Dynamics of coupled harmonic oscillators in an environment using white noise analysis
Bienvenido Masirin Butanas Jr.
White noise analysis has gained considerable attention in the past years in the analysis of quantum systems, polymer entanglement, transport, and diffusion phenomena. However, there is dearth on the application of the analysis into open quantum systems specifically coupled harmonic oscillators in an environment. In this work, white noise analysis was used to study the dy- namics of the propagator of an open quantum system consisting of coupled harmonic oscillators that are coupled to an environment consisting of N-2 multimode harmonic oscillators. The quantum propagators were obtained after solving for the normal modes of the system-environment interaction to decouple the coordinates in the Lagrangian describing the dynamics of the system, the environment and their interaction with each other. The decoupled Lagrangian was used in the path integral corresponding to the propagator of the system, with the path integral evaluated using white noise analysis. The resulting propagator was found to consist of the product of N simple harmonic oscillator propagators. N-3 of these propagators correspond to the degenerate normal mode frequencies of the system-environment interaction, while the other three correspond to the non-degenerate normal mode frequen- cies, two of these nondegeneracies correspond to complex normal modes. This approach of describing the dynamics of the open quantum system greatly simplifies the task mathematically.
AIP conference proceedings•Jan 1, 2020•2 citations