具有多个耦合电子态的宏观系统的量子动力学：有效哈密顿量的层次
Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians
摘要：
我们讨论了具有多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。一般情况下，任意数量的国家和任意数量的核自由度（模式）被认为是。宏系统被分解成一个系统的一部分，携带几个，强耦合的模式，和一个环境，包括大量的剩余模式。通过连续变换环境的模态，构造了环境的有效哈密顿算子的层次。每个有效哈密顿量取决于有效模式的减少数量，这些模式具有累积效应。通过考虑系统的哈密顿量以及一些成员的层次，它是数学上显示的时刻分析，整个宏观系统的量子动力学可以精确地计算在给定的时间尺度上。所需的时间尺度定义了要包括的有效哈密尔顿算子的数量。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。宏系统的波函数在模式的整个空间中是已知的，从而可以评估观测值，例如沿着感兴趣的模式的依赖于时间的个体激发，以及光谱和电子布居动力学。
英文摘要：
We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multi-state 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 wavefunction 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 a spectra and electronic-population dynamics.
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