Mixed Quantum-Classical Dynamics of Quantum Energy Transfer Processes

从预测新现象到解释实验结果，分子动力学已经成为实验者和理论家不可或缺的工具。采用物质的经典描述，可以对含有大量粒子的系统进行分子动力学模拟。然而，当粒子表现出波状性质时，经典的描述就不再有效。量子分子动力学方法是可用的，但它们仅限于非常小的系统，因为它们的计算成本随粒子数量呈指数级增长。为了处理更大的系统，人们可以求助于混合量子经典方法，这种方法用量子力学来处理系统的一个关键部分(即子系统)，而用经典的方法来处理其余的部分(即浴池)。多年来，人们已经开发出了一些混合量子经典动力学算法。其中最准确的算法执行得非常好，但计算成本很高。最近，我们开发了一种方法，该方法在计算成本和精度之间取得了良好的平衡。然而，在目前的公式中，这种方法仅限于势能可以用多项式表示的系统，并且其子系统很快就失去了对浴液动力学的记忆。因此，我们研究计划的第一部分将集中在沿着几个方向推进这一方法，以使其更加通用、准确和高效。这一结果有望成为模拟混合量子经典系统动力学的有力工具。 我们研究计划的第二部分将专注于将我们混合量子-经典方法的当前和未来配方应用于一系列具有基础和技术重要性的量子能量转移/存储过程。具体地说，我们将探索分子电子学和纳米声学应用中涉及的量子热传递过程，以及量子电池中的能量存储。我们的目标将是深入了解各种分子系统中影响热传递速率/机制的因素，并提出实用的量子电池设计方案。通过这项研究获得的知识最终将有助于开发用于量子技术的强大、高效和可控的纳米设备。

From predicting new phenomena to interpreting experimental findings, molecular dynamics has become an indispensable tool for both experimentalists and theorists. Adopting a classical description of matter, one can perform molecular dynamics simulations of systems containing very large numbers of particles. However, when particles exhibit wave-like properties, a classical description is no longer valid. Quantum molecular dynamics methods are available, but they are restricted to very small systems as their computational costs scale exponentially with the number of particles. To treat larger systems, one can resort to mixed quantum-classical methods, which treat a key part of the system (i.e., the subsystem) quantum mechanically and the remainder (i.e., the bath) classically. Over the years, a number of mixed quantum-classical dynamics algorithms have been developed. The most accurate of them perform very well, but at high computational costs. Recently, we developed a method that exhibits a favourable balance between computational cost and accuracy. In its present formulation, however, this method is restricted to systems whose potential energies can be expressed in polynomial form and whose subsystems quickly lose memory of the bath dynamics. Thus, the first part of our research program will focus on advancing this methodology along several directions to make it more general, accurate, and efficient. The result promises to be a very powerful tool for simulating the dynamics of mixed quantum-classical systems. The second part of our research program will focus on applying both the present and future formulations of our mixed quantum-classical methodologies to a host of quantum energy transfer/storage processes of fundamental and technological importance. Specifically, we will explore quantum heat transfer processes involved in molecular electronics and nanophononics applications, and energy storage in quantum batteries. Our goals will be to gain an in-depth understanding of the factors that influence the rates/mechanisms of the heat transfer in a variety of molecular systems, and to propose practical designs for quantum batteries. The knowledge gained by this research will ultimately aid in the development of robust, efficient, and controllable nanoscale devices for use in quantum technologies.