A. Bulgac et al., DYNAMICS OF A SIMPLE QUANTUM SYSTEM IN A COMPLEX ENVIRONMENT, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(1), 1998, pp. 196-214
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.