  A Gaussian operator basis provides a means to formulate phase-space
simulations of the real- and imaginary-time evolution of quantum systems. Such
simulations are guaranteed to be exact while the underlying distribution
remains well-bounded, which defines a useful simulation time. We analyse the
application of the Gaussian phase-space representation to the dynamics of the
dissociation of an ultra-cold molecular gas. We show how the choice of mapping
to stochastic differential equations can be used to tailor the stochastic
behaviour, and thus the useful simulation time. In the phase-space approach, it
is only averages of stochastic trajectories that have a direct physical
meaning. Whether particular constants of the motion are satisfied by individual
trajectories depends on the choice of mapping, as we show in examples.
