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Additional resources for Geometric Structures of Phase Space in Multi-dimensional Chaos (Advances in Chemical Physics)
Both the dividing surface for fragmentation and the bottleneck to energy transfer on a PSS are shown in Fig. 14. Davis and Gray also demonstrated the existence of a series of intramolecular energy transfer bottlenecks, each corresponding to the breakup of a KAM torus. For example, for I2 in the vibrational state v ¼ 20 they found intramolecular bottlenecks associated with frequency ratios equal to ð3 þ gÞ and up. However, Davis and Gray found that the last ‘‘golden mean torus’’ to be broken up is the most effective bottleneck to intramolecular energy transfer and is therefore 36 meishan zhao et al.
A Semiclassical Approximation to the Rigorous Quantum Rate Theory F. Effective Hamiltonian Approach to Unimolecular Dissociation G. Wave Packet Dynamics Approach VII. Quantum Transport in Classically Chaotic Systems A. Quantum Transport Through Cantori B. Quantum Suppression of Arnold Diffusion C. Faster-than-Classical Quantum Anomalous Diffusion VIII. Concluding Remarks Acknowledgment References I. INTRODUCTION Studies of the rate of a unimolecular reaction have been central to the development of our understanding of reaction dynamics for almost a century.
One important property of the Poincare´ map is that it is area-preserving for time-independent systems with two DOFs. In such systems Poincare´ showed that all dynamical information can be inferred from the properties of trajectories when they cross a PSS. For example, if a classical trajectory is restricted to a simple two-dimensional torus, then the associated Poincare´ map will generate closed KAM curves, an evident result considering the intersection between the torus and the surface of section.