Spontaneous particle creation in time-dependent overcritical fields

It is believed that in presence of some strong electromagnetic fields, called overcritical, the (Dirac) vacuum becomes unstable and decays leading to a spontaneous production of an electron-positron pair. Yet, the arguments are based mainly on the analysis of static fields and are insufficient to explain this phenomenon completely. Therefore, we consider time-dependent overcritical fields and show, within the external field formulation, how spontaneous particle creation can be defined and measured in physical processes. We prove that the effect exists always when a strongly overcritical field is switched on, but it becomes unstable and hence generically only approximate and non-unique when the field is switched on and off. In the latter case, it becomes unique and stable only in the adiabatic limit.