  We present a theory for the dynamical evolution of a quantum system coupled
to a complex many-body intrinsic system/environment. By modelling the intrinsic
many-body system with parametric random matrices, we study the types of
effective stochastic models which emerge from random matrix theory. Using the
Feynman-Vernon path integral formalism, we derive the influence functional and
obtain either analytical or numerical solutions for the time evolution of the
entire quantum system. We discuss thoroughly the structure of the solutions for
some representative cases and make connections to well known limiting results,
particularly to Brownian motion, Kramers classical limit and the
Caldeira-Leggett approach.
