Control and Thermodynamics of Nanoscale Systems

技术进步使科学家和工程师能够在单个原子和分子的水平上建立和操纵物理系统。在这些小尺度上，自然法则往往是奇怪的和反直觉的。该奖项支持理论研究和教育，旨在阐明如何控制此类系统的动力学，并加深对量子物理和热力学定律如何结合以确定纳米级系统行为的理解。量子物理学支配着原子和分子的行为，而热力学是用来描述系统如何相互交换能量和物质的。结合这两个领域，特别是对于远离热平衡稳定状态的系统，是一个具有挑战性的研究领域。该奖项资助的活动将解决这一问题的三个方面。其中一个项目涉及发展控制量子力学系统的理论方法，使其在固定的时间内达到理想的最终状态。这将涉及从量子物理学、经典力学和热力学中借鉴的理论工具。第二个项目旨在探索热和功等热力学概念如何应用于受量子物理定律支配的系统。在第三个项目中，PI将调查一个小系统与其周围环境之间的相互作用在系统的热力学行为中所起的作用。这些活动将涉及学生和博士后研究人员，提供量子物理和热力学交叉的理论方法培训。该奖项支持与原子和分子长度尺度的相干量子控制和系统热力学相关的基础理论研究和教育。第一个项目涉及绝热捷径这一令人兴奋的新领域，其目标是引导系统进化，就像它被非常缓慢地操纵一样，即使操纵发生得很快。PI将开发应用经典和统计物理工具来设计这种量子捷径的策略。第二个项目对经典和量子功定义之间的关系进行了仔细的分析，重点是使用半经典方法来确定经典轨迹之间量子干涉的影响。第三个项目涉及研究热力学第一和第二定律如何“按比例缩小”来描述与其热环境强耦合的系统的行为。PI将探索微观上精确的量的定义，如内能、熵和体积，以保持第一和第二定律的结构，而不需要引入修正来解释强的系统-环境相互作用。提出的研究将：(1)开发一种广泛适用的方法，用于使用经典力学设计相干量子系统的操作协议。这种方法在实验环境中是有用的，因为目前许多基于尺度不变驱动的方法不适用。(2)对于由外部参数变化驱动的孤立系统，提供了从量子热力学中产生经典热力学的更深层次的理解。特别地，它将阐明量子干涉在热力学第二定律和非平衡涨落关系中的作用。(3)建立一个一致的微观热力学框架，用于描述系统与其周围环境之间的能量交换，当两者之间的耦合足够强，相互作用的能量本身不能被忽视。这一框架将有助于描述生物分子的热力学，因为生物分子与其水环境有强烈的相互作用。该奖项支持理论和计算统计物理方法的研究生和博士后水平的培训。

NONTECHNICAL SUMMARYTechnological progress has enabled scientists and engineers to build and manipulate physical systems at the level of individual atoms and molecules. At these small scales the laws of Nature are often strange and counter-intuitive. This award supports theoretical research and education aimed to elucidate how the dynamics of such systems can be controlled, and to deepen understanding of how the laws of quantum physics and thermodynamics combine to determine the behavior of nanoscale systems.Quantum physics governs the behavior of atoms and molecules, while thermodynamics was developed to describe how systems exchange energy and matter with one another. Combining the two fields, particularly for systems that are far away from the steady state of thermal equilibrium is a challenging area of research. The activities funded by this award will address three aspects of this problem. One project involves developing theoretical methods for controlling a quantum mechanical system so that it reaches a desired final state in a fixed amount of time. This will involve theoretical tools borrowed from quantum physics, classical mechanics and thermodynamics. The second project is aimed to explore how thermodynamic concepts such as heat and work apply to systems that are governed by the laws of quantum physics. In the third project, the PI will investigate the role played by the interactions between a small system and its surroundings, in the thermodynamic behavior of the system.These activities will involve students as well as postdoctoral researchers, providing training in theoretical methods at the intersection of quantum physics and thermodynamics.TECHNICAL SUMMARYThis award supports fundamental theoretical research and education related to the coherent quantum control and the thermodynamics of systems at atomic and molecular length scales. The first project addresses the new and exciting field of shortcuts to adiabaticity, where the aim is to guide a system to evolve as if it were being manipulated very slowly, even when the manipulation occurs rapidly. The PI will develop strategies that apply the tools of classical and statistical physics to design such quantum shortcuts. The second project undertakes a careful analysis of the relationship between classical and quantal definitions of work, with an emphasis on using semiclassical methods to identify the impact of quantum interference between classical trajectories. The third project involves investigating how the first and second laws of thermodynamics "scale down" to describe the behavior of systems that are strongly coupled to their thermal surroundings. The PI will explore microscopically precise definitions of quantities such as internal energy, entropy and volume that preserve the structure of the first and second laws, without needing to introduce corrections to account for strong system-environment interaction. The proposed research will:(1) Develop a broadly applicable methodology for using classical mechanics to design protocols for the manipulation of coherent quantum systems. This methodology will be useful in experimental settings where many of the current methods, based on scale-invariant driving, do not apply.(2) Provide a deeper understanding of the emergence of classical thermodynamics from quantum thermodynamics, for isolated systems driven by the variation of external parameters. In particular, it will clarify the role of quantum interference on the second law of thermodynamics and on nonequilibrium fluctuation relations.(3) Establish a consistent, microscopic thermodynamic framework for describing the interchange of energy between a system and its surroundings, when the two are sufficiently strongly coupled that the interaction energy itself cannot be ignored. This framework will be useful in describing the thermodynamics of biomolecules, which interact strongly with their aqueous surroundings. This award supports graduate student and postdoctoral level training in the methods of theoretical and computational statistical physics.