  Macroscopic quantum tunneling is described using the master equation for the
reduced Wigner function of an open quantum system at zero temperature. Our
model consists of a particle trapped in a cubic potential interacting with an
environment characterized by dissipative and normal and anomalous diffusion
coefficients. A representation based on the energy eigenfunctions of the
isolated system, i.e. the system uncoupled to the environment, is used to write
the reduced Wigner function, and the master equation becomes simpler in that
representation. The energy eigenfunctions computed in a WKB approximation
incorporate the tunneling effect of the isolated system and the effect of the
environment is described by an equation that it is in many ways similar to a
Fokker-Planck equation. Decoherence is easily identified from the master
equation and we find that when the decoherence time is much shorter than the
tunneling time the master equation can be approximated by a Kramers like
equation describing thermal activation due to the zero point fluctuations of
the quantum environment. The effect of anomalous diffusion can be dealt with
perturbatively and its overall effect is to inhibit tunneling.
