  We study the dynamics of states perturbatively expanded about a harmonic
system of loop quantum cosmology, exhibiting a bounce. In particular, the
evolution equations for the first and second order moments of the system are
analyzed. These moments back-react on the trajectories of the expectation
values of the state and hence alter the energy density at the bounce. This
analysis is performed for isotropic loop quantum cosmology coupled to a scalar
field with a small but non-zero constant potential, hence in a regime in which
the kinetic energy of matter dominates. Analytic restrictions on the existence
of dynamical coherent states and the meaning of semi-classicality within these
systems are discussed. A numerical investigation of the trajectories of states
that remain semi-classical across the bounce demonstrates that, at least for
such states, the bounce persists and that its properties are similar to the
standard case, in which the moments of the states are entirely neglected.
However the bounce density does change, implying that a quantum bounce may not
be guaranteed to happen when the potential is no longer negligible.
