  We investigate the dynamical correlation function of a quantum-mechanical
two-state system which is coupled to a bosonic heat bath, utilizing the
equivalence between the spin-boson Hamiltonian and the 1/r^2 Ising model. The
imaginary-time correlation function is calculated by Monte-Carlo simulations on
the Ising system and then continued to real time by a Pade approximation. In
the unbiased system, the transition from oscillatory to strongly damped
behavior is found to occur at a coupling strength close to alpha = 1/2. The
biased system favors coherent relaxation and displays a significantly larger
crossover value alpha_c. 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.
