Takatsuka Kazuo
Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan.
Entropy (Basel). 2022 Dec 29;25(1):63. doi: 10.3390/e25010063.
Quantum chaos is reviewed from the viewpoint of "what is molecule?", particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is "bifurcation and merging" of quantum wavepackets, rather than "stretching and folding" of the baker's transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule.
从“什么是分子？”的角度对量子混沌进行了综述，特别强调了它们的动力学。分子由重原子核和轻电子组成，因此，由玻恩和奥本海默提出的非常基础的分子理论认为，量子电子态提供作用于原子核的势函数，而原子核通常又被经典地或半经典地处理。因此，分子科学中对混沌的经典研究始于那些核动力学，特别是关于分子内振动能量的随机化。即使对于由几个原子组成的小分子，化学反应概率和速率中的统计规律也是需要混沌概念的化学现象之一。特别是单分子分解背后的动力学被称为分子内振动能量重新分布（IVR）。半经典力学也是量子混沌的主要研究领域之一。我们在此展示仅出现在半经典和全量子动力学中的混沌。可能产生量子混沌的一个基本现象是量子波包的“分叉与合并”，而不是作为经典混沌几何基础的面包师变换和马蹄映射的“拉伸与折叠”。正如我们之前在一系列非绝热化学反应实时探测研究中所展示的那样，这种波包分叉与合并确实是实验可测量的。在追踪分子混沌的这些方面之后，我们将探索在非绝热电子波包动力学中发现的量子混沌，它出现在远远超出玻恩 - 奥本海默范式的领域。在这类混沌中，我们提出了分子内非绝热电子能量重新分布（INEER）的概念，它是分子内电子和能量混沌通量的结果。
