Statistical Mechanics of Systems far from Equilibrium

远离平衡系统的统计力学

• 批准号: 0088451
• 负责人: Beate Schmittmann
• 金额: $ 49.2万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-01-01 至 2004-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0088451&HistoricalAwards=false
• 关键词: Statistical; Mechanics; Systems; far; Equilibrium

0088451SchmittmannThis grant supports theoretical research on systems far from thermal equilibrium. The goal is the characterization and understanding of complex behavior in interacting many-particle systems, driven into steady states far from thermal equilibrium. A combination of computational and analytical techniques, formulated on the lattice or the continuum, will be brought to bear on various systems, from Ising-like models to selected experiments.In contrast to Gibbsean ensemble theory, there is as yet no fundamental theoretical framework for a comprehensive classification of nonequilibrium phenomena. Even the study of nonequilibrium steady states, being the simplest generalizations of equilibrium states, is far from complete. Given the ubiquity of such states in a broad range of physical systems, formulating a theory with predictive power remains one of the key challenges of condensed matter physics. Seeking to characterize generic large scale properties and universal behavior, the focus will be on minimal model systems of the Ising type, inspired by the successful role which the latter played in equilibrium statistical mechanics. An external drive, suitably applied, prevents such systems from reaching equilibrium; instead, they settle into nonequilibrium steady states. Energy is injected by the drive and absorbed by the thermal bath so that a non-trivial, steady through-flux is established. Such systems display much richer phenomena than their equilibrium cousins, including generic long-range correlations, novel nonequilibrium phase transitions and unexpected ordered structures. Significant insights have been gained, illustrating the key role played by global currents and basic symmetries, e.g., detailed balance and conservation laws. In contrast to equilibrium systems, however, the dynamics inherently affects steady state properties, so that even minor modifications of the microscopic rules can affect macroscopic behavior in profound, entirely unanticipated ways. The challenge is to craft a reliable theoretical picture which can serve as a guide from the microscopic to the macroscopic.In the first part of the research, investigations will continue on collective behavior of driven lattice gases. Despite their apparent simplicity, these models provide a variety of complex phenomena and pose new challenges. Examples include shape-dependent thermodynamics, new universality classes of critical behavior, anomalous interfacial correlations, novel phases, and peculiar domain growth. Further investigations of these simple models should furnish steps toward the long-range goal: a meaningful classification of macroscopic nonequilibrium steady states based on their underlying dynamics. The second part of the research introduces three new pursuits: polymer crystallization, granular materials, and population dynamics. Governed by nonequilibrium dynamics, these phenomena have been extensively studied experimentally. Being physical systems, these are clearly much more complex than driven Ising models. However, the tools used here, honed in the study of simple models, should serve well in analyzing experimental data and understanding the essence of these systems. In both parts of the research, projects range from well-defined, short-term studies, for which progress is certain, to long-term ventures involving more fundamental and complex issues. Although they require substantial thought and time, the problems in the latter category deserve attention, since they promise deeper insights into the general nature of nonequilibrium steady states.%%% This grant supports theoretical research on systems far from thermal equilibrium. The goal is the characterization and understanding of complex behavior in interacting many-particle systems, driven into steady states far from thermal equilibrium. A combination of computational and analytical techniques, formulated on the lattice or the continuum, will be brought to bear on various systems, from Ising-like models to selected experiments.***

0088451施米特曼纽基金支持远离热平衡系统的理论研究。 目标是描述和理解相互作用的多粒子系统的复杂行为，这些系统被驱动到远离热平衡的稳态。 计算和分析技术的结合，制定了晶格或连续，将承担各种系统，从伊辛样模型选择experiments.In对比Gibbsean系综理论，还没有一个基本的理论框架，全面分类的非平衡现象。 甚至对非平衡定态的研究，作为平衡态的最简单的概括，也远未完成。 鉴于这种状态在广泛的物理系统中无处不在，制定具有预测能力的理论仍然是凝聚态物理学的关键挑战之一。 为了描述一般的大尺度性质和普遍行为，重点将放在伊辛型的最小模型系统上，灵感来自后者在平衡统计力学中发挥的成功作用。 适当地施加外部驱动力，可以阻止这样的系统达到平衡;相反，它们会进入非平衡稳态。 能量由驱动器注入并由热浴吸收，从而建立了非平凡的、稳定的通流。 这样的系统显示出比它们的平衡表兄弟丰富得多的现象，包括通用的长程关联，新颖的非平衡相变和意想不到的有序结构。 已经获得了重要的见解，说明了全球电流和基本对称性所发挥的关键作用，例如，详细的平衡和守恒定律。 然而，与平衡系统相反，动力学本质上会影响稳态性质，因此，即使对微观规则进行微小的修改，也会以深刻的、完全出乎意料的方式影响宏观行为。 目前的挑战是要建立一个可靠的理论图像，作为从微观到宏观的指导。在研究的第一部分，将继续研究受驱动的晶格气体的集体行为。 尽管这些模型表面上很简单，但它们提供了各种复杂的现象，并提出了新的挑战。 例子包括形状依赖的热力学，新的普遍性类的临界行为，异常的界面相关性，新的阶段，和奇特的域增长。 对这些简单模型的进一步研究应该为实现长期目标提供步骤：根据其潜在动力学对宏观非平衡稳态进行有意义的分类。 研究的第二部分介绍了三个新的追求：聚合物结晶，颗粒材料，和人口动力学。 这些现象受非平衡态动力学的支配，已经在实验上得到了广泛的研究。 作为物理系统，它们显然比驱动伊辛模型复杂得多。 然而，这里使用的工具，在简单模型的研究中磨练，应该很好地服务于分析实验数据和理解这些系统的本质。 在研究的两个部分，项目范围从明确的，短期的研究，其中的进展是肯定的，长期的企业涉及更根本和复杂的问题。 虽然它们需要大量的思考和时间，但后一类的问题值得关注，因为它们承诺对非平衡稳态的一般性质有更深入的了解。 该基金支持远离热平衡系统的理论研究。 目标是描述和理解相互作用的多粒子系统的复杂行为，这些系统被驱动到远离热平衡的稳态。 计算和分析技术的组合，制定了晶格或连续，将承担各种系统，从伊辛样模型到选定的实验。