In previous works, we introduced a geometric route to define our Ehrenfest statistical dynamics (ESD) and we proved that, for a simple toy model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to nonadiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analyzing the appearance of the pointer basis to which the system decoheres, which for our example is composed of the eigenstates of the electronic Hamiltonian.

中文翻译：

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化学中的埃伦弗斯特统计动力学：退相干效应研究

在以前的工作中，我们引入了定义Ehrenfest统计动力学（ESD）的几何方法，并证明了对于简单的玩具模型，所得的ESD无法保持纯度。现在，我们采取了进一步的措施：研究消相干和指针基础在ESD模型中，通过考虑一个简单但现实的分子模型（由两个经典核和一个量子电子组成）的自由度来考虑一些不确定性。Ehrenfest模型有时被丢弃为非绝热耦合量子古典动力学的有效近似，因为它没有描述量子子系统中的退相干。但是，对Ehrenfest动力学的任何严格的统计分析，例如描述的ESD形式主义，都证明存在退相干性。在本文中，通过测量量子子系统纯度的变化并通过分析系统进行去耦的指针基础的外观来研究ESD的去相干性，在我们的示例中，该指针基础由电子哈密顿量的本征态组成。