  We study a quantum quench in a 1D system possessing Luttinger liquid (LL) and
Mott insulating ground states before and after the quench, respectively. We
show that the quench induces power law amplification in time of any particle
density inhomogeneity in the initial LL ground state. The scaling exponent is
set by the fractionalization of the LL quasiparticle number relative to the
insulator. As an illustration, we consider the traveling density waves launched
from an initial localized density bump. While these waves exhibit a particular
rigid shape, their amplitudes grow without bound.
