Constrained Fluctuations

技术概述：该奖项支持关于波动在各种物理环境中的作用的理论研究和教育。波动，无论是量子的、热的还是非平衡的，都是物理物质的固有部分。通过边界、几何或拓扑来约束这些波动，会导致无数的相互作用、模式和相位。本建议的目的是在几种情况下量化这种现象。研究将解决的具体问题包括：(i)中性物体之间的力是由于受约束的电磁波动造成的。这些力是如何取决于这些物体的形状和方向的？仅仅用这样的力就能使物体保持稳定的平衡吗？（二）序参数临界热波动的限制如何导致氦膜在超流动性开始时变薄？（iii）刚性在DNA等双链聚合物的熔化中起什么作用？波动是如何软化聚合物和薄片的弹性的？（iv）在一个比扩散慢的过程中，是什么支配着从一个限定的间隔中逃逸时间的分布？这些过程是否有一个共同的描述？（iv）如何对纠缠蛋白进行分类和编目？波动系统用概率分布函数来表征。统计物理学提供了平衡状态下不同构型的相对权重，以及权重偏离平衡状态的时间演化。统计场论的方法适合于处理电磁场的量子涨落。通过约束物体上的波动，可以得到不同物质间的卡西米尔力及其几何关系。转移矩阵和重整化群方法将用于解决涉及半柔性聚合物的问题。我们将结合标度理论、蒙特卡罗和分子动力学模拟来研究异常动力学。教育是这个奖项的重要组成部分。这个研究项目是跨学科的；统计物理学的方法将应用于广泛的科学问题。这项研究与PI教授的课程密切相关，这些课程通过教科书和网络传播将对更广泛的科学界产生影响。PI还将在Kavli理论物理研究所组织一个关于涨落的研讨会。诱导力。非技术概述：该奖项支持关于统计物理学基本原理的材料和物理结果的理论研究和教育。这项研究涵盖了广泛的物理系统和现象，这些系统和现象通过约束如何改变行为和性质的统一问题联系在一起。约束效应是物理系统固有的一部分，边界和几何的效应导致了无数的相互作用、模式和相。这项研究量化了几种情况下的这种现象。解决了各种研究问题。(i)关于中性物体之间仅仅由于接近而产生的力的理论预测，称为卡西米尔力，已有几十年的历史，但直到最近才被测量出来，甚至最近才成为实验的对象，以研究它们在装置中的应用。这项研究从已知的简单平面几何转向研究这些力如何依赖于物体的形状和方向。没有答案的基本问题被提了出来，比如，一个人能不能只用这样的力把一个物体保持在稳定的位置？（二）这篇文章的重点是氦膜的限制如何改变它们的行为，使其从简单的流体表现出各种不同寻常的流体特性。氦元素的薄膜本质上是存在于极低温度下的二维液体，并表现出受量子力学支配的行为。（iii）一个相关的主题是由拥挤和与其他成员相互作用引起的分子约束的作用。这方面的研究研究了聚合物和柔性片材的软化和弹性。在这种情况下，约束通过长分子的纠缠产生。教育是这个奖项的重要组成部分。这个研究项目是跨学科的；统计物理学的方法将应用于广泛的科学问题。这项研究与PI教授的课程密切相关，这些课程通过教科书和网络传播将对更广泛的科学界产生影响。PI还将在Kavli理论物理研究所为更广泛的理论物理社区组织一个研讨会。

TECHNICAL SUMMARY:This award supports theoretical research and education on the role of fluctuations in various physical contexts. Fluctuations, whether of quantum, thermal, or non-equilibrium origin, are an inherent part of physical matter. Constraining these fluctuations by boundaries, geometry or topology, leads to a myriad of interactions, patterns and phases. This proposal aims at quantifying such phenomena in several contexts.Specific questions that will be addressed by the research include:(i) The forces between neutral objects are due to constrained electromagnetic fluctuations. How do these forces depend on the shapes and orientations of these objects? Can one hold an object in stable equilibrium using only such forces?(ii) How does the confinement of critical thermal fluctuations of the order parameter lead to the thinning of helium films at the onset of superfluidity?(iii) What is the role of rigidity in the melting of double-stranded polymers such as DNA? How do fluctuations soften the elasticity of polymers and sheets? (iv) What governs the distribution of escape times, from a confining interval, in a process that is slower than diffusion? Is there a common description for such processes? (iv) How can we classify and catalog entangled proteins?Fluctuating systems are characterized by probability distribution functions. Statistical physics provides the relative weights of different configurations in equilibrium, and the time evolution of weights away from equilibrium. The methods of statistical field theory are appropriate for handling quantum fluctuations of the electromagnetic field. The Casimir force between different materials and its dependence of geometry can be obtained by constraining the fluctuations on the bodies. Transfer matrix and renormalization group methods will be used to address questions involving semi-flexible polymers. Anomalous dynamics will be studied by a combination of scaling theory, and Monte Carlo and Molecular Dynamics simulations.Education is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop at the Kavli Institute for Theoretical Physics on the subject of fluctuation?induced forces.NONTECHNICAL SUMMARY:This award supports theoretical research and education on the materials and physical consequences of fundamental principles of statistical physics. The research encompasses a wide range of physical systems and phenomena that are connected through the unifying question of how confinement modifies behavior and properties. The effects of confinement are an inherent part of physical systems and the effects of boundaries and geometry lead to a myriad of interactions, patterns and phases. This research quantifies such phenomena in several contexts. Varied research questions are addressed.(i) Theoretical predictions concerning the forces between neutral objects, due to mere proximity, known as Casimir forces, are decades old, but have only recently been measured and even more recently been the subject of experiments to investigate their application in devices. This research moves from what is known for simple planar geometries to investigating how these forces depend on the shapes and orientations of the objects. Unanswered fundamental questions are taken up, such as can one hold an object in stable arrangement using only such forces?(ii) This thrust focuses on how the confinement of helium films alters their behavior from simple fluids to exhibit a variety of unusual fluid properties. Films of the element helium are essentially two dimensional liquids that exist at very low temperatures and exhibit behavior governed by quantum mechanics.(iii) A related topic is the role of confinement induced in molecules by crowding and interacting with other members of bulk collection. This aspect of the research studies the softening and elasticity of polymers and flexible sheets. In this case, confinement arises through the entanglement of long molecules.Education is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop for the broader theoretical physics community at the Kavli Institute for Theoretical Physics.