Wigner function's numerical propagator for open system dynamics
Renán Cabrera, Denys I. Bondar, HERSCHEL A. RABITZ · arXiv (Cornell University) · 2012
We employ a recently developed formalism for describing open quantum systems, to device efficient ab initio numerical techniques for the time propagation of the Wigner function. The propagator's complexity is $O(N\log N)$, where N is the length of the array containing the Wigner function. We illustrate the developed method by propagating single particle systems undergoing decoherence and draw a faithful comparison with the classical evolution governed by both the Fokker-Planck and the Koopman-von Neumann equations. These simulations allow us to witness the emergence of the classical world by observing how the Wigner function converges to the solution of the Fokker-Planck equation with sufficient classical diffusion. As a second example we simulate for first time a numerically challenging quantum system made of two coupled particles and observe the loss of decoherence on one of the particles as a result of continuous measurements performed on the other one, therefore obtaining quantitative predictions for the loss of coherence of both particles as a function of time.