Lefschetz-thimble inspired analysis of the Dykhne–Davis–Pechukas method and an application for the Schwinger Mechanism

Kenji Fukushima, Takuya Shimazaki

Research output: Contribution to journalArticle

Abstract

Dykhne–Davis–Pechukas (DDP) method is a common approximation scheme for the transition probability in two-level quantum systems, as realized in the Landau–Zener effect, leading to an exponentially damping form comparable to the Schwinger pair production rate. We analyze the foundation of the DDP method using a modern complex technique inspired by the Lefschetz-thimble method. We derive an alternative and more adaptive formula that is useful even when the DDP method is inapplicable. As a benchmark, we study the modified Landau–Zener model and compare results from the DDP and our methods. We then revisit a derivation of the Schwinger Mechanism of particle production under electric fields using the DDP and our methods. We find that the DDP method gets worse for the Sauter type of short-lived electric pulse, while our method is still a reasonable approximation. We also study the Dynamically Assisted Schwinger Mechanism in two methods.

Original languageEnglish
Article number168111
JournalAnnals of Physics
Volume415
DOIs
Publication statusPublished - 2020 Apr
Externally publishedYes

Keywords

  • Complex analysis
  • Dykhne–Davis–Pechukas method
  • Schwinger Mechanism
  • Two-level quantum system

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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