  Dynamical Sauter-Schwinger mechanism of pair creation by a time-dependent
electric field comprising of $N_{\rm rep}$ identical pulses is analyzed within
the framework of the spinor and scalar quantum electrodynamics. For linearly
polarized pulses, both theories predict that a single eigenmode of the matter
wave follows the dynamics of a two-level system. This dynamics, however, is
either governed by a Hermitian (for spin 1/2 particles) or pseudo-Hermitian
(for spin 0 particles) Hamiltonian. Essentially, both theories lead to a
Fraunhofer-type enhancement of the momentum distributions of created pairs.
While in the fermionic case the enhancement is never perfect and it
deteriorates with increasing the number of pulses in a train $N_{\rm rep}$, in
the bosonic case we observe the opposite. More specifically, it is at
exceptional points where the spectra of bosonic pairs scale exactly as $N_{\rm
rep}^2$, and this scaling is even enhanced with increasing the number of pulses
in a train.
