NSF/DMR-BSF: FORCES & FLUCTUATIONS OUT OF EQUILIBRIUM

该奖项支持理论研究和教育，这些研究和教育追求波动的结果，这些波动可能是由于服从经典力学的粒子的随机运动或由于海森堡不确定性原理，这是量子力学的基础。物理学研究的是力和运动，而统计物理学研究的是波动的影响。气体的压力、分子间的范德华引力和量子电动力学中的卡西米尔力都是由平衡波动产生的力的经典例子。本研究探讨了波动力的几个方面，特别是在非平衡系统中。目前对“活性物质”的研究研究的是大量自驱动实体的集体行为，比如成群的生物或人工自驱动的物体，它们的随机运动表面上类似于热波动的粒子。然而，内部驱动的存在导致了与平衡物质不同的现象，例如定向力和取决于围壁形状和结构的压力。人造活性粒子的内部驱动很容易调节，例如通过发光。这个项目将研究可以通过不同的时间活动模式来编程的集体行为。分子之间的力和宏观电荷中性体之间的力主要是由于电磁场的热涨落和量子力学涨落。这些力本身表现出微弱的波动，其幅度和相关性将被探讨，特别是对于处于不同温度的物体。这项研究活动与PI的研讨会和课程紧密结合，PI通过出版的教科书和网页向广泛的科学界传播。这项提议的研究是跨学科的，已经在从应用数学到免疫学的各个领域产生了影响。本奖项支持研究波动后果的理论研究和教育。电磁场的量子涨落和热涨落是量子和统计物理的基石。在亚微米尺度上对传热和卡西米尔力的精确测量使得以前所未有的细节探测这些现象成为可能。因此，在诸如熵和自由能等概念不适用的情况下，开发理论工具来处理脱离热平衡的系统是特别相关的。这项研究的目的是发展和完善方法，基于散射理论和所谓的波动QED，以表征这些力的新特征，特别是在不同温度或相对运动的物体的非平衡环境中。有趣的是，有概念上的联系，与非常不同的系统收集的自推进活性粒子。由于守恒定律，比如粒子的数量，驱动物质的波动获得了远程相关性，并表现出类似于卡西米尔力的远程相互作用。利用数值和分析方法的结合，该项目将探索驱动经典粒子的模式和力。数值研究应集中在简单的晶格模型上，如活跃布朗粒子或驱动扩散系统，它们具有足够的复杂性来捕捉集体行为。在分析方面，应采用统计场论的方法，利用对称性和守恒定律来构造活性物质的随机方程，利用应力张量来计算力。

NONTECHNICAL SUMMARYThis award supports theoretical research and education that pursues the consequences of fluctuations which may be due to the random motion of particles that obey classical mechanics or due to the Heisenberg uncertainty principle which lies at the foundations of quantum mechanics. Physics is the study of force and motion, while statistical physics is concerned with the influence of fluctuations. The pressure of a gas, the van der Waals attraction between molecules, and the Casimir force in quantum electrodynamics are classical examples of forces resulting from equilibrium fluctuations. Several aspects of fluctuation-induced force, especially in systems out of equilibrium, are explored in this research. Current research on "Active Matter" studies collective behaviors of large groups of self-driven entities, such as flocks of living or artificial self-powered things, whose random motions superficially resemble thermally fluctuating particles. However, the presence of internal drive leads to distinct phenomena from equilibrium matter, such as directed forces, and a pressure that depends on the shape and structure of the confining wall. The internal drive of artificial active particles is easily tunable, for example by shining light. This project will investigate the collective behaviors that can be programmed by different temporal patterns of activity.Forces between molecules and those between macroscopic charge-neutral bodies are mostly due to thermal and quantum mechanical fluctuations of the electromagnetic field. These forces themselves exhibit weak fluctuations whose magnitude, and relevance will be explored, in particular for bodies at different temperatures.This research activity is closely incorporated in seminars and courses of the PI which through his published textbooks and web-pages reach a broad scientific community. The proposed research is interdisciplinary, and has had impact in diverse areas from applied mathematics to immunology.TECHNICAL SUMMARYThis award supports theoretical research and education that pursues consequences of fluctuations. Quantum and thermal fluctuations of the electromagnetic field are the cornerstone of quantum and statistical physics. Precision measurements of heat transfer and Casimir forces at sub-micron scale have made possible probing these phenomena at unprecedented detail. Thus, developing theoretical tools for treatment of systems out of thermal equilibrium, where concepts such as entropy and free energy are inapplicable, is of particular relevance. This research is aimed at developing and refining methods, based on scattering theory and so-called fluctuational QED, to characterize novel features of these forces, especially in the non-equilibrium contexts of objects held at different temperatures, or in relative motion.Interestingly, there are conceptual connections to the very different system of collections of self-propelled active particles. Due to conservation laws, say of the number of particles, fluctuations in driven matter acquire long-range correlations and exhibit long-range interactions akin to Casimir forces. Using a combination of numerical and analytical methods, this project will explore patterns and forces in driven classical particles. The numerical studies shall focus on simple lattice models, such as Active Brownian Particles or Driven Diffusive Systems, with sufficient complexity to capture collective behaviors. On the analytical front, methods of statistical field theory, used on symmetries and conservation laws to construct stochastic equations for active matter, and stress tensors to compute force, shall be employed.