  When quantum back-reaction by fluctuations, correlations and higher moments
of a state becomes strong, semiclassical quantum mechanics resembles a
dynamical system with a high-dimensional phase space. Here, systematic
computational methods to derive the dynamical equations including all quantum
corrections to high order in the moments are introduced, together with a
(deparameterized) quantum cosmological example to illustrate some implications.
The results show, for instance, that the Gaussian form of an initial state is
maintained only briefly, but that the evolving state settles down to a new
characteristic shape afterwards. Remarkably, even in the regime of large
high-order moments, we observe a strong convergence within all considered
orders that supports the use of this effective approach.
