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

Hidetoshi Taya, Toshiaki Fujimori, Tatsuhiro Misumi, Muneto Nitta, Norisuke Sakai

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22 Citations (Scopus)


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.

Original languageEnglish
Article number82
JournalJournal of High Energy Physics
Issue number3
Publication statusPublished - 2021 Mar


  • Nonperturbative Effects
  • Solitons Monopoles and Instantons

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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