DYNAMICS OF A SIMPLE QUANTUM SYSTEM IN A COMPLEX ENVIRONMENT

We present a theory for the dynamical evolution of a quantum system co upled to a complex many-body intrinsic system (environment). By modeli ng the intrinsic many-body system with parametric random matrices, we study the types of effective stochastic models that emerge from random matrix theory. Using the Feynman-Vernon path integral formalism, we d erive the influence functional and obtain either analytical or numeric al solutions for the time evolution of the entire quantum system. We d iscuss thoroughly the structure of the solutions for some representati ve cases and make connections to well known limiting results, particul arly to Brownian motion, Kramers classical limit, and the Caldeira-Leg gett approach.