Dynamical behavior of the dissipative two-state system

We investigate the dynamical correlation function of a quantum-mechanical two-state system that is coupled to a bosonic heat bath, utilizing the equivalence between the spin-boson Hamiltonian and the 1/r² Ising model. The imaginary-time correlation function is obtained from Monte Carlo simulations on the Ising system and then continued to real time by a Pad\'e approximation. In the unbiased system, the transition from oscillatory to strongly damped behavior is found to occur at a coupling strength close to α=1/2. The biased system favors coherent relaxation and displays a significantly larger crossover value αc. We introduce the quasiparticle picture to describe the relevant behavior at intermediate time scales. Within this approximation, we map out phase diagrams for the unbiased and biased systems.