---
abstract: '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.'
author:
- 'K. Krajewska'
- 'J. Z. Kamiński'
title: 'Unitary vs pseudo-unitary time evolution and statistical effects in the dynamical Sauter-Schwinger process'
---

Introduction {#sec::intro}
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Diffraction and interference of waves [@Crawford] have played the fundamental role in the development of science. While both phenomena have been 