通过参量变化理解高激发态
Understanding highly excited states via parametric variations
摘要：
孤立分子的高激发振动态编码分子中的振动能流路径。最近的研究在理解激发态的性质方面取得了惊人的成功，主要是由于对经典相空间结构及其分叉的广泛研究。这种详细的经典量子对应研究目前仅限于二维或准二维系统。这种约束的主要原因之一是与相关对象的可视化问题有关，如截面表面和与本征态相关的维格纳或胡西米分布。这就需要各种不同的技术，这些技术在本质上比几何更代数。在这项工作中，我们介绍了一个这样的方法的基础上参数变化的特征值的哈密顿量。结果表明，能级速度与相应本征态的相空间性质有关。导出了单共振哈密顿量能级速度的半经典表达式，为关联提供了理论支持。我们使用的水平速度动态分配的高激发态的模型光谱哈密顿量在混合相空间制度。利用最近提出的HCP分子的光谱哈密顿量，简要讨论了分叉对能级速度的影响。
英文摘要：
Highly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive studies of the classical phase space structures and their bifurcations. Such detailed classical-quantum correspondence studies are presently limited to two or quasi two dimensional systems. One of the main reasons for such a constraint has to do with the problem of visualization of relevant objects like surface of sections and Wigner or Husimi distributions associated with an eigenstate. This neccesiates various alternative techniques which are more algebraic than geometric in nature. In this work we introduce one such method based on parametric variation of the eigenvalues of a Hamiltonian. It is shown that the level velocities are correlated with the phase space nature of the corresponding eigenstates. A semiclassical expression for the level velocities of a single resonance Hamiltonian is derived which provides theoretical support for the correlation. We use the level velocities to dynamically assign the highly excited states of a model spectroscopic Hamiltonian in the mixed phase space regime. The effect of bifurcations on the level velocities is briefly discussed using a recently proposed spectroscopic Hamiltonian for the HCP molecule.
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