纯退相系统的量子-经典混合动力学
Hybrid quantum-classical dynamics of pure-dephasing systems
摘要：
考虑了$\widehat{H}(q,p)=H_C(q,p)\boldsymbol{1}+H_I(q,p)\widehatσ_z$型纯退相哈密顿量下经典振子与量子二能级系统的相互作用动力学。这种类型的系统是一个严峻的挑战，流行的混合量子经典描述。例如，在常见的Escherichfest模型的情况下，经典的密度演化被证明是完全解耦的纯退相量子动力学。我们专注于最近提出的混合波动方程，是基于Koopman的波函数描述的经典力学。这个模型保留了量子经典相关性时，耦合势。在这里，几个基准问题被认为是和结果相比，从完全量子动力学所产生的。一个很好的协议，发现一系列的研究情况下，涉及谐振子与线性和二次耦合，以及随时间变化的耦合参数。在所有这些情况下，经典演化与由完全量子描述产生的振子动力学完全一致。在涉及具有变化频率的经典振子的与时间无关的耦合的特殊情况下，量子布洛赫旋转表现出脱离混合描述的特殊特征。此外，谐波哈密顿量的非线性修正导致退相干在长时间内的整体增长，这在全量子处理中是不存在的。
英文摘要：
We consider the interaction dynamics of a classical oscillator and a quantum two-level system for different pure-dephasing Hamiltonians of the type $\widehat{H}(q,p)=H_C(q,p)\boldsymbol{1}+H_I(q,p)\widehatσ_z$. This type of systems represents a severe challenge for popular hybrid quantum-classical descriptions. For example, in the case of the common Ehrenfest model, the classical density evolution is shown to decouple entirely from the pure-dephasing quantum dynamics. We focus on a recently proposed hybrid wave equation that is based on Koopman's wavefunction description of classical mechanics. This model retains quantum-classical correlations whenever a coupling potential is present. Here, several benchmark problems are considered and the results are compared with those arising from fully quantum dynamics. A good agreement is found for a series of study cases involving harmonic oscillators with linear and quadratic coupling, as well as time-varying coupling parameters. In all these cases the classical evolution coincides exactly with the oscillator dynamics resulting from the fully quantum description. In the special case of time-independent coupling involving a classical oscillator with varying frequency, the quantum Bloch rotation exhibits peculiar features that escape from the hybrid description. In addition, nonlinear corrections to the harmonic Hamiltonian lead to an overall growth of decoherence at long times, which is absent in the fully quantum treatment.
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