Poincare's Theorem and Subdynamics for TimeDependent Systems.
Abstract
Large dynamical systems with explicit timedependence are studied. For these systems, there exist resonances between internal frequencies and/or between internal and external frequencies. As in the timeindependent case, the usual canonical or unitary perturbation theory leads to divergences due to the resonances. This is a generalization of Poincare's theorem on nonintegrability and extends the notion of large Poincare systems, i.e. systems with a continuous spectrum and a continuous set of resonances. Using the natural time ordering and a new rule of integration, we can construct timedependent projection operators which decompose the equations of motion and are analytical in the coupling conatant. These projectors are nonHermitian and provide a description with broken time symmetry. As an application, we study the modification of the wellknown three stages of the decay process from a timedependent perturbation. We also develop a timeindependent formalism to treat these timedependent systems by introducing an auxiliary variable and extending the phase space. In this way, the Hamiltonian becomes timeindependent and the original formulation of the timeindependent subdynamics can be applied. The results obtained by these two approaches are completely the same. Based on the recent development in the second quantization for the complex spectral theory, we investigate the nonMarkovian effects by studying an exactly soluble matterfield interaction model. The results show that the ratio of the nonMarkovian to Markovian effects can be enhanced enormously by imposing a nonresonant external field. This mechanism renders an experimental investigation possible. The exact solution obtained in this model also justifies our perturbational scheme mentioned in above.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......208L
 Keywords:

 Physics: General; Physics: Radiation