  A discussion on the momentum evolution of an impurity interacting via a
finite delta potential repulsion with a non-interacting fermionic background
gas is presented. It has recently been shown that the momentum evolution of
this system displays two interesting features, namely a non-zero thermalised
value and a long-lived quantum mechanical oscillation around this plateau named
"quantum flutter" [Mathy, Zvonarev, Demler, Nat. Phys. 2012]. We discuss
revivals in the momentum of the impurity, which have been seen before but not
yet thoroughly investigated. Subsequently it is shown the quantum flutter and
revivals are caused by disjoint sets of eigenstate transitions, and this fact
is used to interpret some of their aspects. This attribution of momentum
features to different eigenstate subsets allows quantitative reproduction of
these features with much less computational expense than has so far been
possible. Finally some results on the distribution of the momentum of
eigenstates and their relation to the momentum of the impurity once the system
has been thermalised are presented along with a discussion on the time averaged
infinite time value of the momentum and its comparison to different eigenstate
subsets.
