Use of Green's functions for the analysis of dynamic couplings: Some examples from chemical kinetics and quantum dynamics

The utility of individual elements of Green's function matrices, in the investigation of dynamic couplings, is illustrated by offering examples from linear and nonlinear kinetics and quantum dynamics. The concept of reduced Green's functions affords a detailed characterization of the actual pathways mediating these couplings. Self-similar behavior between different elements of the Green's function matrix indicates the presence of strong coupling between different variables of the model. We investigate the structure of the entire Green's function matrix to examine such self-similar behavior and other simplifying characteristics of concern for physical insight as well as for economic modeling of the dynamic systems. Global structure in the entire Green's function matrix may be used to reduce the complexity (number of dependent variables) in a model.