Scale Invariance and Dynamic Phase Transitions in Non-Equilibrium Systems

该奖项支持非平衡凝聚态系统的理论研究。 统计力学为我们目前理解相互作用的多粒子系统提供了基础。 在（通常理想化的）热平衡情况下，各种物理实现的概率分布至少在原则上是已知的。 这使得一个系统的热力学结构的一个给定的系统在几个相关的宏观变量，并推导出其状态方程。 对于稍微偏离平衡的系统，线性响应理论可以用来计算动力学的极化率、输运系数和弛豫速率。 然而，对于远离平衡的系统，迄今为止还没有这样的一般理论框架。 除了大量有趣的物理例子，许多化学和几乎所有的生物系统都维持在非平衡稳态（NESS）。 此外，来自生态学、社会学和经济理论的问题可以用随机过程来描述，即，类似于非平衡统计力学中使用的模型。 因此，当前理论物理学中真正的基本问题之一是根据某些全局性质（如对称性、相互作用的总体特征、守恒定律等）来表征NESS的定态概率分布。对于非平衡系统，在这个方向上已经取得了一些进展，这些系统要么被调谐到动态相变附近，要么通常显示尺度不变性：在这些情况下，重整化群（RG）可以作为一个强有力的工具，对随后的相进行分类，并根据普适标度性质来表征跃迁。本项目在前人研究的基础上，对标度不变动力系统中的NESS进行了双重研究，即通过所有可用的数学方法来研究简化模型的情况，以及在远离平衡条件下进行的实验的详细分析。 目标是提取允许NESS分类的一般特征和原则，并在第二种情况下，优化材料特性和工艺。该项目为研究和教育提供了一个综合的跨学科环境。 研究材料将纳入课程。 有关这一主题的教科书仍在编写中。% 这个理论研究项目解决凝聚态系统的非平衡行为。 这种系统的典型例子是材料生长、图案形成和具有驱动力的相变。 大多数化学系统和所有生物系统都处于这些非平衡状态。 研究将寻找有助于理解这些现象的共同主题。该项目为研究和教育提供了一个综合的跨学科环境。 研究材料将纳入课程。 关于这一主题的教科书仍在编写中。

This award supports theoretical studies of non-equilibrium condensed matter systems. Statistical mechanics provides the foundation for our present understanding of interacting many-particle systems. In the (usually idealized) situation of thermal equilibrium, the probability distributions for a variety of physical realizations are known at least in principle. This allows a systematic construction of the thermodynamics of a given system in terms of a few relevant macroscopic variables, and the derivation of its equations of state. For systems slightly disturbed away from equilibrium, linear response theory can be used to compute dynamical susceptibilities, transport coefficients, and relaxation rates. However, no such general theoretical framework exists to date for systems far from equilibrium. Aside from a large variety of interesting physical examples, many chemical and virtually all biological systems are sustained in a non-equilibrium steady state (NESS). In addition, problems from ecology, sociology, and economic theory can be described in terms of stochastic processes, i.e., models akin to those used in non-equilibrium statistical mechanics. Among the truly fundamental problems in current theoretical physics is therefore the characterization of the stationary probability distributions of NESS in terms of certain global properties such as symmetries, overall features of the interactions, conservation laws, etc. Some progress in this direction has been achieved for non-equilibrium systems that are either tuned to the vicinity of a dynamic phase transition, or generally display scale invariance: In these situations the renormalization group (RG) can be employed as a powerful tool to classify the ensuing phases and characterize the transitions in terms of universal scaling properties.Based on previous research, the project here has a double approach to the investigation of NESS in scale-invariant dynamical systems, namely the study of simplified model cases by means of all available mathematical methods, and the detailed analysis of experiments performed far-from-equilibrium conditions. The goal is to extract general features and principles that permit the classification of NESS and, in the second case, optimize material properties and processes.The project offers an integrated interdisciplinary environment for research and education. Research material will be incorporated into courses. A textbook on this subject continues to be written.%%% This theoretical research project addresses the non-equilibrium behavior of condensed matter systems. Typical examples of such systems are materials growth, pattern formation, and phase transitions with driving forces. Most chemical systems and all biological systems are in these non-equilibrium states. Research will look for common themes that can assist the understanding of these phenomena.The project offers an integrated interdisciplinary environment for research and education. Research material will be incorporated into courses. A textbook on this subject continues to be written.***