Unitary vs pseudo-unitary time evolution and statistical effects in the dynamical Sauter-Schwinger process

TL;DR

This paper investigates the effects of multiple pulses on pair creation in the Sauter-Schwinger process, revealing distinct behaviors for fermions and bosons related to Hermitian and pseudo-Hermitian dynamics, with implications for quantum electrodynamics.

Contribution

It introduces a comparative analysis of unitary and pseudo-unitary evolution in the dynamical Sauter-Schwinger process with multiple pulses, highlighting novel scaling behaviors at exceptional points.

Findings

Fermionic pair production enhancement deteriorates with more pulses.

Bosonic pair production exhibits quadratic scaling at exceptional points.

Distinct dynamics governed by Hermitian and pseudo-Hermitian Hamiltonians.

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.