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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >A Hybrid Hydrodynamic-Liouvillian Approach to Mixed Quantum-Classical Dynamics: Application to Tunneling in a Double Well
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A Hybrid Hydrodynamic-Liouvillian Approach to Mixed Quantum-Classical Dynamics: Application to Tunneling in a Double Well

机译：混合量子-经典动力学的流体动力-Liouvillian混合方法：在双井隧道中的应用

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摘要

The hybrid quantum-classical approach of Burghardt and Parlant [Burghardt, I.;Parlant, G. J. Chem. Phys. 2004, 120, 3055], referred to here as the quantum-classical moment (QCM) approach, is demonstrated for the dynamics of a quantum double well coupled to a classical harmonic coordinate. The approach combines the quantum hydrodynamic and classical Liouvillian representations by the construction of a particular type of moments (that is, partial hydrodynamic moments) whose evolution is determined by a hierarchy of coupled equations. For pure states, which are at the center of the present study, this hierarchy terminates at the first order. In the Lagrangian picture, the deterministic trajectories result in dynamics which is Hamiltonian in the classical subspace, while the projection onto the quantum subspace evolves under a generalized hydrodynamic force. Importantly, this force also depends upon the classical (Q, P) variables. The present application demonstrates the tunneling dynamics in both the Eulerian and Lagrangian representations. The method is exact if the classical subspace is harmonic, as is the case for the systems studied here.
机译：Burghardt和Parlant的混合量子经典方法[Burghardt，I.; Parlant，G. J. Chem。物理2004，120，3055]，此处称为量子经典矩（QCM）方法，针对耦合至经典谐波坐标的量子双阱的动力学进行了演示。该方法通过构造特定类型的矩（即部分流体动力学矩）来组合量子流体力学和经典的Liouvillian表示，其演化由耦合方程的层次结构确定。对于处于本研究中心的纯状态，此层次结构以一阶终止。在拉格朗日图中，确定性轨迹产生的动力学是经典子空间中的哈密顿量，而在量子子空间上的投影是在广义流体动力作用下演化的。重要的是，该力还取决于经典（Q，P）变量。本申请证明了欧拉和拉格朗日表示中的隧穿动力学。如果经典子空间是调和的，则该方法是精确的，就像这里研究的系统一样。

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