Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians.
Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians.
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DOI：
10.1063/1.2778682
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发表时间：
2007-07
期刊：
影响因子：
--
通讯作者：
E. Gindensperger;L. Cederbaum
中科院分区：
文献类型：
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作者：
E. Gindensperger;L. Cederbaum
我们讨论了具有几个耦合电子态的宏观系统的非绝热量子动力学，并考虑了多态圆锥相交的可能性。考虑了任意数状态和任意数核自由度（模态）的一般情况。宏观系统被分解为包含少数强耦合模式的系统部分和包含大量剩余模式的环境。通过连续变换环境的模态，构造了环境的有效哈密顿量的层次结构。每个有效的哈密顿量依赖于有效模态的减少数量，这些有效模态具有累积效应。通过考虑系统的哈密顿量以及层次结构的一些成员，通过力矩分析可以在数学上显示整个宏观系统的量子动力学可以在给定的时间尺度上精确地计算出来。所需的时间尺度定义了要包含的有效哈密顿量的数量。环境对宏观系统量子动力学的贡献转化为有效模式的顺序耦合。宏观系统的波函数在整个模态空间中是已知的，允许对观测值进行评估，例如沿感兴趣的模态以及光谱和电子种群动力学的随时间个体激发。
We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multistate conical intersections. The general situation of an arbitrary number of states and arbitrary number of nuclear degrees of freedom (modes) is considered. The macrosystem is decomposed into a system part carrying a few, strongly coupled modes and an environment, comprising the vast number of remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment is constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. By considering the system's Hamiltonian along with a few members of the hierarchy, it is shown mathematically by a moment analysis that the quantum dynamics of the entire macrosystem can be numerically exactly computed on a given time scale. The time scale wanted defines the number of effective Hamiltonians to be included. The contribution of the environment to the quantum dynamics of the macrosystem translates into a sequential coupling of effective modes. The wave function of the macrosystem is known in the full space of modes, allowing for the evaluation of observables such as the time-dependent individual excitation along modes of interest as well as spectra and electronic-population dynamics.