An analysis of the adiabatic switching method: Foundations and applications

The adiabatic switching method is characterized through a discussion of formal adiabatic theory and through a variety of numerical examples. Adiabatic invariance theory for one degree of freedom problems is developed in detail. This provides a formal basis for the analysis of various aspects of the method. The role of: 1) the switching function, 2) the zero order reference Hamiltonian, and 3) ensemble averaging of results are addressed with more rigour function than in previous discussions. The use of adiabatic switching to implement EBK quantization is illustrated by a treatment of the Henon-Heiles system. It is shown how adiabatic switching is useful for periodic orbit determination and adiabatic propagation of semiclassical eigenstates. The behavior of the conjugate angle variables in near adiabatic dynamics is formally and numerically explored. The theory of adiabatic separatrix crossing is developed and several aspects of the theory are numerically tested for a time-dependent quartic double well.