Coherent-incoherent transition and relaxation in condensed-phase tunneling systems

The tunneling dynamics of the spin-boson problem has been computed using discretized path-integral simulations for temperatures T and couplings, i.e., the Kondo parameter {α}, spanning the entire T-{α} plane. The inherent problem of alternating weights has been solved using a combination of the stationary-phase Monte Carlo method and contour-distortion techniques. A transition from coherent to purely incoherent relaxation was observed for the spin correlation function. The time correlation functions and the location of the coherent-incoherent boundary on the T-{α} plane are well described by the noninteracting-blip approximation. In the deep-tunneling limit of large {α}, low T, and high bath frequency, the system relaxes exponentially, with its relaxation time constant following a power-law temperature dependence, in accord with perturbation theory. At higher T and low bath frequency, the relaxation time crosses over to a classical Arrhenius temperature dependence, reflecting the onset of activated processes. For a narrow region within 1/21, numerical results suggest that the system undergoes incoherent relaxation, with a short-time exponential decay, followed by a long-time tail of the power-law type. The short-time exponential relaxation time follows a peculiar power-law temperature dependence, with the relaxation rate increasing as a function of decreasing temperature.