  We study the spreading of correlations after a local quench in a
non-relativistic quantum field theory. We focus on noninteracting
non-relativistic fermions and study the time evolution after two identical
systems in their ground states are suddenly joined together with a localized
impurity at the junction. We find that, even if the quasi-particles of the
system have unbounded dispersion, the correlations show light cone effects. We
carry out a detailed study of these effects by developing an accurate
asymptotic expansion of the two-point function and determining exactly the
density of particles at any time after the quench. In particular, we find that
the width of the light cone region is $\propto t^{1/2}$. The structure of
correlations, however, does not show a pure light cone form - "superluminal
corrections" are much larger than in the bounded-dispersion case. These
findings can be explained by inspecting the structure of excitations generated
by the initial state. We show that a similar picture also emerges in the
presence of a harmonic trapping potential and when more than two systems are
suddenly joined at a single point.
