Dynamical correlation functions of extensive charges after global quantum quenches

We investigate the $n$-time cumulant generating function (or $n$-Full Counting Statistics, $n$-FCS) of extensive $U(1)$ charges following a quantum quench. Exploiting space-time duality we characterise this function when evolving from initial states that are symmetric under the action of the charge. In particular, we show that if the correlations in time are sufficiently weak, e.g.\ the transport is ballistic, the $n$-FCS factorises into a sum of single-time FCS arranged in a time-shell structure. A direct implication of this structure is a drastic simplification of dynamical correlation functions: in the presence of time ordering they only depend on the smallest time entering the correlator. We support these findings with several analytical and numerical tests performed in free and interacting models.