Title: Complex fluid models of mixed quantum-classical dynamics Show Chinese title

Title: 混合量子-经典动力学的复杂流体模型

Abstract: Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential leads to severe computational challenges and one often seeks to neglect its contribution, thereby approximating nuclear motion as classical. The resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component, leading to the structure of a complex fluid system. This type of mixed quantum-classical fluid models have also appeared in solvation dynamics to describe the coupling between liquid solvents and the quantum solute molecule. While these approaches represent a promising direction, their mathematical structure requires a certain care. In some cases, challenging higher-order gradients make these equations hardly tractable. In other cases, these models are based on phase-space formulations that suffer from well-known consistency issues. Here, we present a new complex fluid system that resolves these difficulties. Unlike common approaches, the current system is obtained by applying the fluid closure at the level of the action principle of the original phase-space model. As a result, the system inherits a Hamiltonian structure and retains energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the model in the case of pure-dephasing dynamics. We conclude by presenting some invariant planar models. Show Chinese abstract

Abstract: 非绝热分子动力学的几种方法基于 Madelung 对核运动的流体力学描述，而电子部分则被视为有限维量子系统。 在这种背景下，量子势会导致严重的计算挑战，人们通常试图忽略它的贡献，从而将核运动近似为经典运动。 由此产生的模型将核的经典流体力学与电子成分的量子运动耦合起来，形成了一个复杂的流体系统结构。 这类混合量子-经典流体模型也出现在溶剂化动力学中，用于描述液体溶剂与量子溶质分子之间的耦合。 尽管这些方法代表了一个有前景的方向，但它们的数学结构需要一定的谨慎。 在某些情况下，具有挑战性的高阶梯度使这些方程几乎难以处理。 在其他情况下，这些模型基于相空间表述，存在众所周知的一致性问题。 在这里，我们提出了一种新的复杂流体系统来解决这些问题。 与常见的方法不同，当前系统是通过对原始相空间模型的作用量原理应用流体闭合获得的。 因此，该系统继承了哈密顿结构，并保留了能量/动量平衡。 在讨论了一些结构特性和动力学不变量之后，我们在纯去相位动力学的情况下展示了该模型。 最后，我们介绍了几个不变的平面模型。