  The tunneling probability for a system modelling macroscopic quantum
tunneling is computed. We consider an open quantum system with one degree of
freedom consisting of a particle trapped in a cubic potential interacting with
an environment characterized by a dissipative and a diffusion parameter. A
representation based on the energy eigenfunctions of the isolated system, i. e.
the system uncoupled to the environment, is used to write the dynamical master
equation for the reduced Wigner function of the open quantum system. This
equation becomes very simple in that representation. The use of the WKB
approximation for the eigenfunctions suggests an approximation which allows an
analytic computation of the tunneling rate, in this real time formalism, when
the system is initially trapped in the false ground state. We find that the
decoherence produced by the environment suppresses tunneling in agreement with
results in other macroscopic quantum systems with different potentials. We
confront our analytical predictions with an experiment where the escape rate
from the zero voltage state was measured for a current-biased Josephson
junction shunted with a resistor.
