  We introduce a numerical method and python package,
https://github.com/andillio/CHiMES, that simulates quantum systems initially
well approximated by mean field theory using a second order extension of the
classical field approach. We call this the field moment expansion method. In
this way, we can accurately approximate the evolution of first and second field
moments beyond where the mean field theory breaks down. This allows us to
estimate the quantum breaktime of a classical approximation without any
calculations external to the theory. We investigate the accuracy of the field
moment expansion using a number of well studied quantum test problems.
Interacting Bosonic systems similar to scalar field dark matter are chosen as
test problems. We find that successful application of this method depends on
two conditions: the quantum system must initially be well described by the
classical theory, and that the growth of the higher order moments be
hierarchical.

Computational Physics;Cosmology and Nongalactic Astrophysics;Quantum Physics