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White noise analysis is used to derive the propagator of an open quantumsystem consisting of a harmonic oscillator which is coupled to an environmentconsisting of N multimode harmonic oscillators. The quantum propagators areobtained after solving for the normal modes of the system-environmentinteraction in order to decouple the coordinates in the Lagrangian describingthe dynamics of the system, the environment and their interaction with eachother. The decoupled Lagrangian is then used in the path integral correspondingto the propagator of the system, with the path integral evaluated using whitenoise analysis. The resulting propagator is then found to consist of a productof N simple harmonic oscillator propagators. N-2 of these propagatorscorrespond to the degenerate normal mode frequencies of the system-environmentinteraction, while the other 2 correspond to the non-degenerate normal modefrequencies. This method of deriving the propagators greatly simplifies thetask of mathematically describing the dynamics of the open quantum system. Theease of use of this method suggests that, together with its inherentmathematical rigor, white noise analysis can be a powerful tool in analyzingthe dynamics of an open quantum system.

Quantum Propagator Dynamics of a Harmonic Oscillator in a Multimode Harmonic Oscillators Environment using White Noise Functional Analysis