Vacuum decay and the transmission resonances in space-dependent electric fields

We investigate the decay of a quantum electrodynamical (QED) vacuum in arbitrary space-dependent electric fields. In particular, we analyze the resonance peaks of the positron emission spectrum for the external fields with subcycle structure. For this, we study the transmission probability in the framework of the scattering approach to vacuum pair production. In an under-the-barrier scattering regime, we show that the width of a transmission resonance can be enhanced when the effective scattering potential contains multiple wells. Such a broadening in the resonance width corresponds to a decrease in the tunneling time. This may be relevant for observing the vacuum decay at shorter time scales before the external field is adiabatically turned off. In an above-the-barrier scattering regime, we give a set of coupled differential equations for the numerical computation of the Bogoliubov coefficients.