Statistical Mechanics of Systems far from Equilibrium

[00:884551 . schmittmann]这项资助支持远离热平衡的系统的理论研究。目标是表征和理解相互作用的多粒子系统的复杂行为，驱动到远离热平衡的稳定状态。计算和分析技术的结合，在晶格或连续体上的表述，将被带到各种系统中，从伊辛模型到选定的实验。与吉布西恩系综理论相反，目前还没有一个基本的理论框架来对非平衡现象进行全面的分类。即使是非平衡态的研究，作为平衡态的最简单概括，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。寻求描述一般的大尺度性质和普遍行为，重点将放在伊辛类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。外部驱动，适当地应用，防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，因此建立了一个非平凡的，稳定的通通量。这样的系统比它们的平衡系统表现出更丰富的现象，包括一般的远程相关性，新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，说明了全球洋流和基本对称性所起的关键作用，例如详细的平衡和守恒定律。然而，与平衡系统相反，动力学本质上影响稳态特性，因此即使微观规则的微小修改也会以深刻的、完全意想不到的方式影响宏观行为。我们面临的挑战是创造一个可靠的理论图景，它可以作为从微观到宏观的向导。在研究的第一部分，将继续研究驱动晶格气体的集体行为。尽管这些模型看起来很简单，但它们提供了各种复杂的现象，并提出了新的挑战。例子包括形状依赖热力学，临界行为的新普适性类，异常界面关联，新相，和特殊的区域增长。对这些简单模型的进一步研究，应该能提供迈向长远目标的步骤：根据宏观非平衡稳态的潜在动力学，对它们进行有意义的分类。研究的第二部分介绍了三个新的研究方向：聚合物结晶、颗粒材料和种群动力学。在非平衡动力学的控制下，这些现象已经得到了广泛的实验研究。作为物理系统，它们显然比驱动的Ising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出来的，应该很好地用于分析实验数据和理解这些系统的本质。在这两个部分的研究中，项目范围从明确的短期研究（进展是确定的）到涉及更基本和复杂问题的长期冒险。尽管它们需要大量的思考和时间，但后一类问题值得关注，因为它们有望对非平衡稳态的一般性质有更深入的了解。这项资助支持远离热平衡的系统的理论研究。目标是表征和理解相互作用的多粒子系统的复杂行为，驱动到远离热平衡的稳定状态。计算和分析技术的结合，在晶格或连续体上的表述，将被带到各种系统中，从伊辛模型到选定的实验

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.***