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

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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.