The dynamics of a coupled electron–boson system is investigated by employing a multitude of the Davydov D₁ trial states, also known as the multi-D₁ Ansatz, and a second trial state based on a superposition of the time-dependent generalized coherent state (GCS Ansatz). The two Ansätze are applied to study population dynamics in the spin-boson model and the Holstein molecular crystal model, and a detailed comparison with numerically exact results obtained by the (multilayer) multiconfiguration time-dependent Hartree method and the hierarchy equations of motion approach is drawn. It is found that the two methodologies proposed here have significantly improved over that with the single D₁ Ansatz, yielding quantitatively accurate results even in the critical cases of large energy biases and large transfer integrals. The two methodologies provide new effective tools for accurate, efficient simulation of many-body quantum dynamics thanks to a relatively small number of parameters which characterize the electron–nuclear wave functions. The wave-function-based approaches are capable of tracking explicitly detailed bosonic dynamics, which is absent by construct in approaches based on the reduced density matrix. The efficiency and flexibility of our methods are also advantages as compared with numerically exact approaches such as QUAPI and HEOM, especially at low temperatures and in the strong coupling regime.

中文翻译：

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具有多个Davydov D ₁ Ansatz和广义相干态的电子-玻色子耦合系统的动力学

通过使用多个Davydov D ₁试验状态（也称为multi-D ₁ Ansatz）和基于时间相关广义相干态的叠加的第二试验状态来研究电子-玻色子耦合系统的动力学（GCS Ansatz）。将这两个Ansätze用于研究自旋玻色子模型和Holstein分子晶体模型中的种群动力学，并与通过（多层）多配置时变Hartree方法和运动方法的层次方程获得的数值精确结果进行了详细比较。画。发现与单个D ₁ Ansatz相比，此处提出的两种方法已显着改进。，即使在大的能量偏差和大的传递积分的关键情况下，也能产生定量准确的结果。由于相对较少的表征电子-核波函数的参数，这两种方法为准确，高效地模拟多体量子动力学提供了新的有效工具。基于波函数的方法能够跟踪明确的详细玻色动力学，而基于简化密度矩阵的方法中缺少构造方法。与数值精确的方法（例如QUAPI和HEOM）相比，我们的方法的效率和灵活性也具有优势，尤其是在低温和强耦合条件下。