Field moment expansion method for interacting bosonic systems

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