The spin-bath induced decay of a quantum system out of a metastable state, which can tunnel and undergo thermal activation, is considered. The treatment is based on the $c$-number description of bath degrees of freedom and a canonical thermal distribution of the associated $c$-number variables. We show that, apart from the usual frequency prefactor and its dynamical modification in the spatial diffusion-limited regime, i.e., the Grote-Hynes factor, the rate coefficient contains two other factors. One is a quantum correction to the dynamical factor resulting from quantum transmission and reflection of the particle at the finite barrier. This term exhibits exponential rate enhancement at low temperature. The other one is a quantum corrected Arrhenius factor, which incorporates the effect of thermal saturation. At 0 K, dissipation due to tunneling multiplies the tunneling probability by a factor that gets exponentially damped by friction, implying that, at this temperature, the behavior of spin bath is almost identical to that of a harmonic bath.

• Received 10 July 2011

DOI:https://doi.org/10.1103/PhysRevE.84.041113