| This thesis covers three topics in semiclassical quantum dynamics. Chapters 1 and 2 are devoted to the development and application of a phase-space deformation approach to optimize the classical canonical representation of a nearly integrable Hamiltonian. Chapter 1 develops and tests the theory, while in Chapter 2 the method is successfully applied to several model Hamiltonians. Chapters 3 and 4 are devoted to studies of energy redistribution. Specifically, Chapter 3 compares dynamical tunneling to Arnol'd Diffusion in a model Hamiltonian system, in order to determine the relative importance of the two types of energy flow as a mechanism of vibrational energy redistribution in polyatomic molecules. It is concluded that dynamical tunneling is generally much faster than Arnol'd Diffusion. Chapter 4 studies an analytically solvable stochastic model for energy dispersion due to numerous Landau-Zener transitions on a network of avoided crossings. Finally, Chapters 5 and 6 cover issues related to vibrational predissociation. In Chapter 5, a perturbative model for vibrational predissociation is developed and applied to ArHF. A number of important experimental observations regarding the ArHF system are recovered using our model. In Chapter 6 we develop a semiclassical coupling formula for bound-free dissociative couplings using only classical Fourier coefficients of the Hamiltonian. This formula is successfully applied to several test cases. |
