Chaotic Molecular Motions to be Obseved in Single Molecule Spectroscopy.

我们研究了与化学或分子动力学相关的弱混沌。有几种动力学已被深入研究，作为可能在单分子光谱中观察到的候选者。弱混沌及其在单分子光谱学中的预测意义：我们研究了薄准分离矩阵相空间中的一种经典运动，我们称之为相空间大振幅运动（PSLAM）。这实质上是准分离矩阵中极其精细和微妙的动力学的宏观实现。一个单一的经典轨迹在宏观上不时地以不可预测的方式访问不同的振动模式。我们通过产生沿薄准分离矩阵局域化的波包，研究了PSLAM的量子动力学。因此，可以预测，在所谓的单分子光谱中，可以观察到包的非常长时间的行为，这种行为几乎是非平稳的和混沌的，而这种行为不取系综（或时间）平均值。多维动态隧穿：我们发现Hamilton-Jacobi方程在实值位形空间中有一类新的复（非经典）解，可以沿着非经典轨迹求解。这个理论包括了所谓的瞬子路径作为一个特例。该方法已应用于动力学隧穿和化学反应的研究。团簇动力学中的集体运动：我们最近的一项研究集中在像- ar_77这样的小尺寸团簇的异构化动力学上，它经历了熔化（重排或异构化）。我们进行了30维相空间体积（经典态密度）的直接计算，并与相应的经典动力学进行了比较。首次明确验证了非遍历性，证明了熔炼过程中可以存在两个与“相变”相对应的子相。

We have studied weak chaos that is relevant to chemical or molecular dynamics. Several kinds of dynamics have been intensively studied as possible candidates to be observed in single molecule spectroscopy.1. Weak chaos and its predicted significance in single molecule spectroscopy : We have been studying a classical motion in a thin quasi-separatrix-in phase space, which we call phase-space large amplitude motion (PSLAM). This is essentiaally the macroscopic realization of extremely fine and delicate dynamics in the quasi-separatrix. A single classical trajectory visits different vibrational modes macroscopically from time to time in an unpredictable manner. We have studies quantum dynamics for PSLAM by generating wave packets that localize along a thin quasi-separatrix. As a result, it is predicted that the very long-time behavior, which is almost non-stationary and chaotic, of the packets could be observed in the so-called single molecule spectroscopy for which ensemble (or time) average is not taken.2. Multidimensional dynamical tunneling : We have found out that the Hamilton-Jacobi equation has a new class of complex (non-classical) solutions in a real-valued configuration space that can be solved along a non-classical trajectory. This theory includes the so-called instanton path as a special case. The method has been applied to the study of dynamical tunneling as well as chemical reactions.3. Collective motions in cluster dynamics : One of our recent studies is focused on the isomerization dynamics of small size clusters like-Ar_77, which undergoes melting (rearrangement or isomerization). We have carried out a direct calculation of 30 dimensional phase-space volume (classical density of states) and compared with the corresponding classical dynamics. Non-ergodicity has been explicitly verified for the first time, and it turns out that there can exist two sub-phases in the melting process that corresponds to "phase transition".