Universal short-time response and formation of correlations after quantum quenches

The short-time evolution of two distinct systems, the pump and probe experiments with semiconductor and the sudden quench of cold atoms in an optical lattice, is found to be described by the same universal response function. This analytic formula at short time scales is derived from the quantum kinetic theory approach observing that correlations need time to be formed. The demand of density conservation leads to a reduction of the relaxation time by a factor of four in quench setups. The influence of finite trapping potential is derived and discussed as well as Singwi-Sj{\o}lander local field corrections.