  For the Fermi-Hubbard model in the strongly interacting Mott insulator state,
we study the pre-thermalization dynamics after a quench. To this end, we employ
the method of the hierarchy of correlations and compare different levels of
accuracy. To leading order, the usual free quasi-particle dynamics (as encoded
in the two-point correlation functions) yields the standard picture of
pre-thermalization. Taking into account the back-reaction of these
quasi-particle fluctuations onto the mean-field background as the first
next-to-leading order effect, we observe a strong degradation of
pre-thermalization, especially in low dimensions. In contrast, the inclusion of
three-point correlations enhances pre-thermalization.
