Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, E-50009 Zaragoza, Spain.
J Chem Phys. 2012 Aug 7;137(5):054106. doi: 10.1063/1.4737861.
We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.
我们在 Ehrenfest 模型的背景下讨论了混合量子/经典方法在电子非绝热动力学中的纯度演变。由于不可能为实际系统精确确定初始条件，我们选择在 Alonso 等人引入的统计 Ehrenfest 形式主义中工作[J. Phys. A: Math. Theor. 44, 396004 (2011)]。从中，我们开发了一个新的框架，可以精确地确定量子子系统的纯度变化以及统计 Ehrenfest 系统的演化。在一个简单的情况下，我们验证 Ehrenfest 统计动力学如何以及在何种程度上使具有多个经典轨迹和初始量子纯态的系统成为量子混合态。我们通过数值证明来证明这一点，展示了纯度的演化如何随时间、量子态空间 D 的维数以及初始分布的经典轨迹 N 的数量而变化。这项工作为使用 Ehrenfest 动力学研究退相干开辟了新的视角。
