Vacuum instability in time-dependent electric fields. New example of exactly solvable case

TL;DR

This paper introduces a new exactly solvable model in strong-field QED with an asymmetric, time-dependent electric field, enabling nonperturbative analysis of vacuum instability and particle creation.

Contribution

It presents an exactly solvable asymmetric electric field model, expanding analytical tools for studying vacuum instability in strong-field QED.

Findings

Exact solutions for Dirac equation in asymmetric electric field

Quantitative analysis of particle creation and vacuum stability

Comparison with symmetric Sauter-like field results

Abstract

A new exactly solvable case in strong-field quantum electrodynamics with a time-dependent external electric field is presented. The corresponding field is given by an analytic function, which is asymmetric (in contrast to Sauter-like electric field) with respect to the time instant, where it reaches its maximum value, that is why we call it the analytic asymmetric electric field. We managed to exactly solve the Dirac equation with such a field, which made it possible to calculate characteristics of the corresponding vacuum instability nonperturbatively. We construct the so-called in- and out-solutions and with their help calculate mean differential and total numbers of created charged particles, probability of the vacuum to remain a vacuum, vacuum mean values of current density and energy-momentum tensor of the particles. We study the vacuum instability in regimes of rapidly and slowly changing analytic asymmetric electric field, and compare the obtained results with corresponding ones obtained earlier for the case of the symmetric Sauter-like electric field. We also compare exact results in the regime of slowly changing field with corresponding results obtained within the slowly varying field approximation recently proposed by two of the authors, thus demonstrating the effectiveness of such an approximation.