  We study a 1D-Quantum Ising Model in transverse field driven out of
equilibrium by performing a composite quantum quench to deduce the asymptotic
properties of the transverse magnetization stationary state via the analysis of
the spectral function. What emerges is that, in correspondence of the dynamical
phase transition transition predicted for this model, the spectral function
vanishes giving a hint of the criticality. This result suggests also that
linear response experiment can be used to detect this kind of phase transition.
