We present a systematic numerical iteration approach to study the evolution properties of the spin-boson systems, which works well in whole coupling regime. This approach involves the evaluation of a set of coefficients for the formal expansion of the time-dependent Schr\"{o}dinger equation $\vert t\rangle=e^{-i\hat{H}t}\vert t=0\rangle$ by expanding the initial state $\vert t=0\rangle$ in Fock space. The main advantage of this method is that this set of coefficients is unique for the Hamiltonian studied, which allows one to calculate the time evolution based on the different initial states. To complement our numerical calculations, the method is applied to the Buck-Sukumar model. Furthermore, we pointed out that, when the ground state energy of the model is unbounded and no ground state exists in a certain parameter space, the unstable time evolution of the physical quantities is the natural results. Furthermore, we test the performance of the numerical method to the Hamiltonian that use anti-Hermitian terms for modeling open quantum systems.

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自旋玻色子系统演化的数值方法及其在巴克-苏库马尔模型中的应用

我们提出了一种系统的数值迭代方法来研究自旋玻色子系统的演化特性，该方法在整个耦合状态下运行良好。这种方法涉及对时间相关 Schr \ "{o} dinger 方程 $ \ vert t \ rangle = e ^ {- i \ hat {H} t} \ vert t = 0 \ rangle $ 通过在 Fock 空间中扩展初始状态 $ \ vert t = 0 \ rangle $。这种方法的主要优点是这组系数对于所研究的哈密顿量是唯一的，这使得我们可以计算基于时间演化的为了补充我们的数值计算，将该方法应用于Buck-Sukumar模型。此外，我们指出，当模型的基态能量无界且在某个参数空间中不存在基态时, 物理量的不稳定时间演化是自然结果。此外，我们测试了数值方法对使用反厄米术语来建模开放量子系统的哈密顿量的性能。