  We study the non-equilibrium dynamics of the Luttinger model after suddenly
turning on and off the bare Coulomb interaction between the fermions. We
analyze several correlation functions such as the one particle density matrix
and vertex correlations, its finite time dynamics and the stationary state
limit. Correlations exhibit a non-linear light cone effect: the spreading of
the initial signal accelerates as a consequence of the quantum nature of the
excitations, whose peculiar dispersion of plasmonic type in 1D gives rise to a
logarithmic divergence in the group velocity at $q=0$. In addition we show that
both the static and dynamic stationary state correlations can be reproduced
with a simple generalised Gibbs ensemble despite the long-range character of
the interactions which precludes the application of the Lieb-Robinson bounds.
We propose a suitable experimental setup in which these effect can be observed
based on ultracold ions loaded on linear traps.
