Dynamics Of A Two-level-system Under The Influence Of One Boson-mode

One important issue in the study on macroscopic quantum effect is the quantumdissipation and the most important toy model for quantum dissipation is the spin-boson modelwhich consists of a two-level-system (TLS) coupled to a bath of boson modes. Since thenumber of boson modes of the bath is infinite, the influence from the bath is hard to knownand up to now, the ground state of this toy model is still not found. According to the influencefunctional theory developed by Feynman, the total influence functional of the bath can beexpressed as a direct product of the single-mode influence functional, which implies that theinfluence of the bath can be known from the influence from a single mode. In the presentpaper, the dynamics of a TLS under the influence of one boson mode is studied numerically.The tunneling splitting of the TLS coupled to a boson mode is studied by solving thetime-dependent Schrodinger equation numerically. Five evolution mechanisms under differentconditional parameters, including the frequency of the boson mode and coupling strength, arespecified. We also study under a steady state the influence on tunneling probability by theseevolution mechanisms is studied systematically. The obtained result can help to understandthe physical mechanism on the dynamics of TLS under the influence from a single mode,which can provide the basic elements for understand the influence from the whole bath.