Role of switching-on and -off effects in the vacuum instability

Abstract: We find exact differential mean numbers of fermions and bosons created from the vacuum due to a composite electric field of special configuration. This configuration imitates a finite switching-on and -off regime and consists of fields that switch-on exponentially from the infinitely remote past, remains constant during a certain interval $T$ and switch-off exponentially to the infinitely remote future. We show that calculations in the slowly varying field approximation are completely predictable in the framework of a locally constant field approximation. Beyond the slowly varying field approximation, we study effects of fast switching-on and -off in a number of cases when the size of the dimensionless parameter $\sqrt{eE}T$ is either close or exceeds the threshold value that determines the transition from a regime sensitive to on-off parameters to the slowly varying regime for which these effects are secondary.