QUANTUM LOCALIZATION AND DYNAMICAL TUNNELING OF QUASISEPARATRIX WAVE-FUNCTIONS FOR MOLECULAR VIBRATION

We report a new kind of ''dynamical tunneling'' that can be observed i n chaotic molecular vibration. The present phenomenon has been found i n eigenfunctions quantized in a thin quasiseparatrix (chaotic zone) in phase space. On the classical Poincare section corresponding to this situation, two or more unstable (hyperbolic) fixed points coexist and are connected through the so-called heteroclinic crossings, whereby th e entire quasiseparatrix is generated. When the quasiseparatrix is thi n enough, each of the hyperbolic fixed points is surrounded by the rel atively ''wide lake'' of chaos due to the infinite and violent crossin gs between the stable and unstable manifolds, and these lakes are in t urn connected by ''narrow canals.'' Our finding is, in spite of the fa ct that the narrow canals are classically allowed for the trajectories to pass through fast, wave packets can be quantized predominantly as ''quasistanding-waves'' in each lake area and hence can be mostly loca lized to remain there for much longer time than the corresponding clas sical trajectories do. In other words, the wave packets are localized in the vicinity of the classically unstable fixed points due to the qu antum effect. However, a pair of these ''localized'' wave packets are eventually delocalized into the other lakes, and thereby form a pair o f eigenfunctions (purely standing waves) with a small level splitting. Thus the present phenomenon can be characterized as a tunneling betwe en the states of quantum localization in an oscillator problem. (C) 19 98 American Institute of Physics.