标题： 库普曼波函数和混合量子经典动力学中的经典状态 显示英文标题

标题： Koopman wavefunctions and classical states in hybrid quantum-classical dynamics

摘要： 我们处理耦合量子和经典系统的可逆动力学。 基于作者最近提出的一个方案，我们利用混合量子-经典波函数理论，设计了一个闭合模型，用于耦合动力学，在该模型中，量子密度矩阵和经典Liouville分布都保持其初始的正号。 这样，演化过程允许在所有时间识别相互作用的经典和量子状态，从而满足一系列严格的相容性要求。 在将Koopman的经典力学希尔伯特空间方法与van Hove的前量子理论中的单位表示相结合之后，通过一种合适的波函数分解所隐含的变分结构，提供了该闭合模型。 此外，我们使用对称性下的泊松约化来证明，该混合模型具有一个非规范的泊松结构，这种结构似乎以前未曾出现过。 作为例子，该结构被专门应用于量子二能级系统的情况。 显示英文摘要

摘要： We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics in which both the quantum density matrix and the classical Liouville distribution retain their initial positive sign. In this way, the evolution allows identifying a classical and a quantum state in interaction at all times, thereby addressing a series of stringent consistency requirements. After combining Koopman's Hilbert-space method in classical mechanics with van Hove's unitary representations in prequantum theory, the closure model is made available by the variational structure underlying a suitable wavefunction factorization. Also, we use Poisson reduction by symmetry to show that the hybrid model possesses a noncanonical Poisson structure that does not seem to have appeared before. As an example, this structure is specialized to the case of quantum two-level systems.