Tunneling Probability Of The Single-phonon Model Landau-Zener Model

Quantum coherent tunnelling has been being an interesting subject in both theoretical and experimental research since the so-called "Leggett program" was proposed. One important issue in the study on quantum tunnelling is the dissipation effect from the en-vironment. Theoretically the best-known model of quantum dissipation is the dissipative two-state-system, also called the spin-boson model. In this paper tunnelling probability of the single phonon-model Landau-Zener model was solved by numerical solution of the time-dependent Schrodinger equation. The results showed that in the case of weak coupling, the tunneling probability by solving the time-dependent Schrodinger equa-tion was consistent with the Landau-Zener formula. However, in the strong coupling case, the tunneling probability by numerical solution of the time-dependent Schrodinger equation oscillates with the coupling strength, a result totally different from the simple ground state tunneling. In addition, tunneling probability was solved by choosing the different initial states, the result showed that the choice of the initial state affected the tunneling probability of the single phonon model Landau-Zener model.