Exact WKB analysis of the vacuum pair production by time-dependent electric fields

TL;DR

This paper develops an exact WKB analysis framework to calculate vacuum pair production in time-dependent electric fields, providing a generalized explicit formula that unifies semi-classical methods and explores dynamic effects.

Contribution

It introduces a novel exact WKB approach to derive a comprehensive formula for pair production, connecting various semi-classical techniques and analyzing dynamic electric field effects.

Findings

Derived an explicit formula for pair production number in semi-classical limit.

Unified different semi-classical methods under a common framework.

Analyzed effects of time-dependent electric fields on pair production mechanisms.

Abstract

We study the vacuum pair production by a time-dependent strong electric field based on the exact WKB analysis. We identify the generic structure of a Stokes graph for systems with the vacuum pair production and show that the number of produced pairs is given by a product of connection matrices for Stokes segments connecting pairs of turning points. We derive an explicit formula for the number of produced pairs, assuming the semi-classical limit. The obtained formula can be understood as a generalization of the divergent asymptotic series method by Berry, and is consistent with other semi-classical methods such as the worldline instanton method and the steepest descent evaluation of the Bogoliubov coefficients done by Brezin and Izykson. We also use the formula to discuss effects of time-dependence of the applied strong electric field including the interplay between the perturbative multi-photon pair production and non-peturbative Schwinger mechanism, and the dynamically assisted Schwinger mechanism.