  We study the effects of the environment on tunneling in an open system
described by a static double-well potential. We describe the evolution of a
quantum state localized in one of the minima of the potential at $t=0$, both in
the limits of high and zero environment temperature. We show that the evolution
of the system can be summarized in terms of three main physical phenomena,
namely decoherence, quantum tunneling and noise-induced activation, and we
obtain analytical estimates for the corresponding time-scales. These analytical
predictions are confirmed by large-scale numerical simulations, providing a
detailed picture of the main stages of the evolution and of the relevant
dynamical processes.
