  White noise analysis is used to derive the propagator of an open quantum
system consisting of a harmonic oscillator which is coupled to an environment
consisting of N multimode harmonic oscillators. The quantum propagators are
obtained after solving for the normal modes of the system-environment
interaction in order to decouple the coordinates in the Lagrangian describing
the dynamics of the system, the environment and their interaction with each
other. The decoupled Lagrangian is then used in the path integral corresponding
to the propagator of the system, with the path integral evaluated using white
noise analysis. The resulting propagator is then found to consist of a product
of N simple harmonic oscillator propagators. N-2 of these propagators
correspond to the degenerate normal mode frequencies of the system-environment
interaction, while the other 2 correspond to the non-degenerate normal mode
frequencies. This method of deriving the propagators greatly simplifies the
task of mathematically describing the dynamics of the open quantum system. The
ease of use of this method suggests that, together with its inherent
mathematical rigor, white noise analysis can be a powerful tool in analyzing
the dynamics of an open quantum system.
