Coherent-incoherent Transition In The Dissipative Two-state System With A Super-ohmic Bath

Quantum coherent tunnelling has been being an interesting subject in both theoret-ical 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 environment. Theoretically the best-known model of quantum dissipation is the dis-sipative two-state-system, also called the spin-boson model. At finite temperature, the coherent-incoherent transition in the dissipative two-state-system with a super-ohmic bath is studied by the small polaron theory. The transition temperature is calculated and its dependence on both dissipation strength and bare tunnelling splitting is analyzed. In additional to the traditional transition point described in textbooks, a new kind of transi-tion is found in the low dissipation region, showing different temperature dependence in the transition. The relation to the corresponding transition in the polaron-phonon system is also discussed.