Time evolution during and after finite-time quantum quenches in Luttinger liquids

We consider finite-time quantum quenches in the interacting Tomonaga--Luttinger model, for example time-dependent changes of the nearest-neighbour interactions for spinless fermions. We use the exact solutions for specific protocols including the linear and cosine ramps (or, more generally, periodic pumping). We study the dynamics of the total and kinetic energy as well as the Green functions during as well as after the quench. For the latter we find that the light-cone picture remains applicable, however, the propagating front is delayed as compared to the sudden quench. We extract the universal behaviour of the Green functions and in particular provide analytic, non-perturbative results for the delay applicable to quenches of short to moderate duration but arbitrary time dependency.