Numerical Calculations On Spin-boson Model Of Single-Phonon-Model

The rapid development of integrated circuits industry and remarkable advances in the field of quantum information has made the macroscopic quantum effect an very interesting subject in re-cent years. One important issue in macroscopic quantum effect is the decoherence resulting from the environment and the best-known toy model of quantum dissipation is the dissipative two-level system, or the spin-boson model, where the environment is represented as a bath of harmonic os-cillators. According to the influence functional theory, the total influence functional of the whole bath can be expressed as the product of the individual influence functional of every single phonon-mode. This result shows that the effect of the whole bath can be known from effect of every single mode, at least qualitatively. In the present paper, the single-phonon-model Landau-Zener model is studied by numerical solution of the time-dependent Schrodinger equation. The convergence of the numerical solution is studied and the condition for convergence is found. The dynamics of Landau-Zener model involving phonon is analyzed from the numerical result and the oscillation behavior is explained.