  We investigate the quantum dynamics of a multilevel bistable system coupled
to a bosonic heat bath beyond the perturbative regime. We consider different
spectral densities of the bath, in the transition from sub-Ohmic to super-Ohmic
dissipation, and different cutoff frequencies. The study is carried out by
using the real-time path integral approach of the Feynman-Vernon influence
functional. We find that, in the crossover dynamical regime characterized by
damped \emph{intrawell} oscillations and incoherent tunneling, the short time
behavior and the time scales of the relaxation starting from a nonequilibrium
initial condition depend nontrivially on the spectral properties of the heat
bath.
