  Results are presented for the dynamics arising due to a sudden quench of a
boson interaction parameter with the simultaneous switching on of a
commensurate periodic potential, the latter providing a source of non-linearity
that can cause inelastic scattering. A quantum kinetic equation is derived
perturbatively in the periodic potential and solved within the leading order
gradient expansion. A two-particle irreducible formalism is employed to
construct the stress-momentum tensor and hence the conserved energy. The
dynamics is studied in detail in the phase where the boson spectrum remains
gapless. The periodic potential is found to give rise to multi-particle
scattering processes that relaxes the boson distribution function. At long
times the system is found to thermalize with a thermalization time that depends
in a non-monotonic way on the amount of energy injected into the system due to
the quantum quench. This non-monotonic behavior arises due to the competing
effect of an increase of phase space for scattering on the one hand, and an
enhancement of the orthogonality catastrophe on the other hand as the quench
amplitude is increased. The approach to equilibrium is found to be purely
exponential for large quench amplitudes, and more complex for smaller quench
amplitudes.
