fluctuations in growing systems and drifting aggregates. (v) fluctuations of a single polyelectrolyte (charged polymer) and interactions between several extended charged objects. ***