Chaotic Molecular Motions to be Obseved in Single Molecule Spectroscopy.

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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".