Dynamics and Thermodynamics of Nanoscale Systems

该奖项支持量子力学系统控制和应用基础的理论研究和教育。该项目的第一个主题涉及控制微观系统的能力，这些系统遵循量子物理的反直觉定律。技术进步已经使我们能够分离、观察和操纵单个量子系统。PI和他的团队将开发新的策略来控制量子系统如何随时间进化。一种方法是使用脉冲，在这种方法中，系统短暂地受到非常强的外部强迫，导致其状态迅速改变。该项目将发展设计脉冲所需的理论，以实现系统状态的期望变化。另一种方法将涉及索利斯泵浦，这是一种类似于阿基米德螺旋的量子力学，可用于传输电子。由Thouless在1983年提出的最初理论，在过去的十年中得到了实验验证，要求泵送进行得非常缓慢。PI和他的团队将应用绝热捷径领域的新技术，通过索利斯泵送加速电子的传输。这个项目的第二个主题是由外力驱动的系统，外力随时间周期性地振荡，导致系统吸收能量。当这些振荡非常快时，已经发现能量吸收被极大地抑制。这个项目将探索这种行为是否可以用一个简单的图像来理解，在这个图像中，系统的能量执行“有偏差的随机漫步”。PI和他的团队将对遵循熟悉的经典物理定律的系统和遵循量子力学定律的系统进行研究。如果有偏随机漫步假设被证明是准确的，它将为预测快速和周期性驱动系统的能量吸收速率提供一个定量理论，这将对此类非平衡系统的提出应用有用。该项目的教育部分将包括在一个强有力的协作、支持和跨学科的环境中培训学生。研究成果将通过科学期刊的出版物以及在会议和其他场所的介绍来传播。PI将定期进行学术会议级别的演讲，旨在向广大科学听众介绍非平衡统计物理学的最新进展，并将根据他在马里兰大学多次开发和教授的课程编写该领域的研究生水平教科书。该奖项支持理论研究和教育，以调查控制量子系统动力学的策略，特别关注加速进化。脉冲在经典物理学中很常见，但在量子物理学中却很少受到关注。这个项目将专门研究“超级”脉冲，其中脉冲的强度与持续时间的平方成反比。初步结果表明，这种超脉冲导致波函数以一种非平凡的方式变化，这种方式可以完全用经典轨迹来描述，而不需要调用半经典极限。该项目还将解决索利斯泵送现象，其中电子通过拓扑效应传输。虽然在其原始版本中，Thouless泵送是绝热的（准静态），但PI和他的研究团队将探索Thouless泵送的非绝热扩展，利用最近从绝热捷径领域开发的工具。该项目还将研究预热化现象，这是指随着时间的推移，快速和周期性驱动的系统对能量吸收的指数抑制。在初步结果中，PI和他的团队提出了一个描述这种情况下能量吸收的福克-普朗克方程。研究活动将包括在许多模型系统中验证该方程，探索它是否定量地描述了预热化，并通过将费米黄金法则与量子能量跃迁的半经典处理相结合的模型将这些结果扩展到量子系统。该项目的教育部分将包括在一个强有力的协作、支持和跨学科的环境中培训学生。研究成果将通过科学期刊的出版物以及在会议和其他场所的介绍来传播。PI将定期进行学术会议级别的演讲，旨在向广大科学听众介绍非平衡统计物理学的最新进展，并将根据他在马里兰大学多次开发和教授的课程编写该领域的研究生水平教科书。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on foundations of the control and application of quantum mechanical systems. The first theme of this project involves the ability to control microscopic systems that obey the counter-intuitive laws of quantum physics. Technological progress has brought us to the point where experimentalists can isolate, observe, and manipulate individual quantum systems. The PI and his group will develop new strategies for controlling how quantum systems evolve with time. One approach will use impulses, in which the system is briefly subjected to very strong external forcing, causing its state to change quickly. This project will develop the theory needed to design impulses to achieve a desired change in the system’s state. Another approach will involve Thouless pumping, a quantum-mechanical analogue of Archimedes’ screw that can be used to transport electrons. The original theoretical proposal by Thouless in 1983, which has been verified experimentally during the past decade, requires that the pumping be carried out very slowly. The PI and his group will apply new techniques from the field of Shortcuts to Adiabaticity, to accelerate the transport of electrons by Thouless pumping. The second theme of this project addresses systems that are driven by an external force that oscillates periodically with time, causing the system to absorb energy. When these oscillations are very fast, it has been found that energy absorption is greatly suppressed. This project will explore whether this behavior can be understood in terms of a simple picture in which the system’s energy performs a “biased random walk”. The PI and his group will investigate this question both for systems that obey familiar laws of classical physics and for those that obey the laws of quantum mechanics. If the biased random walk hypothesis proves to be accurate, it will provide a quantitative theory for predicting the rate energy is absorbed by rapidly and periodically driven systems, which will be useful in proposed applications of such out-of-equilibrium systems. The educational component of this project will involve the training of students in a strongly collaborative, supportive and cross-disciplinary environment. Research results will be disseminated through publications in scientific journals as well as presentations at conferences and other venues. The PI will regularly give colloquium-level presentations aimed at introducing a broad scientific audience to recent progress in non-equilibrium statistical physics, and will write a graduate-level textbook on this field based on a course he has developed and taught multiple times at the University of Maryland. TECHNICAL SUMMARY This award supports theoretical research and education to investigate strategies for controlling the dynamics of quantum systems, with a particular focus on accelerated evolution. Impulses are familiar from undergraduate-level classical physics but have received less attention in quantum physics. This project will specifically address “super”-impulses, in which the strength of the impulses scales inversely with the square of its duration. Preliminary results reveal that such super-impulses cause a wavefunction to change in a non-trivial manner that can be described entirely in terms of classical trajectories, without invoking the semiclassical limit. The project will also address the phenomenon of Thouless pumping, in which electrons are transported via a topological effect. While in its original version Thouless pumping is adiabatic (quasi-static), the PI and his research team will explore non-adiabatic extensions of Thouless pumping, making use of recently developed tools from the field of Shortcuts to Adiabaticity. The project will also investigate the phenomenon of prethermalization, which refers to the exponential suppression of energy absorption by systems driven rapidly and periodically with time. In preliminary results, the PI and his group have proposed a Fokker-Planck equation describing energy absorption in this scenario. The research activity will include validating this equation in a number of model systems, exploring whether it quantitatively describes prethermalization, and extending these results to quantum systems through a model that combines Fermi’s Golden Rule with a semiclassical treatment of quantum energy transitions.The educational component of this project will involve the training of students in a strongly collaborative, supportive and cross-disciplinary environment. Research results will be disseminated through publications in scientific journals as well as presentations at conferences and other venues. The PI will regularly give colloquium-level presentations aimed at introducing a broad scientific audience to recent progress in non-equilibrium statistical physics, and will write a graduate-level textbook on this field based on a course he has developed and taught multiple times at the University of Maryland.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.