Dynamics of the spin-boson model at zero temperature and strong dissipation

Based on the stochastic decoupling framework and auxiliary function averaging technique, a functional integral equation for the zero-temperature population dynamics of the spin-boson model is established. This equation naturally displays the hierarchical structure of the dissipative dynamics and is amenable to nonperturbative approximations. It is shown that at strong dissipation the spin-boson model displays exponential decay with the rate decreasing from the maximum at the coherence-incoherence crossover to zero at the critical dissipation, a manifestation of quantum phase transition. Besides, the scaled time does not change in the whole regime of strong dissipation.