Universal energy distribution of quasiparticles emitted in a local time-dependent quench

We study the emission of quasiparticles in the scaling limit of the 1D quantum Ising chain at the critical point perturbed by a time-dependent local transverse field. We compute exactly and for a generic time dependence the average value of the transverse magnetization, its correlation functions, as well as the statistics of both the inclusive and exclusive work. We show that, except for a cyclic perturbation, the probability distribution of the work at low energies is a power law whose exponent is universal, i.e., does not depend on the specific time-dependent protocol, but only on the final value attained by the perturbation.